U.S. patent application number 11/079000 was filed with the patent office on 2005-07-28 for sub-flux quantum generator.
This patent application is currently assigned to D-Wave Systems, Inc.. Invention is credited to Omelyanchouk, Alexander N., Smirnov, Anatoly Y..
Application Number | 20050162302 11/079000 |
Document ID | / |
Family ID | 32302354 |
Filed Date | 2005-07-28 |
United States Patent
Application |
20050162302 |
Kind Code |
A1 |
Omelyanchouk, Alexander N. ;
et al. |
July 28, 2005 |
Sub-flux quantum generator
Abstract
A sub-flux quantum generator includes an N-turn ring having a
plurality of connected turns about a common aperture. The width of
each respective turn in the N-turn ring exceeds the London
penetration depth of a superconducting material used to make the
respective turn. The generator includes a switching device
configured to introduce a reversible localized break in the
superconductivity of at least one turn in the N-turn ring. The
generator includes a magnetism device configured to generate a
magnetic field within the aperture of the N-turn ring. A method for
biasing a superconducting structure that encompasses all or a
portion of an N-turn ring. While a supercurrent is flowing through
the N-turn ring, a quantized magnetic flux is introduced into the
aperture of the N-turn ring using a reversible localized break in a
turn in the ring. The quantized magnetic flux is trapped in the
ring by removal of the localized break. The trapped flux biases the
superconducting structure.
Inventors: |
Omelyanchouk, Alexander N.;
(Kharkov, UA) ; Smirnov, Anatoly Y.; (Vancouver,
CA) |
Correspondence
Address: |
JONES DAY
222 EAST 41ST ST
NEW YORK
NY
10017
US
|
Assignee: |
D-Wave Systems, Inc.
|
Family ID: |
32302354 |
Appl. No.: |
11/079000 |
Filed: |
March 11, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11079000 |
Mar 11, 2005 |
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10445096 |
May 23, 2003 |
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6885325 |
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60383579 |
May 24, 2002 |
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Current U.S.
Class: |
341/200 ;
257/E27.007; 257/E39.014 |
Current CPC
Class: |
H01L 39/223 20130101;
H01L 27/18 20130101; G06N 10/00 20190101; H01L 39/18 20130101; B82Y
10/00 20130101; Y10S 977/933 20130101 |
Class at
Publication: |
341/200 |
International
Class: |
H03M 001/00 |
Claims
1. A sub-flux quantum generator comprising: an N-turn ring
comprising a plurality of connected turns about a common aperture,
wherein a width T.sub.50 of each respective turn in said plurality
of connected turns exceeds the London penetration depth of a
superconducting material used to make the respective turn; a
switching device configured to introduce a localized reversible
break in a superconducting current in at least one turn in said
plurality of connected turns; and a magnetism device configured to
generate a magnetic field within said common aperture.
2-42. (canceled)
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims benefit, under 35 U.S.C. .sctn.
119(e), of U.S. Provisional Patent Application No. 60/383,579 filed
on May 24, 2002 which is incorporated herein, by reference, in its
entirety.
FIELD OF THE INVENTION
[0002] This invention relates to superconducting circuitry. More
specifically, this invention relates to devices that generate
fractions of a flux quantum.
BACKGROUND
[0003] Quantum computing is accomplished using the effects of
qubits that exhibit quantum mechanical behavior. A qubit is a
physical system that is restricted to two or more energy states. A
qubit is a quantum bit, the counterpart in quantum computing to the
binary digit or bit of classical computing. Just as a bit is the
basic unit of information in a classical computer, a qubit is the
basic unit of information in a quantum computer. A qubit is
conventionally a system having two or more discrete energy states.
The energy states of a qubit are generally referred to as the basis
states of the qubit. The basis states of a qubit are termed the
.vertline.0> and .vertline.1> basis states. Typically, in
quantum computing applications, a qubit is placed (e.g., biased) to
a state where two of the discrete energy states of the qubit are
degenerate. Energy states are degenerate when they possess the same
energy.
[0004] A qubit can be in any superposition of two basis states,
making it fundamentally different from a bit in an ordinary digital
computer. A superposition of basis states arises in a qubit when
there is a non-zero probability that the system occupies more than
one of the basis states at a given time. Qualitatively, a
superposition of basis states means that the qubit can be in both
basis states .vertline.0> and .vertline.1> at the same time.
Mathematically, a superposition of basis states means that the
overall state of the qubit, which is denoted .vertline..PSI.>,
has the form
.vertline..PSI.>=a.vertline.0>+b.vertline.1>
[0005] where a and b are coefficients respectively corresponding to
probability amplitudes .vertline.a.vertline..sup.2 and
.vertline.b.vertline..sup.2. The coefficients a and b each have
real and imaginary components, which allows the phase of qubit to
be modeled. The quantum nature of a qubit is largely derived from
its ability to exist in a superposition of basis states, and for
the state of the qubit to have a phase.
[0006] If certain conditions are satisfied, N qubits can define a
state that is a combination of 2.sup.N classical states. This state
undergoes evolution, governed by the interactions that the qubits
have among themselves and with external influences, providing
quantum mechanical operations that have no analogy with classical
computing. The evolution of the states of N qubits defines a
calculation or, in effect, 2.sup.N simultaneous classical
calculations. Reading out the states of the qubits after evolution
completely determines the results of the calculations.
[0007] It is held by some in the art that certain quantum computing
algorithms, such as the Shor algorithm, require that the number of
qubits in the quantum computer must be at least 10.sup.4. See Mooij
et al., 1999, Science 285, p. 1036, which is hereby incorporated by
reference in its entirety. Qubits have been implemented in cavity
quantum dynamic systems, ion traps, and nuclear spins of large
numbers of identical molecules. However, such systems are not
particularly well suited for the realization of the desired high
number of interacting qubits needed in a quantum computer. A survey
of the current physical systems from which qubits can be formed is
Braunstein and Lo (eds.), Scalable Quantum Computers, Wiley-VCH
Verlag GmbH, Berlin (2001), which is hereby incorporated by
reference in its entirety. Of the various physical systems
surveyed, the systems that appear to be most suited for scaling
(e.g., combined in such a manner that they interact with each
other) are those physical systems that include superconducting
structures such as superconducting qubits.
[0008] A proposal to build a scalable quantum computer from
superconducting qubits was published in 1997. See Bocko et al.,
1997, IEEE Trans. Appl. Supercon. 7, p. 3638, and Makhlin et al.,
2001, Rev. of Mod. Phys., 73, p. 357, which are hereby incorporated
by reference in their entireties. Since then, many designs have
been introduced. One such design is the persistent current qubit.
See Mooij et al., 1999, Science 285, 1036; and Orlando et al.,
1999, Phys. Rev. B 60, 15398, which are hereby incorporated by
reference in their entireties.
[0009] A description of the persistent current qubit, as described
in Mooij et al., is illustrated by circuit 700 in FIG. 7. Circuit
700 consists of a loop with three small-capacitance Josephson
junctions (702-1, 702-2, and 702-3) in series. In operation,
circuit 700 encloses a magnetic flux .function.M.sub.o. Here,
M.sub.o is the superconducting flux quantum h/2e (i.e., fluxon,
flux quantum) where h is Plank's constant and e is elementary
charge. See Tinkham, Introduction to Superconductivity,
McGraw-Hill, Inc., New York, 1996, which is hereby incorporated by
reference in its entirety, for a theoretical description of the
fluxon. In operation, the magnetic .function.M.sub.o enclosed by
circuit 700 is created by applying an external magnetic flux with
magnitude .function.M.sub.o to circuit 700. This external magnetic
flux is referred to as an applied magnetic flux, applied magnetic
frustration, or simply frustration flux. Two of the junctions 702
in circuit 700 have equal Josephson coupling energies E.sub.J. The
Josephson coupling energy of the third junction 702 is less than
the coupling energy E.sub.J of the first two junctions 702.
Typically, the Josephson energy of the third junction 702 is
.alpha.E.sub.j, with 0.5<.alpha.<1.
[0010] An important feature of the Josephson energy in circuit 700
is that it is a function of two phases. For a range of frustration
fluxes .function.M.sub.o, where .function. represents some range of
numbers, these two phases permit two stable configurations that
correspond to dc currents flowing in opposite directions. In fact,
for .function.=0.5 (i.e., 0.5.times.M.sub.o, one half a fluxon),
the energies of the two stable configurations (states) are the same
(are degenerate). Thus, when an external magnetic force having the
magnitude .function.M.sub.o (where .function.=0.5) is applied
against circuit 700, the circuit acts as a persistent current qubit
with two degenerate states. One of the degenerate states,
represented by a clockwise dc current 720 circulating in circuit
700, may be arbitrarily assigned the basis state .vertline.0>.
Then the other degenerate state, represented by a counterclockwise
dc current 722 circulating in circuit 700, is assigned the basis
state .vertline.1>. Another property of circuit 700 is that the
barrier for quantum tunneling between the two degenerate states
depends strongly on the value .alpha. Larger values .alpha. (i.e.,
higher Josephson energy in the third junction 702) result in higher
tunneling barriers.
[0011] One advantage of superconducting qubits is that they are
scalable. A disadvantage of persistent current qubit 700 is that it
is difficult to provide a stable source for the applied magnetic
flux .function.M.sub.o that is necessary to produce the two
degenerate states. Fluctuations in the frustration flux can
decohere the states of the qubit making computation difficult or
unreliable. Decoherence is the loss of the phases of quantum
superpositions in a qubit as a result of interactions with the
environment. Thus, decoherence results in the loss of the
superposition of basis states in a qubit. See, for example, Zurek,
1991, Phys. Today 44, p. 36; Leggett et al., 1987, Rev. Mod. Phys.
59, p. 1; Weiss, 1999, Quantitative Dissipative Systems, 2.sup.nd
ed., World Scientific, Singapore; Hu et al; arXiv:cond-mat/0108339,
which are herein incorporated by reference in their entireties.
Inductance from normal electronics is not suitable for producing
degenerate states in a persistent current qubit. Any disruption in
the current through such electronics will disrupt the degenerate
states. Vibrations of the system can cause a change in the level of
frustration (level of bias). Even the briefest interruption in the
degeneracy of the states will destroy the quantum computation
performed on the qubit.
[0012] One approach to trap flux is through flux quantization in a
ring of superconducting material that has a cross section that is
larger than the London penetration depth .lambda..sub.L. In this
approach, an external flux of about one flux quantum is applied to
ring while cooling the ring down through the superconducting phase
transition. Once below the superconducting phase transition
temperature, the center of the ring (the aperture of the ring) will
have a magnetic flux of one flux quantum because it will be trapped
by the surrounding superconducting material. Then, the external
field is removed. When the external magnetic field is removed in a
nonsuperconducting ring, the magnetic flux in the center of the
ring pierces the ring and is annihilated. However, this is not
possible in a superconducting ring because the magnetic flux
trapped in the center of the ring cannot penetrate the
superconducting ring. Thus, in this way, a ring is capable of
trapping magnetic field in multiples of the magnetic flux quantum
(i.e., 1.times.h/2e, 2.times.h/2e, 3.times.h/2e, and so forth). The
flux is quantized because the wavefunction of the supercurrent is
naturally single valued. This means the integral of the phase
around the ring of superconducting material should be a multiple of
2.pi..
[0013] One possibility for providing an applied magnetic flux to a
persistent current qubit is a superconducting ring recently
proposed by Majer et al. See Majer et al., 2002, Applied Physics
Letters 80, p. 3638 which is hereby incorporated by reference in
its entirety. Majer et al. proposed a mesoscopic (e.g., having a
diameter of 3 .mu.m) superconducting ring 800 (FIG. 8) that has no
junctions. A superconducting material is a material that has zero
electrical resistance below critical levels of current, magnetic
field and temperature. The Majer et al. ring has a cross section
802 that is narrower than the London penetration depth
.lambda..sub.L of the ring. The London penetration depth
.lambda..sub.L describes the exponentially decaying magnetic field
in layers just below the surface of a superconductor. In general,
magnetic fields are excluded within superconducting materials. The
exclusion of magnetic fields deep in a superconducting material is
known as the Meissner effect. However, in shallow layers just below
the surface of superconducting materials, the extent to which
magnetic fields are excluded is exponentially dependent on the
distance between the layer and the surface of the superconductor.
The London penetration depth .lambda..sub.L of a superconducting
material is the distance from the material surface to a point in
the material where magnetic flux is e.sup.-1 times less than at the
material surface. Here, e is the base of the natural logarithm.
London penetration depth is material dependent but typically on the
order of 500 .ANG. for some superconducting materials.
[0014] As mentioned above, the ring proposed by Majer et al. has a
cross section 802 that is narrower than the London penetration
depth .lambda. of the ring. However, the ring 800 can be used to
trap magnetic flux through the phenomena of fluxoid quantization,
which is a distinctly different phenomena than the phenomena of
flux quantization described above. The difference between flouxoid
quantization and flux quantization is that, although the resultant
magnetic field is the same, the origins of the magnetic field
differ. In flux quantization of a thick ring, the magnetic field in
the ring is comprised of a trapped magnetic field. In fluxiod
quantization of a ring that is narrower than the London penetration
depth of the ring, the magnetic field in the ring is induced by
circulating current that remains in the ring. See M. Tinkham, 1996,
Introduction to Superconductivity, McGraw Hill, which is hereby
incorporated by reference in its entirety. In one approach, an
external flux quantum is applied to ring 800 while cooling the ring
down through the superconducting phase transition. The center of
ring 800 will have a magnetic flux quantum because of the presence
of the external magnetic flux. Then, once ring 800 is
superconducting, the external field is removed. When the external
magnetic field is removed in a nonsuperconducting ring, the
magnetic flux in the center of the ring pierces the ring and is
annihilated. However, this is not possible in the ring proposed by
Majer et al. because the magnetic flux is induced in the center of
the ring by superconducting current in the ring. A superconducting
ring is capable of trapping magnetic field in multiples of the
magnetic flux quantum (i.e., 1.times.h/2e, 2.times.h/2e,
3.times.h/2e, and so forth). The magnetic field is comprised of the
trapped flux and the flux generated by the circulating current. The
Majer et al. ring provides no mechanism for releasing trapped
magnetic flux. The trapped magnetic flux can be used as a source
for applying a stable magnetic field to a persistent current qubit.
The trapped magnetic flux in the Majer et al. ring is advantageous
because it is not sensitive to fluctuations in applied current. In
fact, no applied current is required to maintain the trapped
magnetic flux in the Majer et al. ring 800 once it has been trapped
in the aperture of the ring.
[0015] While ring 800 represents a significant achievement in the
art, it does not provide a satisfactory device for applying an
external biasing (frustrating) magnetic field to a persistent
current qubit for two reasons. First, ring 800 does not provide a
mechanism for trapping or releasing trapped magnetic flux. The only
way to trap or release the trapped magnetic flux in ring 800 is to
destroy the superconducting properties of the ring. This can be
accomplished, for example, by raising the temperature of the ring
through the critical temperature T.sub.C of the superconducting
material used to manufacture the ring. Second, ring 800 is not
capable of trapping sub-fluxon quantities of magnetic flux. That
is, ring 800 is not capable of trapping a magnetic flux having a
magnitude that is a fraction of h/2e. Yet, many persistent current
qubits, such as circuit 700, require an external magnetic force
having a magnitude that is a fraction of a fluxon in order to
achieve two degenerate states.
[0016] Given the above background, what is needed in the art is a
mechanism for delivering a stable and switchable flux source with
sub-fluxon precision.
[0017] Discussion or citation of a reference herein shall not be
construed as an admission that such reference is prior art to the
present invention.
SUMMARY OF THE INVENTION
[0018] The present invention provides a switchable stable sub-flux
quantum generator. In one embodiment of the invention, an N-turn
ring is used to trap fluxon or sub-fluxon amounts of magnetic flux.
Furthermore, each turn of the N-turn ring includes a switch. By
regulating the switches in the N-turn ring, the amount of magnetic
flux in the N-turn ring can be used to control the amount of
magnetic flux trapped within the ring with sub-fluxon precision.
The switchable N-turn ring provides a reliable external magnetic
flux that can be used to bias a persistent current qubit, such as
circuit 700, so that the two stable states of the qubit are
degenerate.
[0019] One embodiment of the present invention provides a sub-flux
quantum generator. The sub-flux quantum generator comprises an
N-turn ring that includes N connected turns, where N is an integer
greater than or equal to two. Further, each turn in the N-turn ring
has a width that exceeds the London penetration depth
.lambda..sub.L of the superconducting material used to make each
turn in the N-turn ring. The sub-flux quantum generator further
comprises a switching device that introduces a reversible localized
break in the superconductivity of at least one turn in the N-turn
ring. The sub-flux quantum generator also includes a magnetism
device that generates a magnetic field within the N-turn ring.
[0020] In some embodiments, the sub-flux quantum generator includes
a set of leads that is attached to the N-turn ring. The magnetism
device is in electrical communication with the set of leads in
order to drive a current through the N-turn ring. In some
embodiments of the present invention, the superconducting material
used to make a turn in the N-turn ring is a type I superconductor
such as niobium or aluminum. In some embodiments of the present
invention, the superconducting material used to make a turn in the
N-turn ring is a type II superconductor.
[0021] In some embodiments, the switching device in sub-flux
quantum generator is a cryotron that encompasses a portion of one
or more of the turns in the N-turn ring. In some embodiments, the
switching device in the sub-flux quantum generator is a Josephson
junction that is capable of toggling between a superconducting zero
voltage state and a nonsuperconducting voltage state. In some
embodiments, this Josephson junction includes a set of critical
current leads that are used to drive a critical current through the
Josephson junction to toggle the Josephson junction between the
superconducting zero voltage state and the nonsuperconducting
voltage state.
[0022] Another aspect of the present invention provides a
superconducting device comprising an outer structure and an inner
structure. The outer structure comprises a superconducting ring
that encompasses at least a portion of the inner structure. This
superconducting ring includes at least one Josephson junction. The
inner structure comprises an N-turn ring that includes N connected
turns. Turns are connected when they make contact with each other.
In some embodiments, the turns are twined. However, there is no
requirement that the turns in an N-turn ring twine (twist) about
each other in an N-turn ring. In some embodiments, all that is
required is that each turn in an N-turn ring make contact with at
least one other turn in the N-turn ring. As used herein, the value
N for the N-turn ring means an integer greater than or equal to
two. Further, each turn in the N-turn ring has a width that exceeds
the London penetration depth .lambda..sub.L of a superconducting
material used to make each turn in the N-turn ring. In some
embodiments of the present invention, the outer structure is a
qubit, such as a phase qubit, or more specifically, a persistent
current qubit. In some embodiments, the inner structure further
comprises a switching device that is capable of introducing a
reversible localized break in the superconductivity of at least one
turn in the N-turn ring.
[0023] Another aspect of the present invention provides a method
for trapping a quantized magnetic flux in an N-turn ring. Here, N
is an integer greater than or equal to two. In the method, a
supercurrent is allowed to flow through the N-turn ring. Next, a
quantized magnetic flux .PHI..sub.X is induced in an aperture of
the N-turn ring by introducing a localized break in a turn in the
N-turn ring. This localized break interrupts the supercurrent in a
portion of the turn. Later, the supercurrent is restored to the
effected portion of the turn by removing the localized break,
thereby trapping the quantized magnetic flux in the N-turn ring. In
some embodiments, the localized break in the turn is introduced by
passing a bias current through a Josephson junction present in the
portion of the turn. The bias current causes the Josephson junction
to toggle from a superconducting zero voltage state to a
nonsuperconducting voltage state.
[0024] Still another aspect of the present invention provides a
method for frustrating (biasing) a superconducting structure that
encompasses a portion of an N-turn ring (where N is an integer
equal to two or greater). In the method, supercurrent is allowed to
flow through the N-turn ring. Next, a quantized magnetic flux
.PHI..sub.X is induced in an aperture of the N-turn ring by
introducing a localized break in a turn in the N-turn ring. The
localized break interrupts the supercurrent in the portion of the
turn. Then the quantized magnetic flux is trapped in the N-turn
ring by removing the localized break and restoring the supercurrent
to the effected portion of the turn, thereby frustrating the
superconducting structure that encompasses the portion of the
N-turn ring.
BRIEF DESCRIPTION OF THE DRAWINGS
[0025] FIG. 1 illustrates the relationship between generalized
components of one embodiment of the present invention, including an
N-turn ring, a switching device, and a magnetism device.
[0026] FIGS. 2A-2D illustrate a method for manufacturing an N-turn
ring in accordance with an embodiment of the present invention.
[0027] FIGS. 3A-3G illustrate various devices (cyclotron, FIGS.
3A-3C; Josephson junction, FIGS. 3D-3F; and laser, FIG. 3G) that
can locally break the superconducting current in a superconducting
material, in accordance with embodiments of the present
invention.
[0028] FIGS. 4A-4C illustrate sub-flux quantum generators in
accordance with various embodiments of the present invention.
[0029] FIG. 5 illustrates a sub-flux quantum generator in which
each turn in an N-turn ring encloses a different amount of area, in
accordance with one embodiment of the present invention.
[0030] FIG. 6 illustrates an array of persistent current qubits
that are each biased by a sub-flux quantum generator, in accordance
with one embodiment of the present invention.
[0031] FIG. 7 illustrates a persistent current qubit in accordance
with the prior art.
[0032] FIG. 8 illustrates a mesoscopic ring in accordance with the
prior art.
[0033] Like reference numerals refer to corresponding parts
throughout the several views of the drawings.
DETAILED DESCRIPTION
[0034] One embodiment of the present invention provides an N-turn
ring that is used to trap fluxon or sub-fluxon amounts of magnetic
flux when superconducting current flows through the N-turn ring. As
observed experimentally by Henry and Deaver in 1968, the magnetic
flux trapped by a superconducting N-turn ring is quantized in
multiples of h/N2e, where N is the number of times an inaccessible
region is encircled by the N-turn ring, h is Plank's constant, and
e is elementary charge. See Henry and Deaver, 1968, Bull. Am. Phys.
Soc. 13, 1691; and Olariu and Popescu, 1985, Rev. Mod. Phys. 57:2,
pp. 339-436, especially pages 412-413, which are hereby
incorporated by reference in their entireties. This relationship
assumes that each turn in the N-turn ring encircles approximately
the same area. A two-turn superconducting ring can trap one half of
a flux quantum (i.e. one half of a fluxon, 0.5.times.h/2e). An
N-turn ring has N turns. These N turns are optionally intertwined.
Furthermore, in one embodiment of the inventive device, each turn
of the N-turn ring includes a switch. By regulating the switches in
the N-turn ring, the amount of magnetic flux trapped in the N-turn
ring can be controlled with sub-fluxon precision.
[0035] One aspect of the present invention provides a sub-flux
quantum generator that includes an N-turn ring made from
superconducting materials. The sub-flux quantum generator can
produce a stable and switchable flux source with sub-fluxon
precision. Sub-flux quantum generators have numerous applications
in devices that require a reliable magnetic field having a
magnitude in the single fluxon or sub-fluxon range. For example,
the sub-flux quantum generators in accordance with this aspect of
the present invention can be used to reliably frustrate a
persistent current qubit in order to make the basis states of the
persistent current qubit degenerate. In one case, the sub-flux
quantum generators are used to frustrate circuit 700 with a
magnetic flux having a magnitude of one half of a fluxon, in order
to make the two stable states associated with the circuit
degenerate.
[0036] FIG. 1 presents a generic embodiment of one embodiment of
the invention. FIG. 1 illustrates a sub-flux quantum generator 100
that is capable of trapping sub-fluxon magnitudes of magnetic flux.
Sub-flux quantum generator 100 includes three components, (labeled
1, 2, and 3). They are an N-turn ring 1 of superconducting
material, a switching device 2 to break the superconductivity of
N-turn ring 1, and a magnetism device 3 for presenting magnetic
flux to N-turn ring 1. In some embodiments, each turn (ring) in an
N-turn ring of the present invention is made from a different
material. Thus, for example, in some embodiments, a first turn in
the N-turn ring is made from a first superconducting material and a
second turn in the N-turn ring is made from a second
superconducting material. As used herein, N is any integer greater
than or equal to two. Thus, N=2, 3, 4, 5, 6,and so forth. Switching
device 2 is used to interrupt the superconducting current in N-turn
ring 1 in a controllable fashion. Magnetism device 3 provides a
magnetic flux that has a substantial component normal with respect
to the principle plane of N-turn ring 1. Magnetism device 3 is used
to generate magnetic flux that is ultimately trapped by N-turn ring
1.
Description and Fabrication of N-Turn Ring 1
[0037] FIGS. 2A-2D illustrate a method of making an N-turn ring 1
in accordance with one embodiment of the present invention. The
exemplary fabrication process begins in FIG. 2A. A substrate 30 is
presented with one side prepared for material deposition and
patterning. The actual choice of material for substrate 30 is
application dependent. In some embodiments, substrate 30 is made of
silicon, fused-silica (SiO.sub.2), magnesium oxide (MgO), lanthanum
aluminum oxide (LaAlO.sub.3), quartz, or sapphire. In some
embodiments, substrate 30 is made from alkali-free borosilicate
glass (Shott AF45). Superconducting material is deposited on
substrate 30 and patterned to produce a turn 50 with an aperture 49
and a break 62 between leads 61-1 and 61-2. Choices for substrate
30, and methods for material deposition and patterning of turn 50
are described in Van Zant, Microchip Fabrication, Fourth Edition,
McGraw-Hill, New York, 1997; Rai-Choudhury, Microlithography,
Micromachining and Microfabrication Volume 1: Microlithography, The
International Society for Optical Engineering, Bellingham, Wash.,
1997; and Madou, Fundamentals of Microfabrication, Second Edition,
CRC Press, 2002, which are hereby incorporated by reference in
their entireties. Leads 61 are used in a cross-over 60 that creates
an N-turn ring in subsequent processing steps.
[0038] In one embodiment, break 62 between leads 61-1 and 61-2
exceeds the coherence length of the material used to form turn 50
in order to avoid stray Josephson effects. Coherence length is a
material dependent phenomenon that arises because of the inability
for superconducting electron density to change instantaneously. A
minimum length (coherence length) is required to effectuate a
change in the superconducting state of an electrical current. For
example, a transition from the superconducting state to a normal
state will have a transition layer of finite thickness that is
dependent upon the coherence length of the material in which this
transition takes place. Experimental studies of various
superconductors has led to the following approximate values for
coherence length: Sn (230 nm), Al (1600 nm), Pb (83 nm), Cd (760
nm) and Nb (38 nm).
[0039] In some embodiments, separation between leads 61-1 and 61-2
in excess of the coherence length of the material used to make turn
50 is desired in order to avoid stray capacitance in break 62.
Optionally, leads 55 are patterned into ring 1. In one embodiment,
leads 55 are placed at opposite sides of turn 50 as illustrated in
FIG. 2A. In an embodiment of the present invention, turn 50 is made
of a type I superconductor. Examples of type I superconductors
include, but are not limited to, niobium (Nb), aluminum (Al), and
lead (Pb).
[0040] In some embodiments, the material used to form turn 50, as
with all material layers described in conjunction with FIG. 2, is
deposited onto substrate 30 using a process such as dc-magnetron
sputtering or pulsed laser deposition. The exact deposition process
used will depend upon the nature of the compound used to make turn
50. Various deposition methods known in the art can be used
depending on the properties material used to form turn 50. Such
known deposition methods include, but are not limited to, chemical
vapor deposition, low pressure chemical vapor deposition, reduced
pressure chemical vapor deposition, atmospheric chemical vapor
deposition, plasma assisted chemical vapor deposition, remote
plasma chemical vapor deposition, anodic conversion, plasma spray
deposition, jet printing, sol-gel processes, vacuum evaporation,
sputter deposition (e.g., physical vapor deposition), collimated
sputtering, laser ablated deposition, molecular beam deposition,
ionized physical vapor deposition, ion beam deposition, atomic
layer deposition, hot filament chemical vapor deposition, screen
printing, electroless metal deposition, or electroplating. See, for
example, Van Zant, Microchip Fabrication, Fourth Edition,
McGraw-Hill, New York, 1997; Rai-Choudhury, Microlithography,
Micromachining and Microfabrication Volume 1: Microlithography, The
International Society for Optical Engineering, Bellingham, Wash.,
1997; and Madou, Fundamentals of Microfabrication, Second Edition,
CRC Press, 2002. In addition to these deposition techniques, those
of skill in the art will recognize that there are number of other
different methods by which layer 8010 may be deposited and all such
methods are included within the scope of the present invention.
[0041] Once deposited, the superconducting material can be etched
to form ring 50 using, for example, carbon tetra-fluoride reactive
ion etching (CF.sub.4-RIE), argon (Ar) ion etching, or any other
suitable deposition and etching techniques. In some embodiments,
this patterning is assisted by depositing a resist layer over the
superconducting material, patterning the resist layer using a
photomask, etching the resist layer and the underlying
superconducting material, and then developing away the resist layer
in accordance with known lithographic methods.
[0042] Resists used to form a resist layer are typically comprised
of organic polymers applied from a solution. Generally, to coat the
superconducting material with resist, a small volume of the liquid
is first dispensed on the layer of superconducting material that
overlays the substrate. The substrate is then spun at a high rate
of speed, flinging off excess resist and leaving behind, as the
solvent evaporates, a resist layer. In some embodiments, resist
layer has a thickness in the range of 0.1 .mu.m to 2.0 .mu.m.
[0043] In some embodiments, the resist layer that is applied over
the superconducting material is an optical resist that is designed
to react with ultraviolet or laser sources. In some embodiments,
the resist layer is a negative resist in which polymers in the
resist form a cross-linked material that is etch resistant upon
exposure to light. Examples of negative resists that can be used to
make the resist layer include, but are not limited to,
azide/isoprene negative resists, polymethylmethacrylate (PMMA),
polymethylisopropyl ketone (PMIPK), polybutene-1-sulfone (PBS),
poly-(trifluoroethyl chloroacrylate) TFECA, poly-(2-methyl
pentene-1-sulfone) (PMPS). In other embodiments, the resist layer
is a positive resist. The positive resist is relatively unsoluble.
After exposure to the proper light energy, the resist converts to a
more soluble state. One positive photoresist in accordance with the
present invention is the phenol-formaldehyde polymer, also called
phenolformaldehyde novolak resin. See, for example, DeForest,
Photoresist: Materials and Processes, McGraw-Hill, New York, 1975,
which is hereby incorporated by reference in its entirety. In some
embodiments, the resist layer is LOR 0.5A, LOR 0.7A, LOR 1A, LOR
3A, or LOR 5A (MICROCHEM, Newton, Mass.). LOR lift-off resists use
polydimethylglutarimide.
[0044] After the resist layer has been applied, the density is
often insufficient to support later processing. Accordingly, in
some embodiments of the present invention, a bake is used to
densify the resist layer and drive off residual solvent. This bake
is referred to as a softbake, prebake, or post-apply bake. Several
methods of baking the resist layer are contemplated by the present
invention including, but not limited to, convection ovens, infrared
ovens, microwave ovens, or hot plates. See, for example, Levinson,
Principles of Lithography, SPIE Press, Bellingham, Wash., 2001, pp.
68-70, which is hereby incorporated by reference in its
entirety.
[0045] After the resist layer has been overlayed onto the
superconducting layer, the next step is alignment and exposure of
the resist layer. Alignment and exposure is a two-purpose
photomasking step. The first part of the alignment and exposure
step is the positioning or alignment of the required image on the
wafer surface. The image is found on a phtotomask. The second part
is the encoding of the image in the resist layer from an exposing
light or radiation source. In the present invention, any
conventional alignment system can be used to align the photomask
with the resist layer, including but not limited to, contact
aligners, proximity aligners, scanning projection aligners,
steppers, step and scan aligners, x-ray aligners, and electron beam
aligners. For a review of aligners that can be used in the present
invention, see Solid State Technology, April 1993, p. 26; and Van
Zant, Microchip Fabrication, Fourth Edition, McGraw-Hill, New York,
2000, pp. 232-241.
[0046] In one embodiment of the present invention, the tool used to
project the pattern on the phtotomask onto the resist layer is a
wafer stepper, e.g., a step-and-repeat stepper or a step-and-scan,
stepper. See for example, Levison, Principles of Lithography, SPIE
Press, Bellingham, Wash., 2001, pp. 133-174, which is hereby
incorporated by reference. After exposure through the phototmask
the pattern for turn 50 is coded as a latent image in the resist
layer as regions of exposed and unexposed resist. The pattern is
developed in the resist by chemical dissolution of the
unpolymerized resist regions. There are several methods in which a
developer can be applied to the resist in order to develop the
latent image. Such methods include, but are not limited to,
immersion, spray development, and puddle development. In some
embodiments of the present invention, wet development methods are
not used. Rather, a dry (or plasma) development is used. In such
dry processes, a plasma etcher uses energized ions to chemically
dissolve away either exposed or unexposed portions of the resist
layer.
[0047] After development, an etching step is used to pattern the
superconducting layer thereby forming turn 50. Exemplary etching
methods, such as carbon tetrafluoride reactive ion etching
(CF.sub.4-RIE) and argon (Ar) ion etching have been referenced
above. Additional etching techniques include, but are not limited
to, wet etching, wet spray etching, vapor etching, plasma etching,
ion beam etching and reactive ion etching. See, for example, Stolz
et al., Supercond. Sci. Technol. 12 p. 806 (1999); Van Zant,
Microchip Fabrication, Fourth Edition, McGraw-Hill, New York, 1997;
Rai-Choudhury, Microlithography, Micromachining and
Microfabrication Volume 1: Microlithography, The International
Society for Optical Engineering, Bellingham, Wash., 1997; and
Madou, Fundamentals of Microfabrication, Second Edition, CRC Press,
2002 which are hereby incorporated by reference in their
entireties.
[0048] In general, structures can be patterned using the optical
and/or electron beam lithographic steps described above. As
described below, the formation of the N-turn ring of the present
invention typically requires multiple layers with each layer
requiring independent patterning. In such instances, the
lithographic steps described above can be repeated for each layer
as necessary in order to accomplish such patterning.
[0049] In one embodiment of the present invention turn 50, with the
exception of junction 61, has a uniform width T.sub.50 that is
greater than the London penetration depth .lambda..sub.L of the
superconducting material used to make turn 50. As used herein, at
any given position in turn 50, width T.sub.50 is the shortest
distance between interior 204 of turn 50 to exterior 202 of turn 50
as illustrated in FIG. 2A. Such widths are desired so that turn 50
will trap magnetic flux in aperture 49 when the turn is
superconducting. In some embodiments, the thickness of turn 50,
with respect to the plane of substrate 30 (normal to width
T.sub.50), is uniform and is on the scale (e.g., between 1.times.
and 5.times.) of the London penetration depth .lambda..sub.L of the
superconducting material 50. This prevents the formation of weak
spots where quantized magnetic flux may become trapped. London
penetration depths .lambda..sub.L for some superconducting
materials are: Sn (34 nm), Al (16 nm), Pb (37 nm), Cd (110 nm), and
Nb (39 nm).
[0050] An intermediate material layer is deposited onto substrate
30 and turn 50. This intermediate material is patterned to form
shape 40 (FIG. 2B), thereby exposing elements of turn 50, such as
element 60 (including leads 61-1 and 61-2) and leads 55-1 and 55-2.
In one embodiment of the present invention, the intermediate
material layer is made from an insulator such as aluminum-oxide
(AlO.sub.x) or silicon-oxide (SiO.sub.x). In one example,
superconducting material 50 is made from Nb and the intermediate
material is 400 nm thick SiO.sub.x. In some embodiments, shape 40
has a width T.sub.240 (FIG. 2B) that is less than T.sub.50 (FIG.
2A). Embodiments where shape 40 has a width that is less than
T.sub.50 can require that shape 40 be made of an insulator with a
low dielectric constant and high breakdown voltage. This is
preferred in some embodiments in order to prevent electrical
coupling such as stray capacitance or current shortage between
individual turns within the N-turn ring.
[0051] In FIG. 2C, an additional turn is added to the structure
illustrated in FIG. 2B. A superconducting material layer is
deposited and patterned to form turn 51 using techniques similar to
those used to pattern turn 50. In typical embodiments, the same
superconducting material is used to form turns 50 and 51.
Furthermore, in typical embodiments, turns 50 and 51 have the same
dimensions (e.g., same width T.sub.50 as well as the same
thickness). In some embodiments, turn 51 covers turn 50 without
substantially obstructing aperture 49, regardless of whether turns
50 and 51 have the same dimensions. As used herein, aperture 49 is
also termed a common aperture.
[0052] FIG. 2D depicts crossover 60 in a perspective view. Lead
61-1 (not shown) and lead 61-2 of turn 50 are joined with leads
261-1 and 262-2 of turn 51 to create a 30 double turn. In one
embodiment of crossover 60, lead 61-1 (not shown) is coupled to
lead 261-1 without coupling leads 61-2 and 261-2. Some embodiments
of the present invention include additional turns similar or
identical to turn 50 and 51 and additional instances of crossover
60 that includes leads, thereby creating N-turn ring 1. Each of the
additional turns and leads has a width T.sub.50 and a thickness
that exceeds the London penetration depth .lambda..sub.L of the
superconducting material used to make the turns. The N-turn ring
structure, such as two-turn ring 200 (FIG. 2D), can be used as a
static magnetic flux source.
[0053] Because of the superconducting properties of N-turn ring 1,
the magnetic flux enclosed by N-turn ring 1 is quantized in
multiples of h/N2e, where N is the number of times an inaccessible
region is encircled by the N-turn ring, h is Plank's constant, and
e is elementary charge. Thus, the magnetic flux stored in N-turn
ring 1 is .PHI.=n/N .PHI..sub.0, where n is equal to or greater
than one, and N is the number of turns (e.g., number of crossovers
60) in the structure.
[0054] In some embodiments, the width T.sub.50 (FIG. 2A) of each
turn in the N-turn ring is greater than the London penetration
depth .lambda..sub.L of the material used to make the individual
turns in the N-turn ring. In such embodiments, the magnetic flux
stored in the aperture 49 (FIG. 2C) of the N-turn ring can be
trapped because it cannot penetrate through the N-turn ring when
the N-turn ring is in a superconducting state. Escape of the
magnetic flux is possible when the superconductivity is broken in a
global fashion. One method for breaking the superconductivity of
N-turn ring 1 such that it will no longer trap magnetic flux is to
raise the temperature of the ring above the critical temperature
T.sub.C of the material used to make the individual turns in the
N-turn ring. However, in some applications, raising the temperature
of the N-turn ring 1 is not practical. For example, such an
approach is unpractical when the N-turn ring 1 is used in a device
in which other components must remain below the T.sub.C of the
material used to make N-turn ring 1. Furthermore, such an approach
is unpractical in applications where the length of time that it
takes to release the magnetic flux trapped by the N-turn ring 1 is
critical (e.g., must be done quicker than the thermal transition
rates of the system allow).
[0055] The approach of adjusting the temperature of N-turn ring 1
finds useful application when it is desirable to adjust the amount
of flux that is trapped in N-turn ring. For example, in one
embodiment of the present invention, the N-turn ring comprises at
least one turn made of a first superconducting material having a
critical temperature T.sub.c1 and a at least one turn made of a
second superconducting material having a critical temperature
T.sub.c2 where T.sub.c2 is different than T.sub.c1. In such
embodiments, it is possible to adjust the amount of magnetic flux
trapped by the N-turn ring by adjusting the temperature of the
N-turn ring. For example, consider the case in which the N-turn
ring comprises exactly one turn having a critical temperature
T.sub.c1 and exactly turn having a critical temperature of
T.sub.c2. A magnetic flux is applied to the N-turn ring and then
the N-turn ring is cooled to a temperature T.sub.A, where
T.sub.c1<T.sub.A<T.sub.c2. Thus, upon cooling to temperature
T.sub.A, the N-turn ring traps one flux quantum (h/N2e, where N is
equal to one) because only one of the turns is superconducting.
Then, at a later time, when it desired to reduce the magnetic flux
trapped by the N-turn ring, the system is cooled to T.sub.B, where
T.sub.B is less than T.sub.c1 and T.sub.c2. At such a point, both
turns become superconducting and the N-turn ring traps only one
half of a fluxon (0.5.times.h/2e).
[0056] Due to the disadvantages of relying on raising the
temperature of N-turn ring above the T.sub.c for the ring, one
aspect of the present invention provides an alternative method for
releasing magnetic flux trapped in aperture 49 (FIG. 2A). This
aspect of the invention uses switching device 2 to break the
superconductivity of each turn in N-turn ring 1. In one embodiment,
switching device 2 is capable of introducing a reversible
topological cut into each turn in N-turn ring 1. There are many
devices that are capable of serving as switching device 2, and all
such devices are within the scope of the present invention. Such
switching devices include, but are not limited to, a cryotron, a
Josephson junction, and a laser. These devices are switchable
(e.g., can introduce a reversible localized cut in the
superconductivity of a turn in an N-turn ring) and can be used to
permit flux in aperture 49 to escape or flux outside of two-turn
ring 200 to enter.
[0057] Referring to FIG. 2D, the overall dimensions of an N-turn
ring 1, such as two-turn ring 200, are dependent upon the physical
properties of the material used to make the turns in the N-turn
ring. In one embodiment, the total area occupied by a turn (e.g.,
turn 50 or turn 51) in N-turn ring 1 is less than the square of the
coherence length of the material used to make each turn. Coherence
length is the smallest dimension over which superconductivity can
be established or destroyed in a given superconductor. The
coherence length of turns in N-turn ring 1 depend on the type of
material used to make each turn in the N-turn ring as well as the
purity of such material. For example, the addition of impurities to
a metal can cause the coherence length of the metal to decrease.
The coherence length of some superconducting materials are as
follows tin (30 nm), aluminum (1600 nm), lead (83 nm), cadmium (760
nm), and niobium (38 nm). Thus, in the case where a turn in N-turn
ring 1 is made of pure niobium, the turn can occupy an area that is
no larger than 1444 nm.sup.2, in accordance with one embodiment of
the present invention. In some embodiments of the present
invention, the total area occupied by a turn (e.g., turn 50 or turn
51) in N-turn ring 1 is less than the square of the coherence
length of the superconducting material used to make each turn and
the width T.sub.50 (FIG. 2A) of each turn is less than the London
penetration depth .lambda..sub.L of the superconducting
material.
[0058] In some embodiments of the present invention, N-turn ring 1
is a mesoscopic system. A mesoscopic system is one that is
described by quantum mechanical principles rather than classical
mechanical principles. Mesoscopic systems are non-microscopic
because they consist of many atoms. The term mesoscopic is a well
used term in the field of physics and, in general, indicates a
device of physical dimension such that phenomena observed on the
structure require quantum mechanical explanation. In other words,
mesoscopic systems refer to a class of solid systems where the
quantum mechanical single particle accurately describes the
characteristics of the physical system. In some embodiments,
mesoscopic systems are the systems of intermediate size, e.g.,
macroscopic but small enough (less than or equal to 10.sup.-4 cm).
In mesoscopic systems, quantum interference is very important,
since at low enough temperatures (<1 K) the phase coherence
length of quasiparticles ("electrons") exceeds the size of the
system. See, for example, Zagoskin, Quantum Theory of Many-Body
Systems, pp. 19-20, Springer, 1998; and Imry, "Physics of
Mesoscopic Systems", in Directions in Condensed Matter Physics:
Memorial Volume in Honor of Shang-Keng Ma, Grinstein and Mazenko,
eds., World Scientific, 1986, which are hereby incorporated by
reference in their entireties.
[0059] In some embodiments, an N-turn ring 1 is mesoscopic when the
respective overall dimensions (overall height, overall length, and
overall width) of the N-turn ring are each less than the phase
coherence length of the materials used to make the N-turn ring. In
some embodiments, an N-turn ring 1 is mesoscopic when it has
respective overall dimensions (height, length, width) of about
10.sup.-6 meters or less, is cooled to a temperature below the
critical temperature of the superconducting materials used to make
the N-turn ring, and has overall dimensions that are respectively
smaller than the phase coherence length of charges in the N-turn
ring.
Description and Fabrication of Selected Switching Devices 2
[0060] One switching device 2 that can be used to break the
superconductivity of one or more rings in N-turn ring 1 is a
cryotron. FIGS. 3A-3C detail a method used to fabricate an
exemplary cryotron. The exemplary cryotron includes outer layers
and intermediate insulating layers. The outer layers form coils
that conduct current while the insulating intermediate layers are
positioned around the one or more rings in N-turn ring 1. When a
current of sufficient size is run through the outer layers of the
cryotron, the magnetic field inductively generated at the center of
the cryotron interrupts the superconducting current in the one or
more rings of N-turn ring 1.
[0061] Referring to FIG. 3A, on a substrate 30, material is
deposited and patterned to form outer layer 301. In some
embodiments, it is convenient to have outer layer 301 patterned as
strips, as illustrated in FIG. 3A. However, there is no requirement
that outer layer 301 be patterned as strips. Preferably, the
material used for outer layer 301 is able to conduct electrical
current. Therefore, suitable materials for outer layer 301 include
semiconducting materials (e.g., silicon, germanium), conducting
materials (e.g., copper, silver, and gold), or superconducting
materials (e.g., type I superconductors, type II superconductors,
gallium, aluminum, indium, tin, lead, niobium, and
niobium-tin).
[0062] Next, first insulating layer 310 is deposited on a central
portion of outer layer 301 (e.g., a central portion of the disjoint
pieces that comprise layer 301). After the patterning of first
insulator layer 310, the ends of outer layer 301 are exposed, as
depicted in FIG. 3B. Next, intermediate layer 320 (FIG. 3B) is
deposited on insulator layer 310. In some embodiments, intermediate
layer 320 is made from any material used to make outer layer 301,
including semiconducting materials (e.g., silicon, germanium),
conducting materials (e.g., copper, silver, and gold), or
superconducting materials (e.g., type I superconductors, type II
superconductors, gallium, aluminum, indium, tin, lead, niobium, and
niobium-tin). In some embodiments, layer 320 is patterned into one
or more turns of an N-turn ring 1. For example, in some
embodiments, intermediate layer 320 comprises layer 50 and/or layer
51 (FIG. 2). Thus, in such embodiments, intermediate layer 320 is
typically made from materials such as a type I superconductor
(e.g., niobium, aluminum, and lead) or a type II
superconductor.
[0063] In some embodiments, insulator layer 310 is thick enough to
electrically separate outer layer 301 from intermediate layer 320.
For instance, in one embodiment, where outer layer 301 and
intermediate layer 320 are made from superconducting materials,
insulator layer 310 is deeper than the longest superconducting
coherence length of the superconducting materials used to make
layers 301 and 320. In some embodiments, outer layer 301 and
intermediate layer 320 each comprise a single layer of material. In
other embodiments, outer layer 301 and intermediate layer 320 each
comprise several discrete layers of material.
[0064] In FIG. 3C, a second insulator layer 311 is deposited over
intermediate layer 320 and patterned using the lithographic
techniques described above. The material used to make insulator
layers 310 and 311 is dependent upon the physical properties of the
material used to make intermediate layer 320. In the case where
intermediate layer 320 is made from niobium or aluminum, insulator
layers 310 and 311 are typically made of aluminum oxide
(Al.sub.2O.sub.3). In some embodiments, insulator layers 310 and/or
311 are made from silicon oxide. Further, those of skill in the art
will appreciate that insulator layers 310 and 311 can be made from
other materials and all such materials are within the scope of the
present invention.
[0065] Once second insulator layer 311 has been deposited, outer
layer 302 is deposited over layer 311. Then outer layer 302 is
patterned in such a way as to create, in conjunction with outer
layer 301, a multiple winding solenoid around first insulator 310,
intermediate layer 320, and second insulator layer 311.
Accordingly, outer layer 302 is typically made out of the same
materials as outer layer 301. In some embodiments, outer layer 302
has the shape of disjoint strips that connect with the disjoint
strips of outer layer 301 to form coils around the insulating and
intermediate layers, as illustrated in FIG. 3C. In other
embodiments, outer layer 302 has the shape of a single sheet. One
of skill in the art will appreciate that other shapes for outer
layers 301 and 302 are possible and all such shapes are within the
scope of the present invention. Outer layers 301 and 302 together
with insulator layers 310 and 311, as pictured in FIG. 3C, form
cryotron 300. Cryotron 300 represents one form of switching device
2 that can be used to break the superconductivity of N-turn ring
1.
[0066] Now that the methods used to manufacture cryotron 300 have
been disclosed in accordance with one embodiment of the present
invention, the operation of cryotron 300 will be described. The
operation of cryotron 300 includes driving a current through layers
301 and 302 so that a magnetic field is created in the interior of
cryotron 300. In the case where intermediate layer 320 is
superconducting, the material used to make outer layers 301 and 302
is selected such that layers 301 and 302 conduct a current that
exceeds the critical field of intermediate layer 320. The maximum
field that can be applied to a superconductor at a given
temperature without loss of superconductivity is referred to as the
critical field of the superconductor. The critical field varies in
type I and type II superconductors. The maximum critical field
(H.sub.C) in any type I superconductor is about 2000 Gauss (0.2
Tesla), but in type II materials superconductivity can persist to
several hundred thousand Gauss (H.sub.C2). At fields greater than
H.sub.C in a Type I superconductor and greater than H.sub.c2 in a
type II superconductor, the superconductor reverts to the normal
state and regains its normal state resistance.
[0067] Because the critical field of type II materials is so high,
intermediate layer 320 (e.g., turns 50 and 51 of FIG. 2) is
typically made of a type I superconductor. In the case where
intermediate layer 320 is made from Al (or a superconducting
material with a similar H.sub.C), layers 301 and 302 must conduct
enough current to produce a magnetic field that is between 50 Gauss
and 500 Gauss. In another example, in the case where intermediate
layer 320 is made from Nb (or a superconducting material with a
similar H.sub.C), layers 301 and 302 must conduct enough current to
produce a field of about 2000 Gauss. One Tesla is equal to about
10.sup.4 Gauss. The conductivity of layers 301 and 302 is
determined by their dimensions and the material used to form the
layers. The magnetic field produced by layers 301 and 302 is a
function of the number of coils that layers 301 and 302 form around
intermediate layer 320 and the amount of current in these coils. In
one embodiment of the present invention, cryotron 300 is used to
introduce local breaks in the superconductivity in select turns in
the N-ring 1.
[0068] FIGS. 3D-3F describe the manufacture of another switching
device 2 that is used in some embodiments of the present invention.
In particular, FIGS. 3D-3F describe how Josephson junctions are
introduced into one or more turns of N-turn ring 1 in some
embodiments of the invention. In FIG. 3D, a superconducting
material is deposited onto substrate 40 and patterned into a single
piece 331 that includes a biasing lead 332. In some embodiments,
piece 331 is a part of a turn in the N-turn ring 1. For example, in
some embodiments, piece 331 is part of turns 50 or 51 (FIG. 2).
[0069] In FIG. 3E, a material is layered onto a portion of piece
331 to form Josephson layer 340. Many different materials can be
used to form Josephson layer 340. In one example, Josephson layer
340 is an insulating layer with a depth that is less than or equal
to the coherence length of the superconducting material used to
make piece 331. In such embodiments, Josephson layer 340 acts as a
tunneling barrier. When Josephson layer 340 is an insulator, the
layer is deposited such that it has a depth that is less than
approximately the coherence length, .xi., of the superconducting
material used to make piece 331. In another embodiment, Josephson
layer 340 is formed by using a clean normal metal. In such
embodiments, the depth of layer 340 is generally less than the
approximate correlation length of the clean normal metal used to
form Josephson layer 340. The correlation length of a clean normal
metal is .nu..sub.F/kT, where is Planck's constant over 2.pi.,
.nu..sub.F is the Fermi velocity of the metal, and kT is the
thermal energy. Still other Josephson layers 340 are possible. For
example, a dirty normal metal junction with scattering sites could
be used to from Josephson layer 340. See Barone and Patern, Physics
and Applications of the Josephson Effect, John Wiley & Sons,
New York (1982), which is hereby incorporated by reference in its
entirety. One of skill in the art will appreciate that still other
materials can be used to form Josephson layer 340, and all such
materials are within the scope of the present invention.
[0070] In FIG. 3F, an additional superconducting piece 335 is
deposited onto Josephson layer 340 and patterned to include lead
336. In some embodiments, pieces 331 and 335 are portions of the
same turns in N-turn ring 1. Accordingly, in such embodiments,
piece 331 is made of the same material as piece 335 (e.g., a type I
superconductor). In embodiments where piece 331 and piece 335 are
different sections of the same turn in N-ring 1, the net effect of
the processing steps illustrated in FIGS. 3D-3F is the introduction
of a Josephson junction 350 into the ring.
[0071] Josephson junction 350 may be used to locally break the
superconductivity of a turn in N-turn ring 1. Generally, a
Josephson junction, such as Josephson junction 350, can operate in
a zero voltage state or a voltage state. The zero voltage state is
a superconducting state whereas the voltage-state is a
non-superconducting state. A property of all Josephson junctions is
their ability to switch from a zero voltage to a voltage state when
the current through the Josephson junction is greater than a
critical current I.sub.C. To produce such a critical current, leads
332 and 336 are used to introduce a current through Josephson
junction 350. When this current exceeds the I.sub.C of layer 340,
Josephson junction 350 is toggled from a zero voltage state
(superconducting) to a voltage state (nonsuperconducting).
Therefore, Josephson junction introduces a local break in the
superconductivity of a turn in N-turn ring 1.
[0072] FIG. 3G depicts another switching device 2 (device 375) that
can be used to break the superconductivity of one or more turns in
N-turn ring 1. Focused electromagnetic radiation, such as light
from a laser, applied to a superconductor will break the
superconducting current within superconductor. The laser raises the
temperature of a localized portion of the N-turn ring 1 above the
critical temperature of the ring, thereby interrupting the
supercurrent in a localized fashion. This phenomenon is used in
system 380. System 380 includes a laser 360. In some embodiments,
laser 360 is an infrared (IR) laser. In some embodiments, laser 360
has a wavelength in the range of 0.7 .PHI.M to about 10 .PHI.M. In
some embodiments, laser 360 is an Alexandrite laser with a
wavelength of about 0.72 .PHI.M, a GaAlAs diode laser with a
wavelength of about 0.72 .PHI.M, a Ti-Sapphire laser with a
wavelength of about 0.88 .PHI.M, an InGaAs diode laser with a
wavelength of about 0.98 .PHI.M, a Nd-Yag laser with a wavelength
of about 1.06 .PHI.M, a He--Ne laser with a wavelength of about
1.15 .PHI.M, an Nd-YLF laser with a wavelength of 1.31 .PHI.M, or a
Nd-YAG laser with a wavelength of about 1.32 .PHI.M.
[0073] In some embodiments, laser 360 has a wavelength in the
visible spectrum (0.7 .PHI.M. to 0.4 .PHI.M) or ultraviolet
spectrum (0.4 .PHI.M. to 0.15 .PHI.M). However, the heating effect
associated with lasers operating in the ultraviolet wavelength
range is advantageous and has utility in some embodiments of the
present invention. Therefore, lasers operating in the ultraviolet
wavelength range are more commonly used in systems 380 in
accordance with the present invention.
[0074] In some embodiments, laser 360 is a pulsed laser. In some
embodiments, the pulse duration of laser 360 is 100 femtoseconds,
50 femtoseconds, 10 femtoseconds, 5 femtoseconds, 1 femtosecond, or
less. In some embodiments, laser 360 has a wavelength of about one
micron 1 .PHI.M and a pulse duration of about 10 femtoseconds or
less. In some embodiments, laser 360 has a pulse duration that is
about the length of the magnetic diffusion time of N-turn ring 1.
The magnetic diffusion time for a conductor such as N-turn ring 1
is the amount of time needed to annihilate a field inside the
conductor. The magnetic diffusion time is dependent on the
conducting material and the dimensions (size) of the material.
Pulse durations that approximate or exceed the magnetic diffusion
time of N-turn ring 1 are desirable because they insure that the
supercurrent is interrupted for a sufficiently long time to create
or annihilate the flux trapped inside the ring.
[0075] Referring to FIG. 3G, laser 360 is directed down waveguide
370 and projected onto a superconducting structure, such as
two-turn ring 200 (see FIG. 2D). The electromagnetic radiation
travelling down waveguide 370 can be modulated by an optional
switch 365. Examples of switches 365 are well known in the art. In
some embodiments, waveguide 370 comprises a plurality of waveguides
and modulating switch 365 acts as a distributor of the
electromagnetic radiation (not shown). This plurality of waveguides
can be directed on to different portions of two-turn ring 200.
[0076] In system 380, waveguide 370 terminates at a distance
d.sub.370 away from a region of two-turn ring 200. The distance
d.sub.370 can be a distance of zero to several centimeters or more.
Those of skill in the art will appreciate that, at larger
distances, such as several centimeters, a precision optical system
between waveguide 370 and two-turn ring 200 can be used to align
the waveguide with specific regions of N-turn ring 1.
Sub-Flux Quantum Generator 400
[0077] FIG. 4A illustrates a device 400 that includes a two-turn
ring 200 (exemplary N-turn ring 1, FIG. 1), switching devices 405
to break the superconductivity of ring 200 (exemplary switching
device 2, FIG. 1), and a magnetic flux source 412 (exemplary
magnetism device 3, FIG. 1). In FIG. 4A, two-turn ring 200 is
incorporated into device 400 through leads 55. Examples of switches
405 include, but are not limited to, a cryotron 300 (FIG. 3C), a
Josephson junction 350 (FIG. 3F), and a laser 375 (FIG. 3G). In the
example illustrated in FIG. 4A, switch 405 is placed in each turn
of a two-turn ring.
[0078] An alternating current source 412 (magnetic flux source 3)
and a direct current source 411 are arranged parallel and are in
electrical communication with two-turn ring 200 in order to create
a supercurrent through two-turn ring 200. In state 1, switches 405
allow current to flow and supercurrent travels equally through both
turns of two-turn ring 200. Similarly, when two-turn ring 200 is
replaced with a generalized N-turn ring, current flows through each
turn of the N-turn ring. Further, the current flows equally through
both possible paths (paths 470 and 480) of the ring from 55-1 to
55-2. Thus, there is a direct connection 198 (path 480) and an
indirect connection 199 (path 470) through crossover 60. In the
embodiment illustrated in FIG. 4A, two-turn ring 200 includes
crossover 60. Because the current in paths 470 and 480 are equal
and flowing in opposite directions, no magnetic field is induced in
aperture 49 during initial state 1.
[0079] In state 2, switches 405 are set to block the flow of
current. As a result, the superconducting current that was flowing
in path 480 in state 1 is terminated. Supercurrent can only travel
through connection 198 of ring 200 (path 470) because connection
198 does not include the localized break induced by switches 405.
As a result, the symmetry between the superconducting current
following paths 470 and 480 is lost and, therefore, a net magnetic
flux .PHI..sub.X is induced into aperture 49 during state 2. In
state 3, the symmetrical superconducting current is restored to
two-turn ring 200 by closing switches 405, allowing current to flow
through connection 199 (path 480). In a typical embodiment, each
turn in two-turn ring 200 has a width T.sub.50 (FIG. 2A) that
exceeds the London penetration depth .lambda..sub.L of the material
used to make device 200. Therefore, the magnetic flux that arose in
aperture 49 during state 2 is trapped and quantized during state 3.
In this example, the amount of magnetic flux that is trapped in
aperture 49 (.PHI..sub.X) is n/2.PHI..sub.0, where the integer n is
controlled by the amount of supercurrent conducted through 2-turn
ring 200, and the value 2 is found in the equation for the
.PHI..sub.X of two-turn ring 200 because there are two turns in
device 200. In general, the induced magnetic flux is equal to the
product of the electrical current flowing in device 200 during
state 2 and the self-inductance of device 200. When the current is
not superconducting, the induced magnetic flux can take any value.
However, when device 200 becomes superconducting, the magnetic flux
becomes quantized. For this reason, the magnetic flux that is
trapped in aperture 49 (.PHI..sub.X) is n/2.PHI..sub.0.
[0080] The rate at which flux can be introduced into aperture 49 is
application dependent. In the embodiment illustrated in FIG. 4, the
rate is approximately equal to .tau..sub.m the magnetic diffusion
time
.tau..sub.m.apprxeq..mu..sub.o.multidot..sigma..multidot.L.sup.2
where .mu..sub.o is the permeability of free space, .sigma. is the
normal conductivity of superconducting material 50 and L is
proportional to the mean width of two-turn ring 200.
Sub-Flux Quantum Generator 401
[0081] FIG. 4B illustrates another sub-flux source in accordance
with the present invention. Sub-flux quantum generator 401 includes
a two-turn ring 200 that is a variant of the two-turn ring 200
illustrated in FIG. 4A. The two-turn ring illustrated in FIG. 4B
includes two crossovers 60 and three switches 405 (switching
devices 2). Operation of sub-flux quantum generator 401 is similar
to that of sub-flux quantum generator 400. It is possible to trap a
flux .PHI..sub.X in two-turn ring 200. This magnetic flux can be
established in aperture 49 even when an external flux .PHI..sub.E
(not shown) is present.
[0082] In state 1, for sub-flux quantum generator 401, switches 405
allow current to flow and supercurrent travels equally through all
turns of three-turn ring 200 which may be replaced by an N turn
ring. Further, the current flows equally through both possible
paths (472 and 482) of ring 200 from 55-1 to 55-2. There is a
direct connection 198 (path 482) and an indirect connection 199
(path 472) through crossovers 60-1 and 60-2. Because the current in
paths 472 and 482 are equal and flowing in the same principle
direction, no magnetic field is induced in aperture 49 during
initial state 1.
[0083] In state 2, switches 405 no longer allow current to flow and
the superconducting current that was flowing through path 470 in
state 1 is blocked by switches 405-1, 405-2, and 405-3. Current
must flow through direct connection 198 (path 482). As a result,
the symmetry between the current flowing in paths 472 and 482 that
existed in state 1 is lost and, therefore, a magnetic flux
.PHI..sub.X is induced into aperture 49 during state 2. In state 3,
the symmetrical superconducting current is restored to two-turn
ring 200 by closing switches 405, allowing current to flow along
path 472 (through connection 199). In a typical embodiment, each
turn in an N-turn ring 200 has a width T.sub.50 (FIG. 2A) that
exceeds the London penetration depth .lambda..sub.L of the material
used to make device 200. Therefore, the magnetic flux that arose in
aperture 49 during state 2 is trapped and quantized during state 3.
In this example, the amount of magnetic flux that is trapped in
aperture 49 (.PHI..sub.X) is n/3.PHI..sub.0, where the integer n is
controlled by the amount of supercurrent conducted through 3-turn
ring 200, and the value 3 is found in the equation for the
.PHI..sub.X of three-turn ring 200 because there are three rings in
device 200. The rate at which flux can be introduced into aperture
49 is application dependent. In the embodiment illustrated in FIG.
4, the rate is approximately equal to .tau..sub.m the magnetic
diffusion time
.tau..sub.m.apprxeq..mu..sub.o.multidot..sigma..multidot.L- .sup.2
where .mu..sub.o is the permeability of free space, .sigma. is the
normal conductivity of superconducting material 50 and L is
proportional the mean width of two-turn ring 200.
Sub-Flux Quantum Generator 402
[0084] FIG. 4C illustrates another sub-flux quantum generator (402)
in accordance with an embodiment of the present invention. Sub-flux
quantum generator 402 includes an N-turn ring 200 and a switch 406
that shunts crossover 60-2 in N-turn ring 200. Operation of
sub-flux quantum generator 402 differs from that of sub-flux
quantum generators 400 (FIG. 4A) and 401 (FIG. 4B). In particular,
the number of turns in N-turn ring 1 may be adjusted by operation
of switch 406.
[0085] Magnetic flux in sub-flux quantum generator 402 is trapped
by progression through the following states. In state 1, switches
405 in the rings of N-turn ring 200 in which magnetic flux is to be
trapped are opened. A current is driven through N-turn ring 200,
establishing magnetic flux .PHI..sub.X in aperture 49. In state 2,
the magnetic flux is trapped in aperture 49 by closing switches 405
in specific rings of N-turn ring 1. The amount of magnetic flux
trapped in state 2 is a function of the number of switches 405
closed, the state of shunting switch 406, and the amount of current
flowing through N-turn ring 1 when switches 405 were closed. For
example if a flux .PHI..sub.X=n/2 .PHI..sub.0 is desired, switches
405-1, 405-2 and 406 are closed in state 2 while switch 405-3
remains open. When switches 405 and 406 are in this configuration,
the magnetic flux is enclosed in a two-turn superconducting ring.
Therefore, the magnetic flux assumes the quantized value of
.PHI..sub.X=n/2 .PHI..sub.0. In the expression for .PHI..sub.X, the
value n is a function of current driven through N-turn ring 1, and
the value 2 in denominator arises because there are two turns in
the N-turn ring.
[0086] Sub-flux quantum generator 402 can be used to trap magnetic
flux .PHI..sub.X having the quantized value n/3 .PHI..sub.0 by
progression through the following states. First, switches 405-1,
405-2, and 405-3 are opened. A current is driven through N-turn
ring 200, establishing magnetic flux .PHI..sub.X in aperture 49.
Then switch 406 is opened and switches 405-1, 405-2, and 405-3 are
closed. Leaving switch 406 open activates crossover 60-2 and opens
up a third superconducting ring around aperture 49. As a result,
the amount of magnetic flux that is trapped by aperture 49 is n/3
.PHI..sub.0.
[0087] One of skill in the art will appreciate that the sub-flux
quantum generator 402 could be modified to have N rings and at
least N-1 crossovers, where N is any integer greater than 2.
Further, shunt switches could be placed across any number of the at
least N-1 crossovers. In this way, a sub-flux quantum generator
that is capable of trapping a magnetic flux .PHI..sub.X=n/N
.PHI..sub.0 is realized, where N is determined by the configuration
of the switches 405 and shunt switches 406 (not shown) in the
N-turn ring 1. Such devices can be used as calibration units for
magnetometers. Since the value of the flux .PHI..sub.X can be
accurately determined, the device can be used to check the accuracy
and precision of any device that senses magnetic flux. Devices that
sense magnetic flux include a superconducting quantum interference
device (SQUID) and a magnetic force microscope (MFM).
Sub-Flux Quantum Generator 500
[0088] FIG. 5 illustrates a sub-flux quantum generator 500 in
accordance with another embodiment of the present invention.
Previously, it has been disclosed that the amount of magnetic flux
trapped by an N-turn superconducting ring is quantized into some
multiple of h/N2e where N is the number of turns in the N-turn
ring. This relationship assumes that the area within each turn in
the N-turn ring is approximately the same. In sub-flux quantum
generator 500, at least one turn in the N-turn ring 1 encloses an
area A.sub.1 that is larger or smaller than the area A.sub.2
enclosed by another turn in the N-turn ring. Thus, although the
N-turn ring 1 in sub-flux quantum generator still traps a quantized
amount of magnetic flux when in the superconducting state, the
amount of magnetic flux trapped by the N-turn ring 1 is not
governed by the expression h/N2e. In fact, the amount of magnetic
flux stored by N-turn ring 1 can be adjusted by varying the size of
individual rings in the N-turn ring 1. In the embodiment
illustrated in FIG. 5, for example, N-turn ring 1 has two turns.
The outer turn encloses area A.sub.1 and the inner turn encloses
area A.sub.2. Here, the two-turn ring traps magnetic flux at
quantized values that diverge from n/2 .PHI..sub.0, where n is a
natural number, because each turn encloses a different area. Thus,
the amount of magnetic flux that the N-turn ring traps in sub-flux
quantum generator 500 can be modified by adjusting the size of each
turn of the N-turn ring.
[0089] In some embodiments, it is desirable to introduce an
inhomogeneous magnetic field into N-turn ring 1. An inhomogeneous
magnetic field is one that varies in magnitude as a function of
position within aperture 49 (e.g., the magnetic field has a
gradient in at least one direction within aperture 49).
[0090] Thus, an inhomogeneous magnetic field in the case of the
N-turn ring 1 arises when the magnitude of the trapped magnetic
flux within aperture 49 (FIG. 5) of the N-turn ring varies as a
function of position. FIG. 5 illustrates how an inhomogeneous
magnetic field within aperture 49 can be achieved. FIG. 5 includes
a magnetic flux source 550 that includes a current source 551 and
an inductor 553. In FIG. 5, current source 551 is used to drive a
current through N-turn ring 1. Devices (not shown in FIG. 5) such
as cryotrons 300 (FIG. 3C), Josephson junctions 350 (FIG. 3F),
and/or laser systems 380 are used to break the superconducting
current at localized positions of the turns in N-turn ring 1. At a
later stage these localized breaks are restored in order to trap
magnetic flux in the aperture of the N-turn ring using the
techniques described above for other embodiments of the present
invention. In FIG. 5, a magnetic field within aperture 49 that is
inhomogeneous is produced using additional flux generator 501.
Current in 501, from alternating current source 560 and direct
current source 562, produces a magnetic flux in aperture 49. The
magnitude of this flux at any given point in aperture 49 is
inversely dependent on the distance between the point in aperture
49 and the current in 501. Other geometrical configurations of 501
are possible. Additional flux generator 501 includes an alternating
current source 560 that is configured to provide a magnetic field
at a different angle than the flux that is enclosed within the
N-turn ring. This is accomplished by providing a wire adjacent to
the ring 1 out of the plane of the ring. Using current sources 560
and 562 a current in 501 will provide a flux that is not normal to
the plane of 1. Further, flux generator 500 can include a charge
source 562 that makes the magnetic field in the N-turn ring
inhomogeneous. FIG. 5 illustrates another device that can be used
to make the magnetic field in an N-turn ring inhomogeneous. The
device is capacitor 510, which is capable of bending the magnetic
field within the ring.
Use of Sub-Flux Quantum Generators to Bias Persistent Current
Qubits
[0091] FIG. 6 illustrates an embodiment of the present invention in
which a sub-flux quantum generator is used to frustrate a
superconducting structure. An example of a superconducting
structure is a superconducting qubit, such as a persistent current
qubit 700. As described above, persistent current qubit 700 (FIG.
6, FIG. 7) comprises a superconducting loop that has at least three
Josephson junctions 702. The Josephson energy of two of the
junctions 702 is equal while the Josephson energy of the third
junction 702 is slightly less than the other two junctions. In FIG.
6, the presence of a Josephson junction 702 is indicated by an "X".
The size of the "X" used to label each Josephson junction 702 is
proportional to the Josephson energy of the respective
junction.
[0092] In FIG. 6, each sub-flux quantum generator in 400 is used to
bias a persistent current qubit 700 so that the two stable energy
states of the qubit become degenerate (i.e., have equal energy).
These degenerate states correspond to quantum phase states of
persistent current qubit 700. Using these states, which may be
ground states of persistent current qubit 700, it is possible to
perform quantum computation operations. Those of skill in the art
will appreciate that, in some embodiments, it is necessary to
shield the persistent current qubit from leads 55 (FIG. 4A).
[0093] In additional embodiments of the present invention, a
sub-flux quantum generator is used to bias any superconducting
qubit, such as phase qubits and/or charge qubits and/or hybrid
qubits. Qubits are defined by their uncertainty in charge and
phase, which is, in turn, determined by the Heisenberg uncertainty
principle. The Heisenberg uncertainty principle can be expressed as
.DELTA.n.DELTA..phi..ltoreq.1/2- , where .DELTA.n represents an
uncertainty in the charge of the qubit and .DELTA..phi. represents
an uncertainty in the phase of the qubit. There are two classic
types of qubits, charge qubits and phase qubits. In a charge qubit,
the uncertainty of the phase of the qubit is large compared to the
uncertainty of the charge. In a phase qubit, uncertainty of the
charge of the qubit is large compared to the uncertainty of the
phase. When a qubit is in the charge regime, the charge of the
charge device represents a good quantum number and has a finite
number of charge states. A good quantum number in this case means a
small uncertainty in its charge. See, e.g., Nakamura et al., 1999,
Nature 398, p. 786, which is hereby incorporated by reference. When
a qubit is in the phase regime, the phase of a mesoscopic phase
device is a good quantum number (to the extent that the uncertainty
is small) having a finite number of phase states. A hybrid qubit is
a qubit that has neither a charge nor a phase as a good quantum
number. An example of a hybrid qubit is a quantronium. See, for
example, Cottet et al., 2002, Physica C 367, pp. 197-203; and Vion
et al., 2002, Science 296, pp. 886, which are hereby incorporated
by reference in their entireties.
[0094] Further, one or more sub-flux quantum generators can be used
to frustrate (bias) a superconducting structure, such as a qubit.
In some embodiments, the frustration is used to create degenerate
states as in the case illustrated in FIG. 6. In other embodiments,
this frustration need not create degenerate states. Rather, the
frustration can be used to bias two stable states of the
superconducting structure so that they have a predetermined energy
differential. A case where the use of non-degenerate stable states
is useful is described in Lidar et al., 2002, "Quantum Codes for
Simplifying Design and Suppressing Decoherence in Superconducting
Phase-Qubits," Quantum Information Processing 1, p. 155, also
published as LANL preprint ArXiv.org:cond-mat/0204153 (2002), which
is hereby incorporated by reference in its entirety.
[0095] The embodiment of the present invention depicted in FIG. 6
shows an array of coupled qubits. These qubits (e.g., qubits 601-1
and 601-2) are persistent current qubits and are coupled through an
LC-circuit or resonance circuit 610. Here the LC-circuit includes
an inductor 608 and a capacitor 609. This pairwise coupling can be
repeated in order to couple many pairs of qubits to other pairs of
qubits. Such a grouping can serve as a component of a larger
quantum-computing device, such as a quantum register or quantum
computer.
[0096] The operation of persistent current qubit 700 in some
quantum computing operations involves applying quantum gates to the
qubit. A quantum gate is a controlled interaction between qubits
that produces a coherent change in the state of one qubit that is
contingent upon the state of another qubit. See, for example
DiVincenzo in Braunstein and Lo (eds.), Scalable Quantum Computers,
Wiley-VCH Verlag GmbH, Berlin (2001); Makhlin et al., 2001, Reviews
of Modern Physics 73, p. 357; and Nielsen and Chuang, Quantum
Computation and Quantum Information, Cambridge University Press,
2000, which are hereby incorporated by reference in their
entireties. These gates include a biasing operation that makes one
basis state energetically favorable over the other. A method to
accomplish such a biasing operation is to provide a flux bias by
application of an external magnetic field. Such biasing operations
are detailed in Orlando et al., 1999, Phys. Rev. B 60, 15398, which
is hereby incorporated by reference in its entirety.
ALTERNATIVE EMBODIMENTS
[0097] All references cited herein are incorporated herein by
reference in their entirety and for all purposes to the same extent
as if each individual publication or patent or patent application
was specifically and individually indicated to be incorporated by
reference in its entirety for all purposes. While the present
invention has been described with reference to a few specific
embodiments, the description is illustrative of the invention and
is not to be construed as limiting the invention. In particular,
while various embodiments of the present invention have been
described with a two-turn ring, those of skill in the art will
appreciate that an N-turn ring, where N is any integer equal to or
greater than two, can be used in such embodiments. Various
modifications may occur to those skilled in the art without
departing from the true spirit and scope of the invention as
defined by the appended claims.
* * * * *