U.S. patent application number 15/455466 was filed with the patent office on 2018-09-13 for zzz coupler for superconducting qubits.
This patent application is currently assigned to NORTHROP GRUMMAN SYSTEMS CORPORATION. The applicant listed for this patent is DAVID GEORGE FERGUSON, ANTHONY JOSEPH PRZYBYSZ, JOEL D. STRAND. Invention is credited to DAVID GEORGE FERGUSON, ANTHONY JOSEPH PRZYBYSZ, JOEL D. STRAND.
Application Number | 20180261752 15/455466 |
Document ID | / |
Family ID | 61193166 |
Filed Date | 2018-09-13 |
United States Patent
Application |
20180261752 |
Kind Code |
A1 |
FERGUSON; DAVID GEORGE ; et
al. |
September 13, 2018 |
ZZZ COUPLER FOR SUPERCONDUCTING QUBITS
Abstract
Systems and methods are provided for a ZZZ coupler. A first
tunable coupler is coupled to the first qubit and tunable via a
first control signal. A second tunable coupler is coupled to the
first tunable coupler to direct a flux of the first qubit into a
tuning loop of the second tunable coupler, such that when a first
coupling strength associated with the first tunable coupler is
non-zero, a second coupling strength, associated with the second
tunable coupler, is a function of a second control signal applied
to the second tunable coupler and a state of the first qubit. The
second qubit and the third qubit are coupled to one another through
the second tunable coupler, such that, when the second coupling
strength is non-zero it is energetically favorable for the states
of the first and second qubits to assume a specific relationship
with respect to the Z-axis.
Inventors: |
FERGUSON; DAVID GEORGE;
(TAKOMA PARK, MD) ; PRZYBYSZ; ANTHONY JOSEPH;
(HIGHLAND, MD) ; STRAND; JOEL D.; (ELLICOTT CITY,
MD) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
FERGUSON; DAVID GEORGE
PRZYBYSZ; ANTHONY JOSEPH
STRAND; JOEL D. |
TAKOMA PARK
HIGHLAND
ELLICOTT CITY |
MD
MD
MD |
US
US
US |
|
|
Assignee: |
NORTHROP GRUMMAN SYSTEMS
CORPORATION
FALLS CHURCH
VA
|
Family ID: |
61193166 |
Appl. No.: |
15/455466 |
Filed: |
March 10, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06N 10/00 20190101;
H03K 19/1952 20130101; H01L 39/025 20130101 |
International
Class: |
H01L 39/02 20060101
H01L039/02 |
Claims
1. A ZZZ coupler assembly for coupling first, second, and third
qubits comprising: a first tunable coupler coupled to the first
qubit and tunable via a first control signal; and a second tunable
coupler coupled to the first tunable coupler to direct a flux of
the first qubit into a tuning loop of the second tunable coupler
such that, when a first coupling strength associated with the first
tunable coupler is non-zero, a second coupling strength, associated
with the second tunable coupler, is a function of a second control
signal applied to the second tunable coupler and a state of the
first qubit; wherein the second qubit and the third qubit are
coupled to one another through the second tunable coupler, such
that, when the second coupling strength is non-zero, it is
energetically favorable for the states of the first and second
qubits to assume a specific relationship with respect to the Z-axis
of the Bloch sphere.
2. The ZZZ coupler assembly of claim 1, wherein the second qubit
and the third qubit are coupled through the second tunable coupler
via galvanic Josephson mutual inductance.
3. The ZZZ coupler assembly of claim 1, wherein the second control
signal can be varied such that the second coupler can provide any
of a negative coupling, such that it is energetically favorable for
the states of the second and third qubits to align in a same
direction along the Z-axis, a positive coupling, such that it is
energetically favorable for the states of the second and third
qubits to align in opposite directions along the Z-axis, and a zero
coupling between the second qubit and the third qubit.
4. The ZZZ coupler assembly of claim 1, further comprising; a third
tunable coupler coupled to the second qubit and tunable via a third
control signal; and a fourth tunable coupler coupled to the third
tunable coupler to direct a flux of the second qubit into the
fourth tunable coupler such that, when a third coupling strength
associated with the third tunable coupler is non-zero, a fourth
coupling strength, associated with the fourth tunable coupler, is a
function of a fourth control signal applied to the fourth tunable
coupler and a state of the second qubit; wherein the first qubit
and the third qubit are coupled through the fourth tunable coupler,
such that, when a coupling strength of the fourth tunable coupler
is non-zero, it is energetically favorable for the states of the
first and third qubits to assume a specific relationship with
respect to the Z-axis.
5. The ZZZ coupler assembly of claim 4, further comprising; a fifth
tunable coupler coupled to the third qubit and tunable via a fifth
control signal; and a sixth tunable coupler coupled to the fifth
tunable coupler to direct a flux of the third qubit into the sixth
tunable coupler such that, when a fifth coupling strength
associated with the fifth tunable coupler is non-zero, a sixth
coupling strength, associated with the sixth tunable coupler, is a
function of a sixth control signal applied to the sixth tunable
coupler and a state of the third qubit; wherein the first qubit and
the second qubit are coupled through the sixth tunable coupler,
such that, when a coupling strength of the sixth tunable coupler is
non-zero, it is energetically favorable for the states of the first
and second qubits to assume a specific relationship with respect to
the Z-axis.
6. The ZZZ coupler assembly of claim 1, wherein the first control
signal can be tuned to reduce the first coupling strength to zero,
such that the second coupling strength becomes independent of the
state of the first qubit.
7. The ZZZ coupler assembly of claim 6, wherein each of the first
tunable coupler and the second tunable coupler comprises a compound
Josephson junction, and each of the first and second control
signals comprising a first applied flux and a second applied
flux.
8. The ZZZ coupler assembly of claim 7, further comprising a first
classical control, the first classical control being configured to
provide the first applied flux as one half of a flux quantum to
tune the first coupling strength to zero such that the second
coupling strength becomes independent of the state of the first
qubit and a Hamiltonian of a system formed by the first qubit, the
second qubit, the third qubit, and the ZZZ coupler assembly does
not contain a three qubit term.
9. The ZZZ coupler assembly of claim 8, further comprising a second
classical control, the second classical control being configured to
provide the second applied flux as one half of a flux quantum to
tune the second coupling strength to zero.
10. A quantum circuit assembly comprising: the first qubit; the
second qubit; the third qubit; and the ZZZ coupler assembly of
claim 1.
11. The quantum circuit assembly of claim 10, wherein each of the
first qubit, the second qubit, and the third qubit are flux qubits
comprising superconducting loops interrupted by at least one
Josephson junction.
12. The quantum circuit assembly of claim 11, wherein the at least
one Josephson junction comprises respective first and second
Josephson junctions for each of the first qubit, the second qubit,
and the third qubit, and each of the second qubit and the third
qubit further comprise respective third and fourth Josephson
junctions, each of the second and third qubit sharing respective
third and fourth Josephson junctions with the second tunable
coupler.
13. The quantum circuit assembly of claim 12, the first tunable
coupler comprising a first set of Josephson junctions, and the
second tunable coupler comprising a second set of Josephson
junctions, wherein a critical current associated with the third and
fourth Josephson junctions on each of the second and third qubits
is at least twice a critical current associated with any Josephson
junction of the first set of Josephson junctions, the second set of
Josephson junctions, and the at least one Josephson junction for
each of the first qubit, the second qubit, and the third qubit.
14. The quantum circuit assembly of claim 10, wherein each of the
first qubit, the second qubit, and the third qubit are Transmon
qubits.
15. A method for providing a ZZZ coupling among three qubits,
comprising: coupling a first qubit of the three qubits to a second
qubit of the three qubits via a first tunable coupler utilizing
galvanic Josephson mutual inductance; coupling the second qubit to
a third qubit of the three qubits via a second tunable coupler
utilizing galvanic Josephson mutual inductance; coupling the third
qubit to the first qubit via a third tunable coupler utilizing
galvanic Josephson mutual inductance; coupling the first qubit to
the second tunable coupler via a fourth tunable coupler such that a
flux from the first qubit is directed into a tuning loop of the
second tunable coupler; coupling the second qubit to the third
tunable coupler via a fifth tunable coupler such that a flux from
the second qubit is directed into a tuning loop of the third
tunable coupler; and coupling the third qubit to the first tunable
coupler via a sixth tunable coupler such that a flux from the third
qubit is directed into a tuning loop of the first tunable
coupler.
16. A quantum circuit assembly comprising: a first qubit; a second
qubit; a third qubit; a first tunable coupler coupled to the first
qubit; and a second tunable coupler coupled to the first tunable
coupler such that a flux of the first qubit is directed into the
second tunable coupler, the second qubit and the third qubit are
coupled to one another through the second tunable coupler via
galvanic Josephson mutual inductance.
17. The quantum circuit assembly of claim 16, further comprising: a
first classical control that provides a first control signal to
tune a first coupling strength associated with the first tunable
coupler; and a second classical control that provides a second
control signal to tune a second coupling strength associated with
the second tunable coupler; wherein the first classical control is
configured to provide the first control signal as to provide each
of a non-zero first coupling strength, such that a second coupling
strength, associated with the second tunable coupler, is a function
of a second control signal applied to the second tunable coupler
and a state of the first qubit and a zero coupling strength, such
that the second coupling strength is independent of the state of
the first qubit.
18. The quantum circuit assembly of claim 17, wherein each of the
first tunable coupler and the second tunable coupler comprises a
compound Josephson junction, and each of the first and second
control signals comprising a first applied flux and a second
applied flux.
19. The quantum circuit assembly of claim 17, further comprising; a
third tunable coupler coupled to the second qubit and tunable via a
third control signal; a fourth tunable coupler coupled to the third
tunable coupler to direct a flux of the second qubit into the
fourth tunable coupler such that, when a third coupling strength
associated with the third tunable coupler is non-zero, a fourth
coupling strength, associated with the fourth tunable coupler, is a
function of a fourth control signal applied to the fourth tunable
coupler and a state of the second qubit; a fifth tunable coupler
coupled to the third qubit and tunable via a fifth control signal;
and a sixth tunable coupler coupled to the fifth tunable coupler to
direct a flux of the third qubit into the sixth tunable coupler
such that, when a fifth coupling strength associated with the fifth
tunable coupler is non-zero, a sixth coupling strength, associated
with the sixth tunable coupler, is a function of a sixth control
signal applied to the sixth tunable coupler and a state of the
third qubit; wherein the first qubit and the third qubit are
coupled through the fourth tunable coupler, such that, when a
coupling strength of the fourth tunable coupler is non-zero, it is
energetically favorable for the states of the first and third
qubits to assume a specific relationship with respect to the Z-axis
of the Bloch sphere, and the first qubit and the second qubit are
coupled through the sixth tunable coupler, such that, when a
coupling strength of the sixth tunable coupler is non-zero, it is
energetically favorable for the states of the first and second
qubits to assume a specific relationship with respect to the
Z-axis.
20. The quantum circuit assembly of claim 17, wherein the second
control signal can be varied such that the second coupler can
provide any of a negative coupling, such that it is energetically
favorable for the states of the second and third qubits to align in
a same direction along the Z-axis, a positive coupling, such that
it is energetically favorable for the states of the second and
third qubits to align in opposite directions along the Z-axis, and
a zero coupling between the second qubit and the third qubit.
Description
TECHNICAL FIELD
[0001] This invention relates to quantum computing, and more
particularly, to a coupler for coupling the Z basis states of three
superconducting qubits.
BACKGROUND
[0002] A classical computer operates by processing binary bits of
information that change state according to the laws of classical
physics. These information bits can be modified by using simple
logic gates such as AND and OR gates. The binary bits are
physically created by a high or a low signal level occurring at the
output of the logic gate to represent either a logical one (e.g.,
high voltage) or a logical zero (e.g., low voltage). A classical
algorithm, such as one that multiplies two integers, can be
decomposed into a long string of these simple logic gates. Like a
classical computer, a quantum computer also has bits and gates.
Instead of using logical ones and zeroes, a quantum bit ("qubit")
uses quantum mechanics to occupy both possibilities simultaneously.
This ability and other uniquely quantum mechanical features enable
a quantum computer can solve certain problems exponentially faster
than that of a classical computer.
[0003] Quantum annealing is an alternate computing methodology that
uses quantum effects to solve optimization problems. Quantum
annealing operates by initializing qubits into a quantum-mechanical
superposition of all possible qubit states, referred to as
candidate states, with equal probability amplitudes. This is
implemented by applying a strong transverse field Hamiltonian to
the qubits. The computer then evolves following the time-dependent
Schrodinger equation as the transverse field Hamiltonian is
decreased and the problem Hamiltonian is turned on. In some
variants of quantum annealing a driver Hamiltonian is applied at
intermediate times. During this evolution, the probability
amplitudes of all candidate states keep changing, realizing quantum
parallelism. If the rates of change of the Hamiltonians are slow
enough, the system stays close to the ground state of the
instantaneous Hamiltonian. At the end of the evolution the
transverse field is off, and the system is expected to have reached
a ground or other lower energy state of the problem Hamiltonian,
with high probability. The problem Hamiltonian typically encodes
the solution of a constraint satisfaction or other optimization
problem as the ground state of an associated Ising model. Thus, at
the end of the evolution, the quantum annealing computing system
generates the solution or an approximate solution to the target
optimization problem.
SUMMARY OF THE INVENTION
[0004] In accordance with an aspect of the present invention, a ZZZ
coupler assembly is provided for coupling first, second, and third
qubits. A first tunable coupler is coupled to the first qubit and
tunable via a first control signal. A second tunable coupler is
coupled to the first tunable coupler to direct a flux of the first
qubit into a tuning loop of the second tunable coupler, such that
when a first coupling strength associated with the first tunable
coupler is non-zero, a second coupling strength, associated with
the second tunable coupler, is a function of a second control
signal applied to the second tunable coupler and a state of the
first qubit. The second qubit and the third qubit are coupled to
one another through the second tunable coupler, such that, when the
second coupling strength is non-zero, it is energetically favorable
for the states of the first and second qubits to assume a specific
relationship with respect to the Z-axis.
[0005] In accordance with another aspect of the present invention,
a method is provides a ZZZ coupling among three qubits. A first
qubit of the three qubits is coupled to a second qubit of the three
qubits via a first tunable coupler utilizing galvanic Josephson
mutual inductance. The second qubit is coupled to a third qubit of
the three qubits via a second tunable coupler utilizing galvanic
Josephson mutual inductance. The third qubit is coupled to the
first qubit via a third tunable coupler utilizing galvanic
Josephson mutual inductance. The first qubit is coupled to the
second tunable coupler via a fourth tunable coupler such that a
flux from the first qubit is directed into a tuning loop of the
second tunable coupler. The second qubit is coupled to the third
tunable coupler via a fifth tunable coupler such that a flux from
the second qubit is directed into a tuning loop of the third
tunable coupler. The third qubit is coupled to the first tunable
coupler via a sixth tunable coupler such that a flux from the third
qubit is directed into a tuning loop of the first tunable
coupler.
[0006] In accordance with yet another aspect of the present
invention, a quantum circuit assembly includes a first qubit, a
second qubit, a third qubit, and a first tunable coupler coupled to
the first qubit. A second tunable coupler is coupled to the first
tunable coupler such that a flux of the first qubit is directed
into the second tunable coupler. The second qubit and the third
qubit are coupled to one another through the second tunable coupler
via galvanic Josephson mutual inductance.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIG. 1 illustrates one example of a system comprising three
coupled superconducting qubits;
[0008] FIG. 2 illustrates one example of quantum circuit employing
a ZZZ coupler assembly to couple a first qubit, a second qubit, and
a third qubit in accordance with an aspect of the present
invention;
[0009] FIG. 3 is a chart illustrating, for the circuit of FIG. 2, a
strength of a ZZ coupling between the second and third qubits
provided by the second tunable coupler, represented in gigahertz,
as a function of the flux applied to the tuning circuit,
represented in thousandths of the flux quantum (m.PHI..sub.0);
[0010] FIG. 4 is a chart illustrating, for the circuit of FIG. 2, a
strength of a ZZZ coupling among the first, second, and third
qubits provided by the coupler assembly, represented in gigahertz,
as a function of the first applied flux and the second applied
flux, represented in thousandths of the flux quantum
(m.PHI..sub.0);
[0011] FIG. 5 illustrates one example of quantum circuit comprising
three qubits coupled via a galvanic coupler assembly that allows
for arbitrary ZZZ and pairwise ZZ couplings; and
[0012] FIG. 6 illustrates one method for providing a ZZZ coupling
among three qubits.
DETAILED DESCRIPTION
[0013] The ZZZ coupler described herein is intended for use in a
quantum computing environment, in which information is stored and
manipulated in superconducting qubits. A physical implementation of
a qubit can be a Josephson junction, a quantum dot, a SQUID
(superconducting quantum interference device), a Cooper pair box,
or an ion trap. Further, unless specified, the coupling of two
elements may be accomplished according to the invention using any
of various means of physical coupling, for example, a mechanical
coupling by means of an electrical conductor, capacitive coupling,
inductive coupling, magnetic coupling, nuclear coupling, and
optical coupling, or any combination of the foregoing. As used
herein, a "classical control" indicates a device that behaves
generally according to the laws of classical physics that provides
a control signal to a quantum element, such as a qubit or
coupler.
[0014] The systems and methods herein provide arbitrary coupling
among three superconducting qubits, as well as any pair of the
three qubits, along a Z-basis. A ZZ coupling between two qubits
makes it energetically favorable for the states of the first and
second qubits to assume a specific relationship with respect to the
Z-axis of the Bloch sphere, both pointing either in the +Z
direction or both in the -Z direction. Similarly, a ZZZ coupling
among three qubits makes it energetically favorable for the states
of all three qubits to align in the same direction along the
Z-axis, all pointing either in the +Z direction or all pointing in
the -Z direction. Each axis corresponds to a specific quantum state
defined on the Bloch sphere of the qubit. It will be appreciated
that the coupling can be positive or negative, with a negative ZZ
coupling making it energetically favorable for the states of the
first and second qubits to align in the same direction along the
Z-axis, both pointing either in the +Z direction or both in the -Z
direction. A positive ZZ coupling, denoted as +ZZ, making it
energetically favorable for the states of the first and second
qubits to align in different directions along the Z-axis.
[0015] Most particle interactions found in nature are two body in
character. When three body terms exist, they tend to be weak in
comparison to two body interactions. This disclosure describes a
device that solves both of these challenges generating a strong,
tunable, three body ZZZ interactions between flux qubits, as well
as independently tunable two body ZZ interactions, including the
case where two body interactions are zero. Specifically, the
inventors have designed a circuit utilizing a novel coupling method
that generates a three qubit interaction by modulating the strength
of a qubit-qubit interaction based on the state of a third qubit.
In one implementation, compatible with high coherence flux qubits,
the circuit utilizes an inventive galvanic Josephson coupling
between qubits where Josephson junctions provide the mutual
inductance.
[0016] FIG. 1 illustrates one example of a system 10 comprising
three coupled superconducting qubits 12-14. The system includes a
first coupler 16 that couples a first qubit 12 to a second coupler
18, such that a flux produced by the first qubit is directed into a
tuning loop of the second coupler. The first coupler 16 can be
selected to be tunable, such a coupling strength and sign (e.g.,
positive or negative) can be tuned via a control signal provided by
a first classical control 26. It will be appreciated that the
control signal can be selected such that the coupling strength of
the first coupler 16 is zero, and thus no flux from the first qubit
is directed to the second coupler 18. In one implementation, the
first coupler 16 is a split junction tunable coupler, and the
interaction strength between qubits is controlled by an amount of
tuning flux, provided by the first classical control 26, that
threads the tunable junction.
[0017] The second coupler 18 couples the second qubit 13 to the
third qubit 14. Like the first coupler 16, the second coupler 18
can be selected to be tunable, such that a coupling strength and
sign can be tuned via a control signal provided by a second
classical control 28. Accordingly, when the first coupler 16 is
tuned to provide a non-zero coupling, a coupling strength of the
second coupler 18 is a function of the control signal provided by
the second classical control 28 and the state of the first qubit
12. In one implementation, the second coupler 18 is a split
junction tunable coupler, and the interaction strength between
qubits is controlled by an amount of tuning flux, provided by the
second classical control 28, that threads the tunable junction, as
well as an amount of flux from the first qubit 12 directed into the
second coupler by the first coupler 16.
[0018] In one implementation, the second qubit 13 and the third
qubit 14 are coupled through the second coupler 18, with each qubit
coupled to the second coupler via a galvanic Josephson mutual
inductance. Optimizing the strength of ZZZ coupling is important
for successful device operation since the energy scale of the
coupling often needs to be greater than other energies or
frequencies in the problem such as the energy associated with the
achievable base temperature of the experiment. Further, it is
helpful for the coupler to be compatible with highly coherent flux
qubits which typically utilize junctions with small critical
current to minimize dephasing from flux noise. The high coherence
facilitates quantum effects. The small critical current limit
places important restrictions on inductive elements that are part
of qubit-qubit tunable couplers. These constraints are derived from
the relationship between junction critical current, I.sub.C, and
the effective Josephson inductance of a junction
L.sub.J=.PHI..sub.0/2.pi.I.sub.C, where .PHI..sub.0/2.pi..about.330
nA nH.
[0019] For instance, for an I.sub.C.about.50 nA junction, the
Josephson inductance is .about.6.6 nH. To generate a strong
coupling via inductive coupling, the mutual inductance between
coupled qubits should be a significant fraction of this value.
Often mutual inductances, including all geometric mutuals, are
generated with linear inductances. To understand the challenges
involved with generating such a large inductance with linear
inductors, consider that to generate an L.sub.J.about.6.6 nH
inductance with a Z=50 Ohm metal trace and propagation speed
v.about.c/3, where c is the speed of light in a vacuum, requires a
trace length L.sub.jv/Z which is longer than one centimeter. This
presents a technical challenge since geometric couplers would need
to be quite large relative to the rest of the circuit, and stray
capacitance could limit achievable inductance at relevant
frequencies. The inventors have found that the use of galvanic
coupling overcomes many of these challenges.
[0020] FIG. 2 illustrates one example of quantum circuit 50
employing a ZZZ coupler assembly 60 to couple a first qubit 72, a
second qubit 74, and a third qubit 76 in accordance with an aspect
of the present invention. The coupler assembly 60 includes a first
tunable coupler 62, including a first tuning loop 66, and a second
tunable coupler 64, including a second tuning loop 68. In the
illustrated implementation, each of the first and second tuning
loops 66 and 68 are compound Josephson junctions, formed as
superconducting loops interrupted by two Josephson junctions. The
first tunable coupler 62 directs flux from the first qubit 72 into
the second tunable coupler 64. The second tunable coupler 64
couples the second qubit 74 to the third qubit 76 in the Z basis,
with each qubit 74 and 76 coupled to the second tunable coupler via
a galvanic Josephson mutual inductance. Accordingly, when a
coupling strength of the second tunable coupler is non-zero, it is
energetically favorable for the states of the first and second
qubits to assume a specific relationship with respect to the
Z-axis. In the illustrated implementation, the flux from the first
qubit 72 is provided inductively through at least one pair of
inductive elements 69 bridging the first tunable coupler 62 and the
tuning loop 68 of the second tunable coupler 64.
[0021] In the illustrated implementation, each of the first qubit
72, the second qubit 74, and the third qubit 76 are implemented as
four junction flux qubits, with first and second junctions of each
qubit 72, 74, and 76 forming a compound junction 82, 84, and 86 for
biasing the flux qubits. A third and fourth junction 91-94 complete
the flux qubit loops, with junctions 92 and 94 forming the galvanic
Josephson mutual inductance shared by qubits 74 and 76,
respectively, with the tunable coupler 68. A flux qubit, in general
terms, is a superconducting loop interrupted by some number of
Josephson junctions. While a biasing element is not illustrated in
the simplified example of FIG. 2, in general operation, a flux
qubit is biased by a flux, generally described in units of the
superconducting flux quantum .PHI..sub.0. When the applied bias
flux in loops 82, 84, or 86 is near one flux quantum and for
suitable device parameters, the potential energy of the system
exhibits two minima, one corresponding to clockwise and the other
to counterclockwise current flow in the superconducting loop. The
two possible directions of current flow represent the lowest energy
quantum states of the system. While it is also possible to have a
single potential well even at a flux quantum of bias flux, the
double-well regime described here highlights the unique capability
of the inventive coupler to function even with energetically
degenerate states. It will be appreciated that the coupling
assembly 60 can also be used for generating three body inductive
coupling between Transmon qubits. In this case the strength of
three body interaction term is reduced due to the lower RMS current
compared to the static currents in the flux regime.
[0022] The inductive potential of the full circuit can be modelled,
with suitable generalization for mutual inductances, using
-.PHI..sub.0I.sub.C/2.pi. cos .theta. for each junction and
(1/2L)(.PHI..sub.0/2.pi.).sup.2.theta..sup.2 for each inductor,
where .theta. is the gauge invariant phase across the circuit
element. When the flux qubits are tuned to the harmonic oscillator,
or single well, regime, the potential shows a single minimum. When
the flux qubits are tuned to the flux, or double well, regime, and
all the couplings are off, the potential shows eight degenerate
minimums corresponding to the eight qubit states. The energy of
each minimum can be given a label U.sub.abc where, a represents a
state of the first qubit 72, b represents a state of the second
qubit 74, and c represents a state of the third qubit 76, such that
U.sub.010 is the minimum energy of the well corresponding to the
qubit state 010. Tuning either coupler 62 or 64, to a non-zero
coupling strength adjusts the energy of each minimum. For a
Hamiltonian of the form H/h=-g.sub.123ZZZ the value of g.sub.123,
determines the ZZZ coupling energy. Here, his Plank's constant,
which relates coupling energies and coupling frequencies. When the
qubits are in the flux regime the value of g.sub.123 can be
calculated as .SIGMA..sub.abcz(a)z(b)z(c)U.sub.abc/8 where z(0)=1
and z(1)=-1. The ZZ energy between the second qubit 74 and the
third qubit 76 can be calculated as
.SIGMA..sub.abcz(b)z(c)U.sub.abc/8. This method accurately
determines the energy scales of the lowest eigenstates of the
corresponding quantum Hamiltonian as long the control fluxes stay
within an MRT (macroscopic resonant tunneling) spacing, that is, as
long as the difference in energy between potential wells stays
below the local harmonic energy of each well. This depends on the
qubit's shunt capacitance in addition to the inductive
potential.
[0023] By utilizing compound Josephson junction coupling
techniques, the coupler assembly 60 does not bias individual
qubits, that is, no single qubit Z terms are generated in the
Hamiltonian of the system by the assembly. This invention can be
configured to utilize multiple operating points by altering a first
applied flux, .PHI..sub.1, provided to the first tuning loop 66,
and a second applied flux, .PHI..sub.2, provided to the second
tuning loop 68. These fluxes can be adjusted to separately control
the ZZ coupling provided by the second tunable coupler 64 as well
as the ZZZ coupling provided by the assembly 60 through the first
tunable coupler 62. For example, the fluxes can be provided such
that both the ZZ and ZZZ couplings are inactive. In this instance,
example values for the two applied fluxes could include
(.PHI..sub.1,.PHI..sub.2)=(0.5,0.5).PHI..sub.0. To activate the ZZ
coupling, with an arbitrary sign, without the ZZZ coupling, values
of (.PHI..sub.1,.PHI..sub.2)=(0.5,0.5.+-.0.5).PHI..sub.0 could be
used. It will be appreciated that the value of the second applied
flux will vary across the range given depending on a desired
strength and sign of the coupling. When the flux is provided to
avoid the ZZZ coupling, a Hamiltonian of the system would not
include a ZZZ term. To activate the ZZZ coupling, with an arbitrary
sign, without the ZZ coupling, the applied flux values could
include (.PHI..sub.1,.PHI..sub.2)=(0,.+-.0.5).PHI..sub.0. In this
case, a Hamiltonian of the system would not contain a term
representing the ZZ coupling between the second qubit 74 and the
third qubit 76, although it would contain a term representing the
ZZZ coupling. Finally, to provide ZZ coupling and ZZZ coupling,
values including
(.PHI..sub.1,.PHI..sub.2)=(0,.+-.0.5.+-.0.2).PHI..sub.0 can be
used.
[0024] FIG. 3 is a chart 100 illustrating, for the circuit of FIG.
2, a strength of a ZZ coupling between the second and third qubits
74 and 76 provided by the second tunable coupler 64, represented in
gigahertz, as a function of the flux applied to the tuning circuit
68, represented in thousandths of the flux quantum (m.PHI..sub.0).
In this example, it is assumed that the Josephson junctions in the
compound junctions 82, 84, and 86 of the flux qubits 72, 74, and 76
have critical currents of thirty-five nanoamps, the other Josephson
junctions in the qubits have critical currents of seventy nanoamps,
and the junctions in the two couplers 62 and 64 have critical
currents of twenty-five nanoamps. The inductive elements 62 each
have an inductance of one hundred and fifty picohenry, with the
efficiency of the mutual inductance being 0.5. The coupling
strength is represented on the vertical axis 102, while the applied
flux is represented on the horizontal axis 104. As can be seen from
the chart 100, the coupling strength is at a minimum when the
applied flux is near (1000*n+500)m.PHI..sub.0, where n is an
integer. A maximum positive coupling is achieved when the applied
flux is near 2000n m.PHI..sub.0, and a maximum negative coupling is
achieved when the applied flux is near (2000n+1000) m.PHI..sub.0.
Values between these extremes can be selected to tune the coupling
strength to a desired magnitude and sign. One of ordinary skill in
the art will recognize that fabrication variation of the critical
currents will slightly alter the flux values where zero couplings
occur.
[0025] FIG. 4 is a chart 150 illustrating, for the circuit of FIG.
2, a strength of a ZZZ coupling among the first, second, and third
qubits 72, 74, and 76 provided by the coupler assembly 60,
represented in gigahertz, as a function of the first applied flux
and the second applied flux, represented in thousandths of the flux
quantum (m.PHI..sub.0). In this chart, the parameters for the
circuit, such as the bias to the qubits 72, 74, and 76 and the
critical currents of the various Josephson junctions, are selected
such that the ZZ coupling energy is independent of the first
applied flux. As with FIG. 3, it is assumed in this example that
the Josephson junctions in the compound junctions 82, 84, and 86 of
the flux qubits 72, 74, and 76 have critical currents of
thirty-five nanoamps, the other Josephson junctions in the qubits
have critical currents of seventy nanoamps, and the junctions in
the two couplers 62 and 64 have critical currents of twenty-five
nanoamps. The inductive elements 62 each have an inductance of one
hundred and fifty picohenry, with the efficiency of the mutual
inductance being 0.5. The coupling strength is represented on the
vertical axis 152, while the second applied flux is represented on
the horizontal axis 154.
[0026] The value of the first applied flux is represented by the
individual plots 161-171, with each plot representing the ZZZ
coupling strength for a different value of the first applied flux.
A first plot 161 represents the ZZZ coupling strength when the
first applied flux is zero. A second plot 162 represents the ZZZ
coupling strength when the first applied flux is equal to one-tenth
of the flux quantum. A third plot 163 represents the ZZZ coupling
strength when the first applied flux is equal to one-fifth of the
flux quantum. A fourth plot 164 represents the ZZZ coupling
strength when the first applied flux is equal to three-tenths of
the flux quantum. A fifth plot 165 represents the ZZZ coupling
strength when the first applied flux is equal to two-fifths of the
flux quantum. A sixth plot 166 represents the ZZZ coupling strength
when the first applied flux is equal to one-half of the flux
quantum. As can be seen from the chart 150, when the first applied
flux is equal to one-half of the flux quantum, no ZZZ coupling is
present, regardless of the value of the second applied flux.
Further, it will be appreciated that the magnitude and sign of the
ZZZ coupling can be selected by tuning the values for the first and
second applied flux.
[0027] A seventh plot 167 represents the ZZZ coupling strength when
the first applied flux is equal to three-fifths of the flux
quantum. An eighth plot 168 represents the ZZZ coupling strength
when the first applied flux is equal to seven-tenths of the flux
quantum. A ninth plot 169 represents the ZZZ coupling strength when
the first applied flux is equal to four-fifths of the flux quantum.
A tenth plot 170 represents the ZZZ coupling strength when the
first applied flux is equal to nine-tenths of the flux quantum. An
eleventh plot 171 represents the ZZZ coupling strength when the
first applied flux is equal to the flux quantum. It will be
appreciated that this provides a maximum value for the ZZZ coupling
strength.
[0028] FIG. 5 illustrates one example of quantum circuit 200
comprising three qubits 202, 204, and 206 coupled via a galvanic
coupler assembly 210 that allows for arbitrary pairwise couplings.
Compared to the circuit of FIG. 2, the illustrated circuit 200
increases the ZZZ coupling energy by a factor of three and
symmetrizes the design for robustness. In the circuit, the first
qubit 202 and the second qubit 204 are coupled via a galvanic
Josephson mutual inductance through a first tunable coupler 212,
the second qubit and the third qubit 206 are coupled via a galvanic
Josephson mutual inductance through a second tunable coupler 214,
and the first qubit and the third qubit are coupled via a galvanic
Josephson mutual inductance through a third tunable coupler 216.
For the purpose of this example, each of the first tunable coupler
212, the second tunable coupler 214, and the third tunable coupler
216 can be assumed to be substantially equivalent in structure and
function to the second tunable coupler 64 of FIG. 2.
[0029] Each of the first, second, and third qubits 202, 204, and
206 are also coupled, respectively, to the second tunable coupler
212, the third tunable coupler 216, and the first tunable coupler
212 such that flux from the qubits is directed into a tuning loop
of their respective coupler to facilitate the ZZZ interactions
among the qubits. Specifically, the first qubit 202 is coupled to
the second tunable coupler 214 through a fourth tunable coupler
222, the second qubit 204 is coupled to the third tunable coupler
216 through a fifth tunable coupler 224, and the third qubit 206 is
coupled to the first tunable coupler 212 through the sixth tunable
coupler 226. For the purpose of this example, each of the fourth
tunable coupler 222, the fifth tunable coupler 224, and the sixth
tunable coupler 226 can be assumed to be substantially equivalent
in structure and function to the first tunable coupler 62 of FIG.
2.
[0030] The illustrated galvanic coupler 210 allows high coherence,
low critical current flux qubits to be coupled with a ZZZ coupling
strength that can be ten times larger than the energy scale set by
the base temperature of commercial dilution refrigerators, which is
currently .about.10 k.sub.B mK, where kB is Boltzmann's constant,
even with ZZ coupling strength tuned to zero. ZZZ couplings are
helpful for natively generating exculsive or Boolean satisfiability
(XOR-3SAT) problem Hamiltonians for quantum annealers, for
generating coupling Hamiltonians for primitive
controlled-controlled-phase gates, implementing Hamiltonian
operators needed for building encoded qubits from physical qubits,
and implementing logical operations on distance three encoded
qubits. These couplings need to be large compared to the device
temperature in annealing and encoding applications, and larger than
.about.h/GateTime for gate or logical applications where the
operations need to occur in GateTime or faster, where h is Plank's
constant. To take advantage of quantum effects the coupling scheme
needs to be compatible with high coherence, low critical current
flux qubits.
[0031] The coupler of the present invention can generate arbitrary
two and three body terms, allowing the circuit to encode the more
general three satisfiability problem (3SAT) problems. 3SAT is the
canonical NP-complete constraint satisfaction problem. To see that
the circuit 200 is sufficient to natively encode local 3SAT
instances, consider first a single three bit clause function f(a,
b, c) that takes the value 1 when the clause is true and 0 when the
clause is false. If one now considers a set of clause functions
{f.sub.i} that comprise a MAX3SAT instance, then finding the
variables that maximizes the number of satisfied clauses is
equivalent to minimizing the cost function -.SIGMA..sub.if.sub.i.
Now consider the three qubit operator F=.SIGMA..sub.abcf(a, b,
c)|abc><abc| derived from the clause function f. Since the
operator is diagonal in the Z-basis it can be decomposed as
F=g.sub.0III+g.sub.1ZII+g.sub.2IZI+g.sub.3IIZ+g.sub.12ZZI+g.sub.13ZIZ+g.s-
ub.23IZZ+g.sub.123ZZZ, where Z is the Pauli Z operator and I the
identity. After including necessary controls for single qubit bias
fields, the circuit 200 can simultaneously generate all required
couplings to implement the cost function operator
-.SIGMA..sub.iF.sub.i and thus can natively encode the local 3SAT
instance. Finding the global minimum of the cost function not only
solves the associated satifiability problem, but the more general
problem of finding the maximum number of satisfiable clauses
(MAX-SAT). The locality constraint reduces the number 3SAT
instances that can be natively solved using the present invention,
however, MAX-XOR-3SAT remains NP-hard even when restricted to local
(bounded-degree) planer hypergraphs. Given sufficient precision of
the bias fields, the circuit can natively encode more general
weighted MAX-3SAT constraint satisfaction problems.
[0032] In view of the foregoing structural and functional features
described above in FIGS. 1-5, an example method will be better
appreciated with reference to FIG. 6. While, for purposes of
simplicity of explanation, the method of FIG. 6 is shown and
described as executing serially, it is to be understood and
appreciated that the present invention is not limited by the
illustrated order, as some actions could in other examples occur in
different orders and/or concurrently from that shown and described
herein.
[0033] FIG. 6 illustrates one method 250 for providing a ZZZ
coupling among three qubits. At 252, a first qubit of the three
qubits is coupled to a second qubit of the three qubits via a first
tunable coupler utilizing galvanic Josephson mutual inductance. It
will be appreciated that the first tunable coupler can share one or
more Josephson junctions with the first and second qubits to
facilitate the galvanic coupling. At 254, the second qubit is
coupled to a third qubit of the three qubits via a second tunable
coupler utilizing galvanic Josephson mutual inductance. At 256, the
third qubit is coupled to the first qubit via a third tunable
coupler utilizing galvanic Josephson mutual inductance.
[0034] At 258, the first qubit is coupled to the second tunable
coupler via a fourth tunable coupler such that a flux from the
first qubit is directed into a tuning loop of the second tunable
coupler. Accordingly, a state of the first qubit can influence the
coupling strength of the second tunable coupler. At 260, the second
qubit is coupled to the third tunable coupler via a fifth tunable
coupler such that a flux from the second qubit is directed into a
tuning loop of the third tunable coupler. At 262, the third qubit
is coupled to the first tunable coupler via a sixth tunable coupler
such that a flux from the third qubit is directed into a tuning
loop of the first tunable coupler. The resulting circuit allows for
ZZZ coupling among the circuits having a sign and coupling strength
tunable via control signals provided to the tunable couplers, as
well as arbitrary ZZ couplings among the three qubits.
[0035] What have been described above are examples of the present
invention. It is, of course, not possible to describe every
conceivable combination of components or methodologies for purposes
of describing the present invention, but one of ordinary skill in
the art will recognize that many further combinations and
permutations of the present invention are possible. Accordingly,
the present invention is intended to embrace all such alterations,
modifications, and variations that fall within the scope of the
appended claims.
* * * * *