U.S. patent application number 13/606778 was filed with the patent office on 2012-12-27 for modular array of fixed-coupling quantum systems for quantum information processing.
This patent application is currently assigned to INTERNATIONAL BUSINESS MACHINES CORPORATION. Invention is credited to Jay M. Gambetta, Mark B. Ketchen, Chad T. Rigetti, Matthias Steffen.
Application Number | 20120326720 13/606778 |
Document ID | / |
Family ID | 47352966 |
Filed Date | 2012-12-27 |
![](/patent/app/20120326720/US20120326720A1-20121227-D00000.png)
![](/patent/app/20120326720/US20120326720A1-20121227-D00001.png)
![](/patent/app/20120326720/US20120326720A1-20121227-D00002.png)
![](/patent/app/20120326720/US20120326720A1-20121227-D00003.png)
![](/patent/app/20120326720/US20120326720A1-20121227-D00004.png)
United States Patent
Application |
20120326720 |
Kind Code |
A1 |
Gambetta; Jay M. ; et
al. |
December 27, 2012 |
MODULAR ARRAY OF FIXED-COUPLING QUANTUM SYSTEMS FOR QUANTUM
INFORMATION PROCESSING
Abstract
A quantum information processing system includes a first
composite quantum system, a second composite quantum system, a
plurality of electromagnetic field sources coupled to the system
and an adjustable electromagnetic coupling between the first
composite quantum system and the second composite quantum
system.
Inventors: |
Gambetta; Jay M.; (Yorktown
Heights, NY) ; Ketchen; Mark B.; (Hadley, MA)
; Rigetti; Chad T.; (Hopewell Junction, NY) ;
Steffen; Matthias; (Cortlandt Manor, NY) |
Assignee: |
INTERNATIONAL BUSINESS MACHINES
CORPORATION
Armonk
NY
|
Family ID: |
47352966 |
Appl. No.: |
13/606778 |
Filed: |
September 7, 2012 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13224768 |
Sep 2, 2011 |
|
|
|
13606778 |
|
|
|
|
61497018 |
Jun 14, 2011 |
|
|
|
Current U.S.
Class: |
324/307 |
Current CPC
Class: |
G06N 10/00 20190101;
H01L 39/04 20130101; B82Y 10/00 20130101; H01L 39/045 20130101 |
Class at
Publication: |
324/307 |
International
Class: |
G01R 33/44 20060101
G01R033/44 |
Claims
1. A quantum computing method, comprising applying an
electromagnetic field to a plurality of qubits arranged in a
waveguide cavity; adjusting the electromagnetic field to generate a
quantum state in each qubit of the plurality of qubits; and
adjusting the electromagnetic field to couple each qubit of the
plurality of qubits to one another.
2. The method as claimed in claim 1 further comprising measuring
the quantum state of each qubit of the plurality of qubits.
3. A quantum computing method, comprising: generating a first
electromagnetic field in a first housing having a first plurality
of qubits; generating an second electromagnetic field in a second
housing having a second plurality of qubits; and generating a third
electromagnetic field between the first housing and the second
housing to couple the first plurality of qubits to the second
plurality of qubits.
4. The method as claimed in claim 3 further comprising: adjusting
the first electromagnetic field to generate a quantum flux in each
qubit of the first plurality of qubits; and measuring the quantum
flux of each qubit of the first plurality of qubits.
5. The method as claimed in claim 4 further comprising: adjusting
the second electromagnetic field to generate a quantum flux in each
qubit of the second plurality of qubits; and measuring the quantum
flux of each qubit of the second plurality of qubits.
6. The method as claimed in claim 3 further comprising tuning the
third electromagnetic field to adjust coupling between the first
plurality of qubits and the second plurality of qubits.
7. The method as claimed in claim 6 further comprising: adjusting
the first electromagnetic field to adjust coupling between each
qubit of the first plurality of qubits.
8. The method as claimed in claim 5 further comprising: adjusting
the second electromagnetic field to adjust coupling between each
qubit of the second plurality of qubits.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 13/224,768, filed Sep. 2, 2011, which claims
priority to U.S. Provisional Patent Application Ser. No.
61/497,018, filed Jun. 14, 2011, and entitled, "ARRAY OF THREE
DIMENSIONAL SUPERCONDUCTING QUBIT/CAVITY CLUSTERS FOR QUANTUM
COMPUTING", the disclosure of which is incorporated by reference
herein in its entirety.
BACKGROUND
[0002] The present invention relates to quantum information
processing, and more specifically, to a modular design for quantum
information processing hardware based on an array of clusters of
quantum systems.
[0003] Quantum information processing is a new paradigm of
information processing where information is stored and processed
with systems obeying the laws of quantum mechanics rather than
classical mechanics. Such computers have been theoretically shown
to be capable of solving important problems using exponentially
fewer computational resources (e.g. operations, memory elements)
than classical computers. As such, quantum physics provides a basis
for achieving computational power to address certain categories of
problems that are intractable with current machine computation.
[0004] By analogy with classical bits, the fundamental unit of
quantum information is called the quantum bit, or qubit. In order
to realize quantum information processing tasks, one must develop
and implement a physical instantiation of a plurality of quantum
bits. These physical instantiations are likewise referred to as
quantum bits or qubits. The term `qubit` is thus used in reference
to the physical system realizing the instantiation and the unit of
quantum information stored therein.
[0005] The physical quantum mechanical system realizing the
instantiation of a qubit must possess at least two distinct and
distinguishable eigenstates in order to represent at least two
logic states. Instantiations where the number of distinct and
distinguishable eigenstates is greater than two can be likewise
used. These additional eigenstates may be explicitly used to
represent additional logic states, or otherwise made use of for an
information processing task. Specifically, additional eigenstates
may be exploited to facilitate measurement of the two eigenstates
encoding the two logic states; or to facilitate transformations of
the Hilbert space associated to the two eigenstates encoding the
two logic states.
[0006] Several physical systems and fields of physics have been
proposed as potential frameworks and development grounds for
quantum information processing. These include, but are not limited
to: solid state nuclear spins, measured and controlled
electronically or with nuclear magnetic resonance, trapped ions,
atoms in optical cavities (cavity quantum-electrodynamics), liquid
state nuclear spins, electronic charge or spin degrees of freedom
in quantum dots, superconducting quantum circuits based on
Josephson junctions and electrons on Helium.
[0007] Currently the most active areas of research towards quantum
computing are superconducting qubits, trapped ions, trapped atoms,
and quantum dots. The largest quantum computer built in any of
these systems to date consists of around 10-16 qubits, and most
implementations are focused on the demonstration of a specific
quantum algorithm or quantum state.
[0008] The requirements for building a large-scale quantum computer
are more intricate than quantum mechanical properties such as
superposition and entanglement alone. There is a set of
requirements that must be fulfilled in order to build a practical
quantum computer. One requirement is to have a system of qubits
that can be initialized to a known state. Another requirement is
the ability to manipulate this state by applying single and
multi-qubit gate operations such that any arbitrary logic operation
can be implemented. Finally, the outcome of the computation must be
measured through known techniques. In addition, for a quantum
system to retain the delicately created superposition and entangled
states for sufficiently long times (i.e., coherence times) it must
be well isolated from the environment. However, in order to
manipulate the quantum system according to the steps of the desired
algorithm it must inherently also be coupled to the external
environment thereby introducing noise mechanisms that reduce
coherence times.
SUMMARY
[0009] Exemplary embodiments include a quantum information
processing system including a first composite quantum system, a
second composite quantum system, a plurality of electromagnetic
field sources coupled to the system and an adjustable
electromagnetic coupling between the first composite quantum system
and the second composite quantum system.
[0010] Additional exemplary embodiments include a modular computing
system, including a first qubit cluster, a second qubit cluster and
a tunable coupler disposed between and coupling the first qubit
cluster and second qubit cluster.
[0011] Additional exemplary embodiments include a quantum computing
system, including a first qubit cluster having a first interaction
strength, a second qubit cluster having a second interaction
strength and a subcircuit disposed between the first qubit cluster
and the second qubit cluster and configured to tune the first and
second interaction strengths.
[0012] Additional exemplary embodiments include a quantum computing
method, including applying an electromagnetic field to a plurality
of qubits arranged in a waveguide cavity or any suitable quantum
bus, adjusting the electromagnetic field to generate a quantum
state in each qubit of the plurality of qubits and adjusting the
electromagnetic field to couple each qubit of the plurality of
qubits to one another.
[0013] Further exemplary embodiments include a quantum computing
method, including generating a first electromagnetic field in a
first housing having a first plurality of qubits, generating an
second electromagnetic field in a second housing having a second
plurality of qubits and generating a third electromagnetic field
between the first housing and the second housing to couple the
first plurality of qubits to the second plurality of qubits.
[0014] Additional features and advantages are realized through the
techniques of the present invention. Other embodiments and aspects
of the invention are described in detail herein and are considered
a part of the claimed invention. For a better understanding of the
invention with the advantages and the features, refer to the
description and to the drawings.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0015] The subject matter which is regarded as the invention is
particularly pointed out and distinctly claimed in the claims at
the conclusion of the specification. The forgoing and other
features, and advantages of the invention are apparent from the
following detailed description taken in conjunction with the
accompanying drawings in which:
[0016] FIG. 1 illustrates an example of an exemplary three
dimensional qubit cluster apparatus;
[0017] FIG. 2 illustrates an exemplary two-dimensional lattice
multi-qubit system of multiple three dimensional qubit cluster
apparatuses;
[0018] FIG. 3 illustrates an exemplary three-dimensional lattice
multi-qubit system of multiple three-dimensional qubit cluster
apparatuses; and
[0019] FIG. 4 illustrates a flow chart of a method for a quantum
computing method in accordance with exemplary embodiments.
DETAILED DESCRIPTION
[0020] The systems and methods described herein implement large
collections (e.g., on the order of thousands and more) of coupled
qubits in a modular system that can be modified, tested,
characterized, assessed and operated as a smaller system. Each
smaller subsystem can be localized and isolated from the remainder
of the system for these purposes. Additional subsystems can be
added to or removed from the full system without affecting the
performance of the preponderance of the subsystems making up the
full system. The systems and methods described herein are a
framework for the construction, assembly, testing,
characterization, assessment, and operation of a modular quantum
computer.
[0021] In exemplary embodiments, the systems and methods described
herein relate to a modular design for a quantum information
processing system wherein the physical instantiations of qubits are
arranged into two levels of physical organization and structure.
These two levels are termed `cluster` and `array`.
[0022] The first level of structure is a `cluster`. In exemplary
embodiments, qubits are grouped into small clusters of
approximately one to twenty qubits. Each qubit in a cluster is
coupled, electromagnetically or otherwise, to at least one other
qubit in the cluster. This coupling is enacted through a physical
or electromagnetic structure or mechanism embedded within, near to,
or serving as the housing of the cluster. In this way each cluster
is imbued with qubit-qubit interactions between pairs of qubits
comprising the cluster. Each cluster therefore forms a composite
quantum system.
[0023] In exemplary embodiments, the systems and methods described
herein implement tunable and adjustable elements: the structure
mediating the intra-cluster qubit-qubit coupling is considered to
be fixed on the time scale set by the coherent lifetime of a qubit
within the cluster. Because tunability requires the coupling to the
cluster of external field sources, the use of only fixed
intra-cluster couplings during a computation allows the
construction and operation of qubit clusters with only minimal
connections to the external electromagnetic environment.
[0024] In this way, each cluster is predominantly
electromagnetically isolated from the electromagnetic environment
and from all other clusters except for the specific purpose of
inducing interactions between clusters or for applying
electromagnetic fields via external sources for the purpose of
controlling, measuring or otherwise carrying out constituent
processes which build up to form a quantum information processing
task. Each cluster may therefore be regarded as an independent
composite quantum system.
[0025] In exemplary embodiments, a second level of structure is an
`array`. A plurality of clusters as described above are arranged
and connected to form an array of clusters. Each cluster is similar
to each other cluster with respect to the physical instantiation of
the qubits in the cluster. However, different clusters may have
different numbers of qubits (though always in the range described
above) and have slightly different or varying properties from one
to another.
[0026] Each cluster in the array is coupled to at least one other
cluster in the array through a physical or electromagnetic
structure or mechanism that is tunable or adjustable in a manner so
as to change the interaction strength between a qubit in one
cluster and a qubit in the neighboring cluster on a time scale much
faster than the typical coherent lifetime of qubits in two
connected clusters.
[0027] As each cluster in the array is materially similar to each
other cluster in the array, so each connection between a pair of
clusters in the array is materially similar to each other
connection between other pairs of clusters in the array.
[0028] When the mechanism controlling the interaction between two
clusters is set to the OFF position, the strengths of the
interactions between each of the qubits in the first cluster with
the qubits in the second cluster are weaker than the time scale
typical of the coherent lifetime of the qubits in the two connected
clusters. In this way the interactions between neighboring clusters
is such that when the interactions are set to the OFF position,
each cluster forms a composite quantum system that remains
independent of and isolated from the composite quantum system
formed be each other cluster in the array. Each cluster may be
characterized, tested, optimized and operated independent of each
other cluster. In this way the exemplary embodiments described
herein realize a modular quantum information processing system.
[0029] In exemplary embodiments, the systems and methods described
herein implements clusters of qubits that include classically
simulable number of quantum levels. Multiple clusters can be
coupled together to generate an array of clusters that can be used
for larger quantum computing applications. As described further
herein, an array includes multiple clusters and a mechanism (i.e.,
a tunable coupler) that connects and disconnects each cluster from
other clusters to which it is connected (i.e., neighboring clusters
in the array). Each of the clusters in the array can be isolated
from all other clusters for purposes of tune-up, test,
characterization, assessment and operation. Each array therefore
includes classically simulable (i.e., capable of being simulated on
a modern classical computer) subsystems, connected to one another
with a tunable coupler that effectively allows each subsystem to be
isolated from all other subsystems in the array. As such, a quantum
computer is built up and operated based upon the addition or
connection of additional subsystems to the array. The systems and
methods described herein also characterize, assess, and validate
the performance of the quantum computer piecewise, consistent with
classical computational limits to simulations of large quantum
systems. The arrays described herein are therefore modular physical
systems including clusters of qubits coupled to electromagnetic
field sources and tunable couplers connected to electromagnetic or
mechanical controls. The clusters of qubits each have fixed
interaction strengths coupled to one another by a subcircuit (e.g.,
the tunable coupler) that tunes interaction strengths between
clusters.
[0030] In exemplary embodiments, a quantum information processing
system can include a first composite quantum system (e.g., a first
qubit cluster), a second composite quantum system (e.g., a second
qubit cluster), electromagnetic field sources coupled to the system
and adjustable electromagnetic coupling between the first composite
quantum system and the second composite quantum system. The
composite quantum systems can each include a housing defining a
cavity, quantum systems disposed in the cavity and an
electromagnetic field source coupled to the cavity. Each of the
composite quantum systems is coupled to an electromagnetic field
source from the electromagnetic field source. In addition, the
electromagnetic field source is configured to produce
transformations or inhibit transformations of the quantum state of
the first and second composite quantum systems. The electromagnetic
field source is also configured to produce a projective quantum
measurement of part or all of the composite quantum system. In
exemplary embodiments, each of the first and second composite
quantum systems includes one or more measurable attributes
indicative of an aspect of the quantum state of the composite
quantum system. In addition, each of the first and second composite
quantum systems is coupled to an apparatus to facilitate
measurement of an attribute of the composite quantum system
indicative of the quantum state of the composite quantum system.
Furthermore, an evolution and measurement of the system implements
and executes at least one of a quantum information processing
algorithm, task, and protocol. In exemplary embodiments, the system
can include an electronic circuit disposed between the first
composite quantum system and the second composite quantum system,
thereby electromagnetically coupling the first system to the second
system. In addition, the first composite quantum system and the
second composite quantum system can be clusters of qubits, and the
electromagnetic field source is configured to generate one or more
quantum states in the clusters of qubits.
[0031] FIG. 1 illustrates an example of an exemplary qubit cluster
apparatus 100. The apparatus 100 includes a housing 105 with a
cavity 110 defined therein. The apparatus 100 can further include a
cluster of qubits 115 disposed within the cavity 110. As described
herein, an example of a superconducting Josephson junction is
described as each of the qubits 115. However, as described herein,
it is appreciated that any type of qubit can be implemented
including but not limited to quantum dots, electron or nuclear
spins or collections thereof. The apparatus 100 can further include
an external electromagnetic source 120 (e.g., a coaxial cable)
coupled to the housing 105 and providing an electromagnetic field
within the cavity 110. As such, it can be appreciated that the
housing 105 is an electromagnetic waveguide for the electromagnetic
field applied to the housing 105. The qubits 115 can be arranged in
a wide variety of ways within the cavity 110. The location and
orientation of a qubit within the cavity can affect how strongly
coupled it is to the cavity mode. Each qubit 115 can be viewed as a
dipole, with an associated dipole moment vector. The strength of
its interaction with the cavity 110 is determined predominantly by
the dot product of the dipole moment vector with the electric field
vector at the location of the qubit 115. As such, adjustments of
the qubit location and orientation relative to the electric field
profile of the mode of interest can be used to adjust the strength
of qubit-cavity coupling, and in turn the qubit-qubit coupling, as
the qubits acquire a direct qubit-qubit effective interaction
through their mutual interaction with the cavity mode. The
apparatus 100 is a scaled apparatus including multiple qubits 115.
As such, the cavity 110 can support a high volume of
electromagnetic modes, with strong coupling between the cavity 110
and the qubits. Furthermore, there is also strong coupling among
the individual qubits 115 within the cavity that can be controlled
and tuned by adjusting the electromagnetic field from the
electromagnetic source 120. The apparatus 100 is therefore scaled
up from the single 3D qubit to a large platform of coupled 3D
qubits for quantum computing. In exemplary embodiments, the scaling
up process is modular. FIG. 1 illustrates a single qubit cluster
100 as described. In exemplary embodiments, eight qubits 115 are
illustrated and can be arranged in a variety of ways in order to
achieve desired coupling among the qubits. It will be appreciated
that there are numerous ways and manners in which the qubits 115
can couple. The qubits 115 are illustrated in an octagonal pattern
but in no way are other exemplary embodiments limited to this
pattern. Furthermore, there can be fewer or more than eight qubits
115 arranged in the cavity 110. Eight qubits 115 are illustrated
because they behave much like a conventional NMR molecule, as
further described herein, and therefore are well-understood and
characterized.
[0032] As such, FIG. 1 illustrates superconducting qubits (e.g.,
eight transom-style qubits) inside the cavity 115, which, as
described is an ultra-high Q superconducting waveguide resonator,
to form the qubit cluster apparatus 100. In scaling up further,
additional qubit cluster apparatuses can be coupled to the qubit
cluster apparatus 100 as now described.
[0033] FIG. 2 illustrates an exemplary two-dimensional lattice
multi-qubit system 200 of multiple 3D qubit cluster apparatuses A1,
A2, B1, B2. The apparatuses A1, A2, B1, B2 are illustrative only,
and can be scaled to a larger number of qubit cluster apparatuses
such as a number of rows and columns on the order of A1-An, B1-Bm,
where n and m are integers. Furthermore, each of the apparatuses
A1, A2, B1, B2 includes similar structure of the apparatus 300 of
FIG. 3. For example, the apparatus A1 includes a housing 205 with a
cavity 210 defined therein. The apparatus A1 can further include a
cluster of qubits 215 disposed within the cavity 210. The apparatus
A1 can further include an external electromagnetic source 220
(e.g., a coaxial cable) coupled to the housing 205 and providing an
electromagnetic field within the cavity 210. The system 200 further
includes electromagnetic resonators 250 coupled between adjacent
apparatuses A1, A2, B1, B2 via coupling elements 251 (e.g.,
transmission lines) coupling the cavities 210 to the
electromagnetic resonators 250. The resonators 250 are coupled to
the respective apparatuses A1, A2, B1, B2 via a suitable coupling
device such as, but not limited to, a transmission line and a
waveguide depending on the type of resonator implemented in the
coupling. For example, the resonators 250 can be microwave
resonators constructed from either lumped elements (explicit
capacitances and inductors) or from a short section of transmission
line. The transmission line could be coaxial, planar, waveguide,
among others. These resonators are made tunable by incorporating
into them some non-linear materials or circuit elements. An example
of a non-linear circuit element would be a Josephson junction,
which can behave like a tunable inductor. One possible design would
be a transmission line resonator made from a short section of
coplanar waveguide with Josephson junctions embedded in the center
conductor or in the gap between the center conductor and the ground
plane. Another resonator can include a superconducting loop
interrupted by one or more Josephson junctions, which behaves like
a magnetic field-dependent inductance. Regardless of the type of
resonator implemented, the resonators 250 are tunable such that
adjacent apparatuses A1, A2, B1, B2 are coupled to one another. By
tuning the respective electromagnetic fields, groups of qubits in
one apparatus A1, A2, B1, B2 can be coupled to an adjacent group of
qubits in another of the apparatuses A1, A2, B1, B2. As such, not
only are qubits coupled to their respective cavities and other
qubits residing in their cavities, but groups of qubits can also be
coupled in the entire system 200 as further described herein.
[0034] The system 200 is capable of non-local entanglement,
teleportation and error correction using the full multi-qubit
system 200. At this point of scaling, other issues related to
scaling can be addressed such as but not limited to thermalization,
physical assembly, and signal delivery (i.e., I/O issues). It can
be appreciated that the scaling from the 3D qubit apparatus 200
from FIG. 2 scales to the qubit cluster apparatus 300 of FIG. 3 and
to the two dimensional array of these unit cells, as shown in FIG.
2(b), using nominally identical copies of the systems developed in
the first two stages. Finally a number of two dimensional arrays
can be stacked vertically to form a three dimensional array. FIG. 3
illustrates an exemplary 3D lattice multi-qubit system 300 of
multiple 3D qubit cluster apparatuses as described herein. For
illustrative purposes two of the systems 200 of FIG. 2 are shown.
FIG. 3 is illustrated to further show scaling of the systems and
methods described herein. It will be appreciated that additional
systems 200 can be added to the system 300 to further scale the
size of the quantum computer.
[0035] In exemplary embodiments, as described herein, the coupling
of qubits within a cluster as well as coupling of individual qubits
between clusters can be achieved by the application of
electromagnetic fields. Measurements of the qubits can be
subsequently taken in order to determine the quantum states of the
qubits. The application of the electromagnetic fields as well as
the subsequent quantum state measurements described an overall
quantum computing method. FIG. 4 illustrates a flow chart of a
method 400 for a quantum computing method in accordance with
exemplary embodiments. At block 410, a first electromagnetic filed
can be applied and adjusted to a first qubit cluster (such as the
apparatus A1 of FIG. 2). At block 420, a second electromagnetic
field can be applied and adjusted to a second qubit cluster (such
as the apparatus A2 of FIG. 2). As described herein, the
application of the electromagnetic fields to the respective qubit
clusters couples qubits within the clusters to one another as well
as induces quantum states. At block 430, a third magnetic field can
be applied and adjusted between the first and second qubit clusters
(such as applying a resonating frequency from the resonator 250
disposed between the apparatuses A1, A2). For example, a third
field is applied to the electromagnetic resonators 250 as well as
apparatuses A1 and A2. As described herein, the application of the
third magnetic field couples individual qubits within the first
qubit cluster with individual qubits in the second qubit cluster,
thereby coupling the qubit clusters. Blocks 410, 420 and 430 are
repeated and modified during each iteration to execute a specific
quantum algorithm or error correction scheme (block 450). At block
440, appropriate measurements of the quantum states of the qubits
can be taken, such as by measuring the quantum flux of individual
qubits.
[0036] Several properties of the exemplary systems and methods are
now further described. As discussed herein, the physics of a system
with multiple transom style qubits dispersively coupled to a single
bosonic resonator mode is well understood (e.g., an NMRQC). In
exemplary embodiments, the systems and methods described herein are
implemented with fixed qubit frequencies and fixed qubit-qubit
coupling. In this way, known NMR control techniques can be
implemented. In NMR technology, Larmor frequencies are implemented
in which the qubits tend to align with the applied electromagnetic
fields. In addition, chemical shifts, which describe the dependence
of energy levels on the electronic environment in a molecule, can
be implemented to determine the dependence of the energy levels in
a given cavity in the exemplary qubit clusters described herein. By
implementing such known techniques, universal control of the
exemplary qubit clusters described herein can be attained. In
exemplary embodiments, qubit frequencies could be controlled via
wires introduced into the cavity. By judicious selection of qubit
frequencies and anharmonicities, Hamiltonians identical to
Hamiltonians in NMR can be attained, where there are both secular
and non-secular coupling terms of comparable strength, but only the
secular portion is important because it enters to first order in
perturbation theory. In exemplary embodiments, spins can be
selected on individual qubits within a cavity.
[0037] In NMRQC, ZZ exchange and interaction describes the spin
exchange between adjacent molecules. This concept can be extended
to describe spin exchange in qubits as described in exemplary
embodiments. An NMR-style Hamiltonian emerges when the effective ZZ
interaction between qubits in a particular cavity is significant
compared with the off-diagonal J-coupling term, that is, coupling
of angular momentum of interacting qubits. This ZZ interaction has
two physical origins. First, ZZ interaction emerges in the
two-level approximation when the cavity-qubit coupling is treated
to fourth-order in perturbation theory. Second, it emerges when
additional qubit levels outside the computational subspace are
properly modeled. The two effects can be made to add rather than
cancel. In exemplary embodiments, the systems and methods described
herein that include circuits that implement an NMR-type Hamiltonian
requires understanding and exploiting both these origins of the ZZ
interaction term. The strength of the effect increases rapidly as
the 1->2 transition of one qubit in a cluster approaches the
0->1 transition of another. By exploiting these physical
phenomena, the qubit clusters described herein can be scaled as
described.
[0038] In exemplary embodiment, in order to produce the NMR-type
Hamiltonian characterized by: a) fixed qubit transition
frequencies, and b) fixed qubit-qubit couplings dominated by a ZZ
interaction, the systems described herein possess the following
qualities: 1) Each qubit is controlled and manipulated in such a
manner that it behaves as an effective two-level system; 2) Each
qubit interacts with at least one other qubit with a coupling
energy that is much greater than the qubit relaxation and
decoherence rates; 3) The system allows for the application to the
qubits of a frequency and amplitude modulated microwave control
field; and 4) The system allows for the readout of the quantum
state of all qubits.
[0039] In exemplary embodiments, two qubit gates are performed by
doing nothing to the two qubits that are to be entangled, while
interactions between all other pairs are refocused. In recent
liquid state NMR experiments on multi-spin molecules, very-high
fidelity control of E.sub.1q=1.3.times.10.sup.-4 and
E.sub.2q=4.7.times.10.sup.-3 has been demonstrated. It is believed
that these are limited by the difficulty to polarize the spins at
the outset. In contrast, in exemplary embodiments, the qubits
described herein (i.e., superconducting qubits can be easily
initialized. However, the higher Larmor frequencies (roughly 1-10
GHz as compared to 50-500 MHz), additional steps are taken to make
accurate numerical pulse optimization.
[0040] In exemplary embodiments, qubits within the exemplary
clusters described herein are measured through the application of
resonant or near-resonant signals to the cavity that houses them.
The readouts can be done according to the established methods of
joint dispersive readout. Single shot readouts can be realized by
also applying drive signals to a neighboring coupling element,
whose non-linearity makes it suitable for signal amplification.
[0041] As such, it can be appreciated that the exemplary clusters
described herein combine known and well-characterized features of
NMRQC and desirable attributes of qubits such as superconducting
attributes.
[0042] As further described herein, to go beyond the qubit clusters
as illustrated in FIG. 3, for example, to larger arrays as
described, for example in FIGS. 2 and 3, additional clusters are
added. The exemplary systems 200, 300 as described in FIGS. 2 and 3
the high-Q tunable resonators (e.g., the resonator 250) mediates
interactions between "identical" qubits in separate clusters. For
example, in FIG. 2, some of the qubits 215 have been labeled Q1.
The resonator 250 between the apparatuses A1, A2 can be tuned into
resonance with one par of qubits (e.g., qubits A1Q1, A2Q1) to a
frequency fq1. The application of this frequency fq1, results in an
enhanced exchange of quantum information from qubits A1Q1 and A2Q1
to the coupling resonator 250 between the apparatuses A1, A2.
Resonant enhancement of the qubit exchange rate into the resonator
250 rather than a suppression of the qubit relaxation is
implemented. Each of the qubits A1Q1, A2Q2 interacts with the
resonator according to the expression:
H.sub.eff.apprxeq.g.sub.cg.sub.q(.sigma..sub.q.sup.-c.sup.t+.sigma..sub.-
q.sup.+c)/.DELTA..sub.q
[0043] Where g.sub.c is the coupling strength between the resonator
250 and the cQED cluster cavity (i.e. either of the cavities 210 of
the apparatuses A1, A2), g.sub.q and .DELTA..sub.q are the standard
cQED qubit-cavity coupling strength and detuning within the cluster
of qubits 215, respectively, .sigma..sub.q is the qubit operator
and c the resonator 250 operator. When the apparatuses A1, A2 and
the resonator 250 are resonant, the qubit-qubit interaction
proceeds at half this rate, or g.sub.cg.sub.q/2 .DELTA..sub.q. With
currently demonstrated tunable cavity performance this coupling
scheme between qubits in separate cavities can produce an operation
with a gate error rate of 10.sup.-2, and it increases linearly with
any improvements in the Q of the tunable resonator 250. It has been
theorized that the gate error rate can be increased by up to a
factor of 5 to 10.
[0044] In exemplary embodiments, when the resonator 250 is detuned
residual coupling acts only via a third-order dispersive coupling
through each of the apparatuses A1, A2 and the resonator 250, an
effect proportional to:
H.sub.eff.sup.off.apprxeq.g.sub.c.sup.2g.sub.q.sup.2(.sigma..sub.a.sup.--
.sigma..sub.b.sup.++.sigma..sub.a.sup.+.sigma..sub.b.sup.-).DELTA..sub.q.s-
up.2.DELTA..sub.c.sup.off
[0045] The on/off ratio of this tunable coupling is thus:
H.sub.eff.sup.off.apprxeq..DELTA..sub.q.DELTA..sub.c.sup.off/g.sub.cg.su-
b.q
which is 100-1000 for accessible parameters.
[0046] As described herein, many different types of resonators can
be implemented for the resonator 250. For example, a basic tunable
coupling element used to intermediate interactions between qubits
of neighboring clusters (e.g., apparatuses A1, A2) can include
Josephson junctions embedded within the mode volume of either 2D or
3D resonator structures and applying bias fields. This tunable
coupler could be a passive but tunable device, such as a frequency
tuned resonator; or it could be an active device such as a
Josephson parametric converter, which frequency converts with gain
dependent on the pump power. Presently available technologies have
achieved tunable resonators with Q.sub.tunable=3.times.10.sup.4.
Lossless Josephson frequency converters can also be implemented as
the resonator 250. Lossless Josephson frequency converters can act
as frequency converters with gain that depends on the applied pump
power, and thus possesses the possibility to produce very strong
cluster-cluster coupling with a greater on/off ratio. Lossless
Josephson frequency converters could also be implemented as a
readout element capable of single shot projective joint readout, a
valuable resource for quantum error correction schemes.
[0047] In exemplary embodiments, scaling can further include not
only the adjacent apparatuses A1, A2 as just described, but also
the full 2D arrangement including the apparatuses B1, B2 as shown
in FIG. 2. In exemplary embodiments, a 2.times.2 array of clusters
(e.g., apparatuses A1, A2, B1, B2) can be implemented for quantum
computing by coupling nearest neighbors, via intervening resonators
250. Similarly, any 3.times.3 array or larger, and any 3D array as
shown in FIG. 3 can further be developed implementing resonators
250 to couple nearest neighbors. In these examples, a 2.times.2
array can include 32 qubits, a 3.times.3 array can include 72
qubits, an 8.times.8 array can include 512 qubits and so on, thus
demonstrating the quantum computing capabilities. This scaling
approach advantageously includes modular repeated units that
exploit known and demonstrated physics as described herein and
reduces the I/O challenges because one control line can be
implemented per qubit cluster, for example.
[0048] The examples illustrated in FIGS. 1-3 show an exemplary
arrangement of qubits. It can be appreciated that the qubit
clusters can be arranged in other lattice structures, such as
trigonal, hexagonal or other. They can also be extended to
three-dimensional lattices, (e.g. the cubic lattice of FIG. 3).
Whether the qubit clusters are arranged in a 1D, 2D or 3D lattice,
the physical structures can be arranged to occupy a 3D volume to
facilitate IO issues or for other reasons. In the case of a 3D
cubic lattice of FIG. 3, two dimensional square lattice sheets can
be connected two each other by additional tunable resonators in any
of several ways, for example to form topologically a large extended
two dimensional array or a truly three dimensional array with each
interior qubit cluster connected to its six nearest neighbors, four
in the same plane and one each directly above and below.
[0049] Technical effects include the implementation of clusters of
qubits arranged to couple individual qubits for quantum
computing.
[0050] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting of
the invention. As used herein, the singular forms "a", "an" and
"the" are intended to include the plural forms as well, unless the
context clearly indicates otherwise. It will be further understood
that the terms "comprises" and/or "comprising," when used in this
specification, specify the presence of stated features, integers,
steps, operations, elements, and/or components, but do not preclude
the presence or addition of one more other features, integers,
steps, operations, element components, and/or groups thereof.
[0051] The corresponding structures, materials, acts, and
equivalents of all means or step plus function elements in the
claims below are intended to include any structure, material, or
act for performing the function in combination with other claimed
elements as specifically claimed. The description of the present
invention has been presented for purposes of illustration and
description, but is not intended to be exhaustive or limited to the
invention in the form disclosed. Many modifications and variations
will be apparent to those of ordinary skill in the art without
departing from the scope and spirit of the invention. The
embodiment was chosen and described in order to best explain the
principles of the invention and the practical application, and to
enable others of ordinary skill in the art to understand the
invention for various embodiments with various modifications as are
suited to the particular use contemplated
[0052] The flow diagrams depicted herein are just one example.
There may be many variations to this diagram or the steps (or
operations) described therein without departing from the spirit of
the invention. For instance, the steps may be performed in a
differing order or steps may be added, deleted or modified. All of
these variations are considered a part of the claimed
invention.
[0053] While the preferred embodiment to the invention had been
described, it will be understood that those skilled in the art,
both now and in the future, may make various improvements and
enhancements which fall within the scope of the claims which
follow. These claims should be construed to maintain the proper
protection for the invention first described.
* * * * *