WO2017111937A1 - Intégration double triangulaire pour recuit quantique - Google Patents

Intégration double triangulaire pour recuit quantique Download PDF

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Publication number
WO2017111937A1
WO2017111937A1 PCT/US2015/067309 US2015067309W WO2017111937A1 WO 2017111937 A1 WO2017111937 A1 WO 2017111937A1 US 2015067309 W US2015067309 W US 2015067309W WO 2017111937 A1 WO2017111937 A1 WO 2017111937A1
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hamiltonian
quantum
graph
dual
constraint
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PCT/US2015/067309
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Nan Ding
Hartmut Neven
Alireza Shabani BARZEGAR
Masoud MOHSENI
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Google Inc.
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Publication of WO2017111937A1 publication Critical patent/WO2017111937A1/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena

Definitions

  • optimization tasks can be translated into machine learning optimization problems.
  • quantum hardware e.g., a quantum computing device
  • quantum hardware is constructed and programmed to encode the solution to a corresponding machine optimization problem into an energy spectrum of a many-body quantum Hamiltonian characterizing the quantum hardware.
  • the solution is encoded in the ground state of the Hamiltonian.
  • This specification relates to constructing and programming quantum hardware for quantum annealing processes.
  • this specification describes technologies for solving an optimization task by encoding the solution to the optimization task in a local or non-local &-body Hamiltonian and embedding the &-body Hamiltonian model in a dual form with auxiliary degrees of freedom that may be realized with a system of qubits and only local two-body interactions.
  • the first Hamiltonian is represented by a graph comprising nodes and real edges, the graph defining a plurality of loops; mapping the first Hamiltonian to a second Hamiltonian, the second Hamiltonian consisting of one or more local two-body interaction terms given by one or more dual variables, the mapping comprising: for a loop in the graph representing the first Hamiltonian, determining a constraint that corresponds to the loop; and subjecting one or more of the dual variables to the constraint; providing the second Hamiltonian to a quantum computing device for solving the optimization task.
  • a system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a
  • One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions.
  • mapping the first Hamiltonian to the second Hamiltonian comprises removing real edges from the graph to construct a largest subgraph of the graph that contains no loops; sequentially adding back to the graph a real edge that was removed to the subgraph to recover the graph, and for a sequential addition of a real edge that was removed, incurring one dual variable constraint.
  • the method comprises preprocessing the graph prior to constructing the largest subgraph of the graph, wherein preprocessing the graph comprises: adding one or more virtual edges to the graph such that the smallest loop that includes a real edge has three edges, wherein a virtual edge is an edge that connects two nodes that were not connected by a real edge.
  • the first Hamiltonian is a Hamiltonian H of an Ising model given by
  • the second Hamiltonian includes a penalty term given by
  • the second Hamiltonian includes a penalty term given by
  • q represents a constraint loop
  • C q represents a penalty strength for a constraint corresponding to the constraint loop
  • s q represents a multi-level quantum system
  • the penalty strength C q satisfies C q >
  • the first Hamiltonian comprises one or more local or non-local &-body interaction terms and the dual variables are given by
  • the dual variables of the second Hamiltonian include a dummy dual variable a d for k odd, wherein the dummy variable is connected to all nodes in the graph of the first Hamiltonian by virtual edges.
  • the dual constraints include
  • H total A(t H D + B(t)H p + C t H c wherein Aft), Bft), Cft) represent general time-dependent annealing parameters, H D represents a drive Hamiltonian, H p represents the second Hamiltonian and
  • H c represents a constrained Hamiltonian.
  • the method further comprises solving, by the quantum computing device, the optimization task by performing quantum annealing.
  • performing quantum annealing comprises selecting all parameters of the constrained Hamiltonian inhomogeneously in space.
  • a system implementing triangular dual embedding may embed the arbitrary &-body interactions of nodes in a graphical representation of an optimization problem into a triangular dual architecture involving only physically local two-body interactions of qubits where the interaction strengths between nodes become local fields, significantly easing quantum chip design.
  • a system implementing triangular dual embedding enables an inhomogeneous realization of constraint Hamiltonians within an annealing schedule, improving the overall performance of a quantum annealer solving an optimization task. Furthermore, a system implementing triangular dual embedding requires less computational resources, since, for example, qubits may be used more efficiently than other systems that do not implement triangular dual embedding, for example systems based on 4-qubit constraints.
  • FIG. 1 depicts an example system for solving an optimization task using triangular dual embedding for quantum annealing.
  • FIG. 2 is a flow diagram of an example process for solving an optimization task.
  • FIG. 3 is a flow diagram of an example process for performing triangular dual embedding.
  • FIG. 4 illustrates an example graph during a triangular dual embedding process.
  • This specification describes an architecture and method for embedding an optimization task into a form that may be implemented and solved using the restricted connectivities and interactions that are available within a given architecture on a given computing technology.
  • the techniques described enable arbitrary &-body interactions of nodes in a graphical representation of the optimization problem to be mapped to a triangular dual architecture involving only physically local two-body interactions of qubits.
  • the optimization task may then be provided to a quantum computing device for solving by a quantum annealing process and subsequent measurement.
  • FIG. 1 depicts an example system 100 for solving an optimization task using triangular dual embedding for quantum annealing.
  • the example system 100 is an example of a system implemented as classical or quantum computer programs on one or more classical computers or quantum computing devices in one or more locations, in which the systems, components, and techniques described below can be implemented.
  • the system includes a classical processor 102 in communication with a quantum computing device 104.
  • the classical processor 102 receives data specifying an optimization task 106 as input and generates as an output data specifying a dual Hamiltonian 108 and dual variable constraints 110.
  • the classical processor 102 may include an encoder subsystem that receives the data specifying the optimization task 106 and encodes the solution to the task into the energy spectrum of an interacting many -body quantum system characterized by a first Hamiltonian.
  • the classical processor 102 may include a mapping subsystem that receives data specifying the first Hamiltonian and maps the first Hamiltonian to a second, dual Hamiltonian including dual variables satisfying dual variable constraints.
  • the classical processor 104 may communicate with the quantum computing device and determine physical connectivities and interactions that are available within the quantum computing device 104 in order to map the first Hamiltonian to a suitable dual
  • Hamiltonian 108 e.g., a dual Hamiltonian that may be implemented by the quantum hardware of the quantum computing device 104.
  • the classical processor provides the generated output data specifying the dual Hamiltonian 108 and the dual variable constraints 1 10 to the quantum computing device 104.
  • the quantum computing device 104 includes a classical processing subsystem 1 12 and a quantum annealer 1 14.
  • FIG. 1 depicts the classical processor subsysteml 12 as separate to the classical processor 102, however, in some implementations the classical processor 102 may be included in the quantum
  • the classical processor 102 is the classical processor subsystem 1 12, or the classical processor may be in direct data communication with the quantum computing device 104 such that a separate classical processor subsystem 1 12 is redundant.
  • the quantum annealer includes one or more qubits, e.g., qubit 1 16. For clarity, six qubits are depicted in FIG. 1, however the system may include a much larger number of qubits, e.g., millions of qubits.
  • the qubits may interact with one another through one or more couplers, e.g., coupler 1 18. Each coupler is configured to couple a pair of qubits to facilitate interaction between the qubits.
  • the interactions between qubits may consist of local two-body interactions.
  • the Hamiltonian of the quantum annealer characterizing the qubits and the couplers may be given by:
  • H total A(t H D + B(t)H p + C t H c
  • Aft), Bft), Cft) represent general time-dependent annealing parameters
  • H D represents a drive Hamiltonian
  • H p represents a problem, or dual
  • Hamiltonian represents a constrained Hamiltonian.
  • the drive Hamiltonian may be given by:
  • H D + Jij a ij + Jij a ij) + fourth order terms
  • ⁇ -j, and ⁇ represent Pauli x, y and z matrices, respectively
  • J j , j j and J j represent the interaction strengths for each corresponding Pauli matrix between nodes i and j.
  • the problem Hamiltonian may be given by: where ⁇ ⁇ ; - represents a dual variable, represents a local field and E represents the set of real edges of the graph that represents the first Hamiltonian.
  • the constraint Hamiltonian may be given by:
  • the quantum computing device 104 receives the data specifying the dual Hamiltonian 108 and the dual variable constraints 110, performs quantum annealing on the dual Hamiltonian 108 with the dual variable constraints 110 and determines the solution 120 to the optimization task by performing a measurement.
  • FIG. 2 is a flowchart of an example process 200 for solving an optimization task.
  • the process 200 will be described as being performed by a system of one or more classical or quantum computing devices located in one or more locations.
  • a classical processing system and a quantum computing device e.g., the classical processing system 102 and quantum computing device 104 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 200.
  • the system encodes the solution to an optimization task into an energy spectrum of a first Hamiltonian (step 202).
  • the system may encode an optimization problem in the first Hamiltonian where the low energy states are known to encode a solution to the optimization problem.
  • the first Hamiltonian may include one or more local or non-local &-body interaction terms, e.g., where k > 1.
  • Each node in the set of nodes corresponds to a multi-level quantum system, e.g., a qubit, and each edge in the set of real edges corresponds to an interaction between two multi-level quantum systems according to the first Hamiltonian.
  • the graph may be a sparse graph of N nodes with K « N(N-l)/2 edges.
  • the first Hamiltonian may represent an Ising model and be given by the Hamiltonian H f j rst in equation (1) below.
  • equation (1) first ij " i ⁇ Z ( u Tj Z (1)
  • o represents a Pauli z matrix
  • E represents the set of real edges of the graph G that represents the Hamiltonian H f j rst . It is noted that equation (1) neglects local terms ⁇ i since such terms may be incorporated into equation (1) through the use of a dummy variable equal to one.
  • the system maps the first Hamiltonian to a second dual Hamiltonian that consists of local two-body interaction terms given by one or more dual variables (step 204).
  • the dual variables of the second Hamiltonian include a dummy dual variable ⁇ ⁇ , e.g., when k is odd.
  • the dummy variable may be graphically represented as being connected to all nodes in the graph G of the first Hamiltonian by virtual edges, i.e., edges of the graph that do not represent physical interactions between nodes.
  • the system may determine a constraint that corresponds to the loop and subject one or more of the dual variables of the second Hamiltonian to the constraint. In this manner, the constraints of the dual form of the first Hamiltonian originate from the loops of the graph G. Mapping a first Hamiltonian to a second Hamiltonian using triangular dual embedding is described in more detail below with reference to FIG. 3.
  • Hamiltonian may represent an Ising model and be given by the Hamiltonian Hfj rst in equation (1) above, and the system may map the Hamiltonian Hfj rst to a second
  • the dual variables ⁇ ⁇ ; - satisfy a number of constraints, ensuring that the overall configuration described by Hsecond is valid. Imposing dual variable constraints is described in more detail below with reference to Fig. 3.
  • all model parameters represent local fields, reducing the complexity of quantum chip design.
  • the system provides the second Hamiltonian to a quantum computing device for solving the optimization task (step 206).
  • the system may provide the second Hamiltonian to the quantum computing device 104 of FIG. 1.
  • a Hamiltonian H total characterizing the quantum computing device may be given by equation (3) below.
  • H total A(t H D + B(t)H p + C(t)H c (3)
  • Aft), Bft), Cft) represent general time-dependent parameters
  • H D represents a drive Hamiltonian
  • H p represents a problem Hamiltonian, e.g., the second dual Hamiltonian in which the solution to the optimization task is encoded
  • H c represents a constraint Hamiltonian
  • the drive Hamiltonian may be given by equation (4) below.
  • ⁇ - , and of j represent Pauli x, y and z matrices, respectively, and J j , j j and Jij represent the interaction strengths for each corresponding Pauli matrix between nodes i and j.
  • the drive Hamiltonian drives the system to a final ground state.
  • a dual problem Hamiltonian e.g., H P as given in equation (3)
  • the drive Hamiltonian is required to respect the dual variable constraints, since the constraints ensure that the problem Hamiltonian is effectively N-qubit rather than K ⁇ N(N-l)/2 and the drive Hamiltonian is to respect this dimensionality reduction.
  • the system selects a drive Hamiltonian that commutes with the dual variable constraints, as given below in equation (5).
  • s is a multi-level quantum system.
  • the ground state of this drive Hamiltonian may be degenerate, e.g.,
  • ⁇ ; - of may be turned on and off quickly at the beginning.
  • the problem Hamiltonian may be given by equation (6) below.
  • ⁇ ⁇ ; - represents a dual variable, represents a local field and E represents the set of real edges of the graph that represents the first Hamiltonian.
  • Equation (7) ⁇ ⁇ ; - represents a dual variable, C q represents a penalty strength and s q represents a multi-level quantum system.
  • the form of the constraint Hamiltonian is discussed in more detail below with reference to FIG. 3.
  • the system solves the optimization task by performing quantum annealing using the quantum computing device (step 208).
  • the constraint Hamiltonian may have sufficiently large strength compared to local fields and the driver Hamiltonian at the quantum critical point given the degree of the connectivity of the graph G.
  • This quantum annealing schedule may strongly enforce the dual variable constraints at all time.
  • the system follows a quantum annealing schedule that includes selecting all parameters of the constrained Hamiltonian inhomogeneously in space, that is all the parameters of the constraint Hamiltonian may be locally time-dependent.
  • This quantum annealing schedule may lead to an inhomogeneous quantum phase transition in space which may be used to enhance the effective gap of the system at the quantum critical point, which is often a bottleneck of the annealing schedule.
  • FIG. 3 is a flowchart of an example process 300 for performing triangular dual embedding.
  • the process 300 will be described as being performed by a system of one or more classical computing devices located in one or more locations.
  • a classical processing system e.g., the classical processing system 102 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 300.
  • the system preprocesses the graph that represents the first Hamiltonian (step 302).
  • the system preprocesses the graph by "triangularising" the graph, that is by adding one or more virtual edges to the graph such that the smallest loop that includes a real edge has three edges.
  • additional dual variables are introduced to the second dual Hamiltonian, with a maximum increase of the number of nodes of the graph N.
  • the triangularising step 302 ensures that all constraint loops have three edges, which enables the multi-level quantum system s to be encoded by a single qubit.
  • the system constructs a largest subgraph of the graph that contains no loops by removing edges from the graph. For example, for a connected graph with N nodes and K edges, the largest subgraph that contains no loops will be a tree with N-l edges. The N-l edges would correspond to N-/dual variables in the dual form. At this stage, since there are no loops in the subgraph, there are no constraints imposed on the dual variables. In other examples where the graph has N nodes but is not a connected graph, the number of edges in the subgraph will be smaller than N-l. An example of a largest subgraph that contains no loops is given below with reference to FIG. 4.
  • the system sequentially adds back to the graph an edge that was removed to the subgraph to recover the graph (step 306).
  • the system incurs one constraint to the dual variables (step 308). For example, for a connected subgraph with N nodes and K edges, the total number of edges that are sequentially added back to the graph is K-N+1.
  • the incurred constraints to the dual variables maintain the dual form of the second Hamiltonian' s legality.
  • the first Hamiltonian may represent an Ising model, as shown in equation (1), and may be mapped to a second dual Hamiltonian given by equation (2) above.
  • the incurred constraints for the three dual variables ⁇ ⁇ ; -, o ik , Oj k to satisfy include the constraints given by equation (8) below.
  • the set of dual variables of the second Hamiltonian may include a dummy dual variable o d when k is odd.
  • the dummy variable may be defined as being connected to all nodes in the graph of the first Hamiltonian by virtual o edges.
  • a number of the constraints for the dual variables are redundant and may not need to be explicitly enforced.
  • the system may perform constraint minimization by using soft5 constraints such as penalty functions to replace hard constraints. Based on the first constraint in equation (9) above, the system may construct a penalty term Ca 12 , ... , a L1 and the second Hamiltonian may include a penalty term H c given by equation (10) below.
  • Equation (10) q represents a constraint loop in the dual form and C q represents a penalty strength for a constraint corresponding to the constraint loop.
  • the5 system may construct a penalty term min(C(a 12 +— V a L1 — s) 2 ), where s G
  • Equation (11) ⁇ L, L— 4, ... ,— L + mod 4 (2L) ⁇ is a multi-level quantum system, and the second Hamiltonian may include a penalty term given by equation (11) below.
  • q represents a constraint loop in the dual form
  • C q represents a penalty strength for a constraint corresponding to the constraint loop
  • s q represents a multi-level quantum system.
  • L 3
  • s q may be realized as a two level quantum system (even without performing the triangularisation preprocessing step 302).
  • Equation (12) the second Hamiltonian in the dual is given by equation (12) below.
  • the system may select the penalty strength C so that the energy spectrum of the first Hamiltonian, for example as given by equation (1) above, remains the same as the energy spectrum of the second Hamiltonian in the dual including the penalty term, for example as given by equation (12) above, since the solution to the optimization task is encoded into the energy spectrum of the first Hamiltonian, as described above with reference to FIG. 2. It is therefore required that C is large enough so as to appropriately penalize dual configurations that violate constraints, for example by setting C large enough so that dual configurations have higher energies than suboptimal configurations that do not violate constraints.
  • a ground state may satisfy all constraints. If one qubit is flipped in the original form, the resulting dual graph may also satisfy all constraints.
  • the change in energy for flipping the qubit may be given by dE t ⁇ ⁇ i
  • dE t ⁇ C for all nodes / ' resulting in equation (13) below.
  • ) is the maximum degree of the nodes in the graph.
  • the system terminates the process when the graph has been recovered (step 3 10). Upon termination, the system may provide the second Hamiltonian in the dual along with the dual variable constraints to a quantum computing device for solving the optimization task encoded in the energy spectrum of the corresponding first Hamiltonian.
  • FIG. 4 illustrates an example graph 400 during a triangular dual embedding process, e.g., the triangular dual embedding process 300 described above with reference to FIG. 3.
  • the original first Hamiltonian that the graph 400 represents is therefore given by equation (15) below.
  • tffirst ki°l°l + / 13 ⁇ 1 ⁇ ⁇ 3 ⁇ + / 23 ⁇ 2 ⁇ ⁇ 3 ⁇ + / 24 ⁇ 2 ⁇ ⁇ 4 ⁇ + ] ⁇ + ] 5 ⁇
  • / ⁇ ; - represents the interaction strength between nodes i and j, and o is a Pauli z operator acting on node j.
  • the edge connecting nodes 2 and 4, i.e., edge (2,4) is not included in a loop of size 3, rather the edge (2,4) is only included in a loop of size 4, that is the loop made up of nodes 2, 3, 4 and 5.
  • edges (4,5) and (3,5) may therefore determine that the graph 400 requires preprocessing, or "triangularising" as described above at step 302 of FIG. 3.
  • edges (2,5) and (4,5) are now included in the loop (2,4,5) of size 3 defined by nodes 2, 4, and 5.
  • edge (3,5) is now included in the loop (2,3,5) of size 3 defined by nodes 2, 3, and 5.
  • the graph 420 at stage (c) represents a largest subgraph of the graph 410 that does not include any loops, as described above at step 304 of FIG. 3.
  • the corresponding Hamiltonian for the graph 420 is given by equation (16) below. ⁇ second -/ ⁇ 2 ⁇ 12 + / ⁇ 3 ⁇ 13 +/35 ⁇ 35 + /45 ⁇ 45 (15)
  • the dual variables in this example are given by ⁇ 12 , ⁇ 13 , ⁇ 35 and ⁇ 45 .
  • No penalty term is included in the Hamiltonian at this stage, since the graph 420 is loop-less.
  • the graph at stage (d) represents step 306 of the triangular dual embedding process 300, where the system sequentially adds back to the graph each edge that was removed from the subgraph 420 to recover the graph 410.
  • edges (2,5) and (2,4) are sequentially added to the graph 420, incurring respective dual variable constraints about the loops (2,3,5) and (2,4,5) with corresponding penalty functions P 2 5 and P 2 4 , respectively.
  • the resulting graph 430 is the same as the triangularised graph 410.
  • Implementations of the digital and/or quantum subject matter and the digital functional operations and quantum operations described in this specification can be implemented in digital electronic circuitry, suitable quantum circuitry or, more generally, quantum computational systems, in tangibly-embodied digital and/or quantum computer software or firmware, in digital and/or quantum computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them.
  • quantum computational systems may include, but is not limited to, quantum computers, quantum information processing systems, quantum cryptography systems, or quantum simulators.
  • Implementations of the digital and/or quantum subject matter described in this specification can be implemented as one or more digital and/or quantum computer programs, i.e., one or more modules of digital and/or quantum computer program instructions encoded on a tangible non-transitory storage medium for execution by, or to control the operation of, data processing apparatus.
  • the digital and/or quantum computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubits, or a combination of one or more of them.
  • the program instructions can be encoded on an artificially-generated propagated signal that is capable of encoding digital and/or quantum information, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode digital and/or quantum information for transmission to suitable receiver apparatus for execution by a data processing apparatus.
  • digital and/or quantum information e.g., a machine-generated electrical, optical, or electromagnetic signal
  • quantum information and quantum data refer to information or data that is carried by, held or stored in quantum systems, where the smallest non- trivial system is a qubit, i.e., a system that defines the unit of quantum information.
  • qubit encompasses all quantum systems that may be suitably approximated as a two-level system in the corresponding context.
  • Such quantum systems may include multi-level systems, e.g., with two or more levels.
  • such systems can include atoms, electrons, photons, ions or superconducting qubits.
  • the computational basis states are identified with the ground and first excited states, however it is understood that other setups where the computational states are identified with higher level excited states are possible.
  • data processing apparatus refers to digital and/or quantum data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing digital and/or quantum data, including by way of example a programmable digital processor, a programmable quantum processor, a digital computer, a quantum computer, multiple digital and quantum processors or computers, and combinations thereof.
  • the apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array), an ASIC (application-specific integrated circuit), or a quantum simulator, i.e., a quantum data processing apparatus that is designed to simulate or produce information about a specific quantum system.
  • a quantum simulator is a special purpose quantum computer that does not have the capability to perform universal quantum computation.
  • the apparatus can optionally include, in addition to hardware, code that creates an execution environment for digital and/or quantum computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.
  • code that creates an execution environment for digital and/or quantum computer programs e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.
  • a digital computer program which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a digital computing environment.
  • a quantum computer program which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or can be written in a quantum programming language, e.g., QCL or Quipper.
  • a digital and/or quantum computer program may, but need not, correspond to a file in a file system.
  • a program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub-programs, or portions of code.
  • a digital and/or quantum computer program can be deployed to be executed on one digital or one quantum computer or on multiple digital and/or quantum computers that are located at one site or distributed across multiple sites and
  • a quantum data communication network is understood to be a network that may transmit quantum data using quantum systems, e.g. qubits.
  • a digital data communication network cannot transmit quantum data, however a quantum data communication network may transmit both quantum data and digital data.
  • the processes and logic flows described in this specification can be performed by one or more programmable digital and/or quantum computers, operating with one or more digital and/or quantum processors, as appropriate, executing one or more digital and/or quantum computer programs to perform functions by operating on input digital and quantum data and generating output.
  • the processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA or an ASIC, or a quantum simulator, or by a combination of special purpose logic circuitry or quantum simulators and one or more programmed digital and/or quantum computers.
  • a system of one or more digital and/or quantum computers to be "configured to" perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions.
  • one or more digital and/or quantum computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by digital and/or quantum data processing apparatus, cause the apparatus to perform the operations or actions.
  • a quantum computer may receive instructions from a digital computer that, when executed by the quantum computing apparatus, cause the apparatus to perform the operations or actions.
  • Digital and/or quantum computers suitable for the execution of a digital and/or quantum computer program can be based on general or special purpose digital and/or quantum processors or both, or any other kind of central digital and/or quantum processing unit.
  • a central digital and/or quantum processing unit will receive instructions and digital and/or quantum data from a read-only memory, a random access memory, or quantum systems suitable for transmitting quantum data, e.g. photons, or combinations thereof .
  • the essential elements of a digital and/or quantum computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and digital and/or quantum data.
  • the central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry or quantum simulators.
  • a digital and/or quantum computer will also include, or be operatively coupled to receive digital and/or quantum data from or transfer digital and/or quantum data to, or both, one or more mass storage devices for storing digital and/or quantum data, e.g., magnetic, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information.
  • mass storage devices for storing digital and/or quantum data, e.g., magnetic, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information.
  • a digital and/or quantum computer need not have such devices.
  • Digital and/or quantum computer-readable media suitable for storing digital and/or quantum computer program instructions and digital and/or quantum data include all forms of non-volatile digital and/or quantum memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; CD-ROM and DVD-ROM disks; and quantum systems, e.g., trapped atoms or electrons.
  • semiconductor memory devices e.g., EPROM, EEPROM, and flash memory devices
  • magnetic disks e.g., internal hard disks or removable disks
  • magneto-optical disks e.g., CD-ROM and DVD-ROM disks
  • quantum systems e.g., trapped atoms or electrons.
  • quantum memories are devices that can store quantum data for a long time with high fidelity and efficiency, e.g., light-matter interfaces where light is used for transmission and matter for storing and preserving the quantum features of quantum data such as superposition or quantum coherence.
  • Control of the various systems described in this specification, or portions of them, can be implemented in a digital and/or quantum computer program product that includes instructions that are stored on one or more non-transitory machine-readable storage media, and that are executable on one or more digital and/or quantum processing devices.
  • the systems described in this specification, or portions of them, can each be implemented as an apparatus, method, or system that may include one or more digital and/or quantum processing devices and memory to store executable instructions to perform the operations described in this specification.
  • implementation can also be implemented in multiple implementations separately or in any suitable sub-combination.
  • features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a subcombination.

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  • Optical Modulation, Optical Deflection, Nonlinear Optics, Optical Demodulation, Optical Logic Elements (AREA)

Abstract

L'invention concerne des procédés, des systèmes et des appareils pour effectuer un recuit quantique. Dans un aspect, un procédé comprend le codage d'une solution pour une tâche d'optimisation en un spectre d'énergie d'un premier graphe hamiltonien, le premier graphe hamiltonien étant représenté par un graphique comprenant des nœuds et des bords réels, le graphique définissant une pluralité de boucles ; mise en correspondance du premier graphe hamiltonien avec un deuxième graphe hamiltonien, le deuxième graphe hamiltonien étant composé d'un ou plusieurs termes d'interaction à deux corps locaux donnés par une ou plusieurs variables doubles, la mise en correspondance comprenant : pour une boucle dans le graphique représentant le premier graphe hamiltonien, détermination d'une contrainte qui correspond à la boucle ; et soumission d'une ou plusieurs des variables doubles à la contrainte ; fourniture du deuxième graphe hamiltonien à un dispositif de calcul quantique pour résoudre la tâche d'optimisation.
PCT/US2015/067309 2015-12-22 2015-12-22 Intégration double triangulaire pour recuit quantique WO2017111937A1 (fr)

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US11514134B2 (en) 2015-02-03 2022-11-29 1Qb Information Technologies Inc. Method and system for solving the Lagrangian dual of a constrained binary quadratic programming problem using a quantum annealer
US11797641B2 (en) 2015-02-03 2023-10-24 1Qb Information Technologies Inc. Method and system for solving the lagrangian dual of a constrained binary quadratic programming problem using a quantum annealer
US10713582B2 (en) 2016-03-11 2020-07-14 1Qb Information Technologies Inc. Methods and systems for quantum computing
US10826845B2 (en) 2016-05-26 2020-11-03 1Qb Information Technologies Inc. Methods and systems for quantum computing
US10824478B2 (en) 2016-06-13 2020-11-03 1Qb Information Technologies Inc. Methods and systems for quantum ready and quantum enabled computations
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WO2019241879A1 (fr) 2018-06-18 2019-12-26 1Qb Information Technologies Inc. Résolveurs propres quantiques à navigation variationnelle et adiabatique
US10671696B2 (en) 2018-10-04 2020-06-02 International Business Machines Corporation Enhancing hybrid quantum-classical algorithms for optimization
US11947506B2 (en) 2019-06-19 2024-04-02 1Qb Information Technologies, Inc. Method and system for mapping a dataset from a Hilbert space of a given dimension to a Hilbert space of a different dimension
WO2024027933A1 (fr) * 2022-08-05 2024-02-08 Friedrich-Alexander-Universität Erlangen-Nürnberg Procédé de calcul quantique pour résoudre des problèmes d'optimisation combinatoire
CN117497092A (zh) * 2024-01-02 2024-02-02 合肥微观纪元数字科技有限公司 基于动态规划和量子退火的rna结构预测方法及系统
CN117497092B (zh) * 2024-01-02 2024-05-14 微观纪元(合肥)量子科技有限公司 基于动态规划和量子退火的rna结构预测方法及系统

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