Quantum processors and methods for training quantum processors

Abstract

A method for solving computational tasks, including optimization or inference tasks, includes: receiving data representing the computational task; processing the data using a quantum processor; and outputting a solution to the computational task. The quantum processor has been trained on training data to process inputs representing the computational task to output a solution to the computational task. Training the quantum processor includes determining training values ​​for system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of the initial state of the quantum processor, which includes a plurality of logical quantum nodes and a control quantum node, and the state of the bath; and iteratively determining whether to enter a hidden node training phase or a control node training phase, and for each iteration in which it is determined to enter the hidden node training phase, setting the control node to a non-interactive state and iteratively changing the learning and non-learning phases of the quantum nodes.

Description

[0001] This application is a divisional application of the invention patent application filed on December 22, 2016, with Chinese application number 201680082538.9 and entitled "A device for coupling qubits and a method for training a quantum processor to solve machine learning inference problems". Technical Field

[0002] This specification relates to the construction and programming of quantum hardware for machine learning processing. Background Technology

[0003] Artificial intelligence tasks can be transformed into machine learning optimization problems. To perform artificial intelligence tasks, information processing models can be trained using dissipative quantum dynamics graphs to generate desired probability distributions for hard optimization and inference tasks.

[0004] Information processing models can provide statistical descriptions of some input patterns consistent with the model's internal state and the noisy world around it. The model can develop stable internal states through sufficient exposure to the training data, enabling it to make its own predictions about the statistical behavior of other patterns not included in the training data. Learning strategies can be designed for encoding, programming, and machine reading, and can be used to solve hard combinatorial optimization and inference tasks with desired accuracy.

[0005] Quantum processors inevitably exist in the hybrid quantum-classical world due to quantum fluctuations caused by environmental interactions and inherent control errors in the system. The structure and dynamics of such processors can be extremely complex, making it nearly impossible to solve the equations of motion that analytically or digitally capture their behavior using known algorithms. Furthermore, quantum processors typically require additional quantum error correction processes, which can be very demanding. In particular, analog quantum processors (such as quantum annealing processors and adiabatic quantum computing architectures) struggle with scalability when encoding solutions to a given hard optimization or inference task into equilibrium ground states with typically small minimum gaps given by Boltzmann distributions.

[0006] The information processing model includes quantum hardware constructed and programmed to perform quantum computing without the extremely demanding process of quantum error correction. Quantum hardware provides a realistic, near-term engineering approach to quantum computing that does not suffer from known scalability and implementation problems. It offers robust encoding that guarantees dynamic robustness with respect to perturbations and enhances performance with respect to time complexity. Specifically, quantum hardware constructs non-informational units with auxiliary degrees of freedom, which can be used to perform dissipative quantum engineering without bath engineering. Summary of the Invention

[0007] The innovative aspects of the subject matter described in this specification can be embodied in a device comprising: a plurality of logical quantum nodes, each logical quantum node including an input quantum node, a hidden quantum node, and an output quantum node, wherein each of the plurality of logical quantum nodes is configurable to switch between a clamped state and an unclamped state; a plurality of control quantum nodes, each of the plurality of control quantum nodes being configurable to switch between a clamped state, an unclamped state, or a non-interacting state, wherein in the non-interacting state, the control quantum node does not affect any other node it is coupled to; and a plurality of quantum node couplers, each coupler being configured to couple a pair of quantum nodes, wherein: the coupler couples at least an input quantum node and a hidden quantum node to a first control quantum node; and the coupler couples at least a hidden quantum node and an output quantum node to a second control quantum node.

[0008] Other embodiments of this aspect include corresponding computer systems, apparatus, and methods. A system of one or more computers can be configured to perform specific operations or actions by software, firmware, hardware, or combinations thereof installed on the system, which, in operation, cause the system to perform the actions. One or more computer programs can be configured to perform specific operations or actions by including instructions that, when executed by a data processing device (e.g., one or more computers or computer processors), cause the device to perform the actions.

[0009] Each of the foregoing and other embodiments may optionally include one or more of the following features, individually or in combination. In some implementations, during the hidden node training phase, the control quantum node is in a non-interacting state during the learning and non-learning phases, and during the control node training phase, the control quantum node is in an unclamped state during the learning and non-learning phases.

[0010] In some implementations, the hidden quantum node is in an unclamped state during the training phase and non-learning phases.

[0011] In some implementations, during the training phase of the hidden node, the input quantum node and the output quantum node are in a clamped state during the learning phase and in an unclamped state during the non-learning phase.

[0012] In some implementations, during the training phase of the control node, the hidden quantum node is in a clamped state during both the learning and non-learning phases.

[0013] In some implementations, during the training phase of the control node, the input quantum node and the output quantum node are in a clamped state during the learning phase and in an unclamped state during the non-learning phase.

[0014] In some implementations, the first and second control quantum nodes are the same control quantum node; a coupler couples the input quantum node to the hidden quantum node; and a coupler couples the hidden quantum node to the output quantum node.

[0015] In some implementations, one or more of the plurality of control quantum nodes include a quantum speed controller node.

[0016] In some implementations, one or more of the plurality of control quantum nodes represent non-information carrying degrees of freedom.

[0017] In some implementations, one or more of the plurality of logical quantum nodes represent information carrying degrees of freedom.

[0018] In some implementations, one or more of the quantum nodes are superconducting units.

[0019] In some implementations, one or more of the quantum nodes are constructed from Josephson junctions and capacitors connected in parallel.

[0020] In some implementations, one or more of the plurality of logical quantum nodes are configured to have the same precision as the control superconducting unit.

[0021] In some implementations, one or more of the plurality of control superconducting units are configured to have lower precision than the logic superconducting unit.

[0022] In some implementations, one or more of the superconducting qubits of the logic superconducting unit are constructed from Josephson junctions and capacitors connected in parallel, and the superconducting qubits of the control superconducting unit are constructed from multi-junction Josephson cells, inductors and capacitors connected in parallel and / or in series to construct the desired N-level controllable control system.

[0023] In some implementations, one or more of the quantum node couplers are inductive couplers.

[0024] The innovative aspects of the subject matter described in this specification can be embodied in a method comprising the actions of: receiving a set of training data; preparing an arbitrary initial quantum state, wherein the initial quantum state is a tensor product of the initial state of a quantum processor comprising multiple logical quantum nodes and a control quantum node with the state of the bath; defining (i) a hidden node training phase of the quantum node, (ii) a control node training phase of the quantum node, (iii) a learning phase of the quantum node, and (iv) a non-learning phase of the quantum node; iteratively determining whether to enter the hidden node training phase or the control node training phase; for each iteration in which it is determined to enter the hidden node training phase: setting the control node to a non-interacting state; iteratively changing the learning and non-learning phases of the quantum node.

[0025] Other embodiments of this aspect include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform actions of the method. A system of one or more computers can be configured to perform specific operations or actions by software, firmware, hardware, or combinations thereof installed on the system, which, in operation, causes the system to perform the actions. One or more computer programs can be configured to perform specific operations or actions by including instructions that, when executed by a data processing device (e.g., one or more computers or computer processors), cause the device to perform the actions.

[0026] Each of the foregoing and other embodiments may optionally include one or more of the following features, individually or in combination. In some implementations, iteratively changing the learning and non-learning phases of a quantum node includes, for each iteration prior to an event completion,: switching the learning and non-learning phases of the quantum node; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the machine learning problem is encoded in the steady state; performing a quantum measurement in the steady state; determining whether the measurement consequence is within a given distance of a known result; and determining that a completion event has occurred when the measurement consequence is within a given distance of a known result.

[0027] In some implementations, the method further includes: for each iteration in which it is determined to enter the training phase of the control node: setting the control node to an unclamped state; iteratively changing the learning and non-learning phases of the quantum node.

[0028] In some implementations, iteratively changing the learning and non-learning phases of a quantum node includes, for each iteration prior to the completion event: switching the learning and non-learning phases of the quantum node; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein the solution to the machine learning problem is encoded in the steady state; performing a quantum measurement in the steady state; determining whether the measurement consequence is within a given distance of the known result; and determining that the completion event has occurred when the measurement consequence is within a given distance of the known result.

[0029] In some implementations, for each iteration in which the hidden node is determined to enter the training phase, the method further includes setting the hidden quantum node to an unclamped state during the learning phase and the non-learning phase.

[0030] In some implementations, the method also includes setting the input and output quantum nodes to a clamped state during the learning phase and setting the input and output quantum nodes to an unclamped state during the non-learning phase.

[0031] In some implementations, setting the input and output quantum nodes to a clamped state during the learning phase includes clamping the input and output hidden nodes to the training data.

[0032] In some implementations, for each iteration in which the control node is determined to enter the training phase, the method further includes setting the hidden quantum node to a clamped state during the learning phase and the non-learning phase.

[0033] In some implementations, setting the hidden quantum node to the clamped state includes clamping the hidden quantum node to the learning value during the training phase of the hidden node.

[0034] In some implementations, the method further includes setting the input and output quantum nodes to a clamped state during the learning phase and setting the input and output quantum nodes to an unclamped state during the non-learning phase.

[0035] In some implementations, setting the input and output quantum nodes to the clamped state during the learning phase includes clamping the input and output hidden nodes to the training data.

[0036] In some implementations, the initial state of the quantum processor is an entangled quantum state.

[0037] In some implementations, the evolution of the quantum state under the dissipative quantum graph ensures that a steady state is reached.

[0038] In some implementations, the steady state is the only steady state.

[0039] In some implementations, the steady state is a non-equilibrium state.

[0040] In some implementations, the non-equilibrium steady state has a corresponding fictitious Hamiltonian, wherein the energy spectrum of the fictitious Hamiltonian encodes the solution to the machine learning problem.

[0041] In some implementations, the evolution of the quantum state is designed by a quantum speed controller without obtaining any bath of degrees of freedom.

[0042] In some implementations, the steady state essentially converges to the desired state, and the desired state gives a result that is substantially close to the desired outcome.

[0043] In some implementations, the quantum measurement is a positive operator value measurement.

[0044] In some implementations, the method also includes providing a training quantum processor for use in machine learning tasks.

[0045] In some implementations, determining whether the measurement consequence is within a given distance from the known result further includes calculating the relative entropy between the measurement consequence and the known result.

[0046] In some implementations, determining whether the measurement consequence is within a given distance from the known result further includes performing a chi-square test.

[0047] Further innovations of the subject matter described in this specification can be embodied in a device comprising: a plurality of logical quantum nodes, each logical quantum node including an input quantum node, a hidden quantum node, and an output quantum node, wherein each of the plurality of logical quantum nodes is configurable to switch between a clamped state and an unclamped state; a plurality of control quantum nodes, each of the plurality of control quantum nodes being configurable to switch between a clamped state, an unclamped state, or an initial default state; and a plurality of quantum node couplers, each coupler being configured to couple a pair of quantum nodes, wherein: the coupler couples at least an input quantum node and a hidden quantum node to a first control quantum node; and the coupler couples at least a hidden quantum node and an output quantum node to a second control quantum node.

[0048] Other embodiments of this aspect include corresponding computer systems, apparatus, and methods. A system of one or more computers can be configured to perform specific operations or actions by software, firmware, hardware, or combinations thereof installed on the system, which, in operation, cause the system to perform the actions. One or more computer programs can be configured to perform specific operations or actions by including instructions that, when executed by a data processing device (e.g., one or more computers or computer processors), cause the device to perform the actions.

[0049] Each of the foregoing and other embodiments may optionally include one or more of the following features, individually or in combination. In some implementations, the control quantum node is in a clamped state during a first learning phase and a first non-learning phase, and in an unclamped state during a second learning phase and a second non-learning phase.

[0050] In some implementations, the hidden quantum node is in an unclamped state during the first learning phase and the first non-learning phase.

[0051] In some implementations, during the first learning phase, the input quantum node and the output quantum node are in a clamped state, and during the first non-learning phase, the input quantum node and the output quantum node are in an unclamped state.

[0052] In some implementations, the hidden quantum node is in a clamped state during the second learning phase and the second non-learning phase.

[0053] In some implementations, during the second learning phase, the input quantum node and the output quantum node are in a clamped state, and during the second non-learning phase, the input quantum node and the output quantum node are in an unclamped state.

[0054] In some implementations, the first and second control quantum nodes are different control quantum nodes; the input quantum node and the hidden quantum node are not coupled by a coupler; and the hidden quantum node and the output quantum node are not coupled by a coupler.

[0055] In some implementations, one or more of the plurality of control quantum nodes include a quantum speed controller node.

[0056] In some implementations, one or more of the plurality of control quantum nodes represent non-information carrying degrees of freedom.

[0057] In some implementations, one or more of the plurality of logical quantum nodes represent information carrying degrees of freedom.

[0058] In some implementations, the quantum node is a superconducting unit.

[0059] In some implementations, one or more of the quantum nodes are constructed using parallel-connected Josephson junctions and capacitors.

[0060] In some implementations, one or more of the plurality of logical quantum nodes are configured to have the same precision as the control superconducting unit.

[0061] In some implementations, one or more of the plurality of control superconducting units are configured to have lower precision than the logic superconducting unit.

[0062] In some implementations, one or more superconducting qubits of the logic superconducting unit are constructed using parallel-connected Josephson junctions and capacitors, and the superconducting qubits of the control superconducting unit are constructed using parallel and / or series-connected multi-junction Josephson cells, inductors, and capacitors to construct the desired N-level controllable control system.

[0063] In some implementations, one or more of the plurality of quantum node couplers are inductive couplers.

[0064] Further innovative aspects of the subject matter described in this specification can be embodied in a method comprising the actions of: receiving a set of training data; preparing an arbitrary initial quantum state, wherein the initial quantum state is a tensor product of the initial state of a quantum processor comprising multiple logical quantum nodes and a control quantum node and the state of the bath; defining (i) a first learning phase of the quantum node, (ii) a second learning phase of the quantum node, (iii) a first non-learning phase of the quantum node, and (iv) a second non-learning phase of the quantum node; iteratively determining whether to enter the first learning phase or the first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting the control node to a clamped state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to a machine learning problem is encoded in the steady state; performing a quantum measurement in the steady state; determining whether the measurement consequence is within a given distance from a known result; and determining that a completion event has occurred when the measurement consequence is within a given distance from a known result.

[0065] Other embodiments of this aspect include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform actions of the method. A system of one or more computers can be configured to perform specific operations or actions by software, firmware, hardware, or combinations thereof installed on the system, which, in operation, causes the system to perform the actions. One or more computer programs can be configured to perform specific operations or actions by including instructions that, when executed by a data processing device (e.g., one or more computers or computer processors), cause the device to perform the actions.

[0066] Each of the foregoing and other embodiments may optionally include one or more of the following features, individually or in combination. In some implementations, the method includes: entering a second learning phase, including setting a control node to an unclamped state; evolving a quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to a machine learning problem is encoded in the steady state; performing a quantum measurement in the steady state; determining whether the measurement consequence is within a given distance from a known result; and determining that a completion event has occurred when the measurement consequence is within a given distance from the known result.

[0067] In some implementations, the method further includes, for each iteration in which entry into the first non-learning phase is determined: setting the control node to a clamped state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the machine learning problem is encoded in the steady state; performing a quantum measurement in the steady state; determining whether the measurement consequence is within a given distance from the known result; and determining that a completion event has occurred when the measurement consequence is within a given distance from the known result.

[0068] In some implementations, the method further includes: entering a second non-learning phase, including setting the control node to an unclamped state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein the solution to the machine learning problem is encoded in the steady state; performing a quantum measurement in the steady state; determining whether the measurement consequence is within a given distance from the known result; and determining that a completion event has occurred when the measurement consequence is within a given distance from the known result.

[0069] In some implementations, the method further includes setting the hidden quantum node to an unclamped state for each iteration in which it is determined to enter the first learning phase and for each iteration in which it is determined to enter the first non-learning phase.

[0070] In some implementations, the method further includes setting the input and output quantum nodes to a clamped state for each iteration in which it is determined to enter the first learning phase, and setting the input and output quantum nodes to an unclamped state for each iteration in which it is determined to enter the first non-learning phase.

[0071] In some implementations, setting the input and output quantum nodes to a clamped state for each iteration in which the first learning phase is determined includes clamping the input and output quantum nodes to the training data.

[0072] In some implementations, the method further includes setting the hidden quantum node to a clamped state for each iteration in which the second learning phase is entered, and for each iteration in which the second non-learning phase is entered.

[0073] In some implementations, the method further includes setting the input and output quantum nodes to a clamped state for each iteration in which the second learning phase is entered, and setting the input and output quantum nodes to an unclamped state for each iteration in which the second non-learning phase is entered.

[0074] In some implementations, the method further includes setting the input and output quantum nodes to a clamped state for each iteration in which the second learning phase is entered, including clamping the input and output quantum nodes to the training data.

[0075] In some implementations, setting the control node to the clamped state for each iteration in which the first non-learning phase is determined to be entered also includes clamping the control node to the equilibrium state of the second learning phase.

[0076] In some implementations, setting the control node to the clamped state for each iteration in which it is determined to enter the first learning phase after the second non-learning phase has been completed also includes clamping the control node to the equilibrium state of the second non-learning phase.

[0077] In some implementations, the initial state of the quantum processor is an entangled quantum state.

[0078] In some implementations, the evolution of quantum states under a dissipative quantum graph ensures that a steady state is reached.

[0079] In some implementations, the steady state is the only steady state.

[0080] In some implementations, the steady state is a non-equilibrium state.

[0081] In some implementations, the non-equilibrium steady state has a corresponding fictitious Hamiltonian, wherein the energy spectrum of the fictitious Hamiltonian encodes the solution to the machine learning problem.

[0082] In some implementations, the evolution of quantum states is designed by a quantum speed controller without requiring any bath of degrees of freedom.

[0083] In some implementations, the steady state essentially converges to the desired state, and the desired state gives a result that is substantially close to the desired outcome.

[0084] In some implementations, the quantum measurement is a positive operator value measurement.

[0085] In some implementations, the method also includes providing a training quantum processor for use in machine learning tasks.

[0086] In some implementations, determining whether the measurement consequence is within a given distance from the known result further includes calculating the relative entropy between the measurement consequence and the known result.

[0087] In some implementations, determining whether the measurement consequence is within a given distance from the known result further includes performing a chi-square test.

[0088] Details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the following description. Other features, aspects, and advantages of this subject matter will become apparent from the specification, drawings, and claims. Attached Figure Description

[0089] Figure 1 This is a flowchart of an example iteration used to obtain solutions to hard optimization or inference tasks.

[0090] Figure 2A This is a flowchart of an example process for training a QSM with weak plasticity to obtain solutions to hard optimization or inference tasks.

[0091] Figure 2B This is a flowchart of an example learning process used to train hidden nodes of a QSM with weak plasticity.

[0092] Figure 2C This is a flowchart of an exemplary non-learning process for training hidden nodes of a QSM with weak plasticity.

[0093] Figure 2D This is a flowchart of an example learning process used to train control nodes of a QSM with weak plasticity.

[0094] Figure 2E This is a flowchart of an exemplary non-learning process for training control nodes of a QSM with weak plasticity.

[0095] Figure 3A This is a flowchart of an example process for training a highly plastic QSM to obtain solutions to hard optimization or inference tasks.

[0096] Figure 3B This is a flowchart of an example learning process used to train nodes of a highly plastic QSM.

[0097] Figure 3C This is a flowchart of an exemplary non-learning process for training nodes of a highly plastic QSM.

[0098] Figure 4A This is a schematic diagram of an exemplary quantum processor 400 for a QSM with weak plasticity, based on superconducting qubits within the connectivity of a chimeric graph.

[0099] Figure 4B This is a schematic diagram of an exemplary quantum processor 401 for a highly malleable QSM based on superconducting qubits within the connectivity of a chimeric graph.

[0100] Figure 5A This is a schematic diagram showing a one-dimensional chain of qubits in a quantum processor used to perform quantum inference processing with strong quantum plasticity without introducing auxiliary qubits.

[0101] Figure 5B This is a schematic diagram showing a one-dimensional chain of qubits in a quantum processor used to perform quantum inference processing with strong quantum plasticity.

[0102] Figure 6A This is a schematic diagram illustrating the structure and interaction of three qubits in a quantum processor.

[0103] Figure 6B This is a schematic diagram illustrating the structure and interaction of three qubits in a quantum processor. Detailed Implementation

[0104] Overview

[0105] Machine learning and statistical modeling can be used to encode dependency between variables in a learning model, which in turn can be used to infer the values ​​of unknown variables given the values ​​of known variables. Energy-based learning models capture this dependency by associating a scalar energy with each configuration of a variable. During the statistical inference phase, some observed values ​​of the variables can be clamped, and configurations of the remaining variables that minimize the scalar energy can be found. Learning can then include finding an energy function in which the observed configurations, or correct values, of the variables are assigned lower energy than unobserved or incorrect configurations. A loss function can be used to measure the quality of the available energy function.

[0106] For example, Boltzmann machines can be used to learn a probability distribution over a set of inputs. A Boltzmann machine is a neural network that includes hidden and visible nodes connected by weighted connections. During the learning process, training data can be fed to the network, and the connection weights can be updated according to learning rules. The learning process involves iterative updates until the network reaches an equilibrium state. A Boltzmann machine has a scalar energy value associated with each state of the network, and the equilibrium state can be associated with a local minimum in the energy function.

[0107] The information processing model and corresponding quantum hardware in this specification can be considered as a generalization of the quantum mechanism (regime) and nonequilibrium dynamics of this energy-based learning model, such as the Boltzmann machine. The model defines a quantum statistical machine (“QSM”) that can, for example, utilize dissipative quantum dynamical mappings to solve hard optimization and inference tasks by generating desired probability distributions.

[0108] A QSM consists of three distinct classes of strongly interacting degrees of freedom: visible quantum space, hidden quantum subspace, and control quantum subspace or subsystem. Each class of strongly interacting degrees of freedom can be referred to as a class of qubits or nodes. A QSM can be defined as a programmable, non-equilibrium ergodic open quantum Markov chain with a unique attractive steady state in the space of density operators. The solution to an information processing task (e.g., statistical inference or optimization task) can be encoded into the quantum statistics of the attractive steady state, where quantum inference can be performed by minimizing the energy of the real or fictitious quantum Hamiltonian. A QSM can be constructed such that the dynamics of the control degrees of freedom ensure that the QSM approaches an effective steady state in a desired finite mixing time τ without access to any bath degrees of freedom, i.e., the control degrees of freedom perform dissipative quantum engineering without bath engineering. All statistical properties of this state can be derived with desired accuracy δ. Furthermore, the coupling between the visible and hidden nodes of the QSM can be trained to solve hard optimization or inference tasks. For example, QSM coupling can be trained such that the quantum statistics of the attractive steady state associated with a set of quantum observables on the visible node follow the desired accuracy ∈ sampling arbitrary probability distribution function.

[0109] Similar to classical machine learning, quantum inference is a crucial process in QSM learning. Quantum inference may involve clamping a set of quantum observables or their consequences and finding the configuration of the residual variables that leads to a low-rank attractive steady state in a quantum Hamiltonian system. These low-rank steady states can be viewed as minimizing energy functions that represent the ground state of a real or hypothetical Hamiltonian system under equilibrium or non-equilibrium mechanisms.

[0110] QSM introduces the concept of quantum plasticity as a quantum counterpart to biologically inspired post-von Neumann architectures known as neuromorphic computing architectures, capable of becoming plastic or actual biological neural networks, such as those known to be plastic in the neocortex. QSM can be implemented in quantum hardware to realize quantum plasticity in quantum processors.

[0111] Overview of the QSM algorithm

[0112] To obtain a solution to a given hard optimization or inference task, QSM can implement iterative quantum inference and quantum machine learning and non-learning algorithms. For example, in some implementations, QSM can perform several iterations to sample the desired probability distribution. Figure 1 A flowchart of a single iteration of example process 100 for obtaining a solution to a hard optimization or inference task is shown. Example process 100 can be executed multiple times to obtain a solution. Quantum inference tasks can be transformed into quantum machine learning problems, which can be represented in a machine-readable form.

[0113] The quantum system is prepared in a random quantum state (step 102), which includes the QSM density operator and the tensor product of the thermal bath degrees of freedom, and can be given by the following formula (1).

[0114]

[0115] In formula (1), ρ VHG (0) is a random state of the visible v, hidden h, and control g nodes, and ρ B (0) represents the thermal state of the bath at the initial time. In some implementations, ρ VHG (0) is an entangled state.

[0116] In some implementations, the QSM can rely on one or more auxiliary control nodes acting as quantum speed controller (QG) nodes. The QG nodes can represent the set of all non-informational quantities with quantum degrees of freedom and manage the interaction between the informational quantities with the bath. For time-independent Hamiltonians, using QG nodes as control nodes can increase the interaction between the QSM system and the bath in a controlled manner to create a robust steady state and reduce the required mixing time. For time-dependent Hamiltonians, using QG nodes as control nodes can be further viewed as an error correction strategy. QG nodes can enable the execution of energy-dissipative quantum engineering without bath engineering, as will be further described below with reference to step (106).

[0117] The quantum system evolves under the action of a linear quantum dynamical map. In some embodiments, the linear quantum dynamical map may be a subset of linear quantum dynamical maps that are completely positive and preserve the trajectory under the assumption that the initial system and the bath are separable. In other embodiments, the QSM can be generalized to evolve under the action of a more general linear Hermitian map, since the general linear map can be constructed by subtracting two completely positive quantum graphs. The quantum graph can be induced by the Hamiltonians of the visible, hidden, and QG nodes and their interactions with the bath (step 104). The total Hamiltonian of the QSM's interaction with the bath can be given by the following formula (2).

[0118] H tot =H VHG +H B +H VHG-B (2)

[0119] Typically, the Hamiltonian of the QSM, the thermal bath, and their interactions can be time-dependent. The evolution of the quantum state of the QSM can be expressed as given by the following formula (3).

[0120]

[0121] In formula (3), depending on, for example, whether the Hamiltonian of QSM and its interaction with the hot bath is time-dependent or time-independent, the unitary operator can be expressed as: or U tot (t)=exp[-itH tot Assuming the system and bath are initially separable, the effective dynamics of the QSM can be expressed as a dynamical mapping of quantum trajectory preservation, given by the following equation (4).

[0122]

[0123] In formula (4), and A set of output states formed by a quantum graph can be closed under convex combinations and multiplication.

[0124] Quantum states evolve under the influence of quantum graphs. Quantum dynamics can be designed using QG degrees of freedom, allowing the quantum system to perform dissipative engineering without bath engineering (step 106). QG nodes can facilitate the engineering environment, and the corresponding control parameters are QG interaction Hamiltonians.

[0125] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss (Step 106). For any non-ergodic or weakly ergodic quantum dynamics mapping acting on information with degrees of freedom, there can exist an auxiliary system including auxiliary nodes such that the quantum dynamics of information with degrees of freedom becomes strongly ergodic. As described above regarding step 102, the QSM can be constructed to include a class of quantum speed controller auxiliary nodes, which include non-information with degrees of freedom. In addition to managing the interaction between information with degrees of freedom and the heat bath, the quantum speed controller mode can ensure that the quantum system containing information with degrees of freedom is strongly ergodic. Furthermore, for any programmable multi-agent open quantum system with one or more steady states that interacts with a controllable but well-characterized heat bath and includes information with degrees of freedom, the quantum speed controller auxiliary system can generate a unique programmable quantum attractor in the information of the system with degrees of freedom. Thus, by construction, the QSM can have a unique attractor steady state ρ. ss It can always asymptotically reach...

[0126] The existence and uniqueness of steady states enable the introduction of energy-based learning models into quantum states. Solutions to optimization or statistical inference problems can be encoded into the attractive steady state of a QSM. The attractive steady state can be consistent with the ground state of the corresponding fictitious Hamiltonian, which can be used to encode the solution to the problem. A quantum thermodynamic scheme can be used to define the fictitious Hamiltonian and the corresponding partition function of the nonequilibrium system. The explicit relation of the fictitious Hamiltonian can be written as given by the following formula (5).

[0127]

[0128] The density operator ρ can be recovered using the relationship given above. ss =ρ VHG (τ).

[0129] The aforementioned relationships, such as equations (1)-(5), can provide scalability for the QSM because any quantum measurement on the QSM is derived from the ground state of the fictitious Hamiltonian rather than H. VHG The actual thermal state of (τ) is sampled. In contrast, quantum annealers or adiabatic quantum computers rely on the encoding and readout of the ground state of the physically free Hamiltonian or any other form of thermal distribution of its eigenstates. In particular, simulated quantum processors encode the solution to the inference task as an equilibrium ground state with a minimal gap, given by the Boltzmann distribution at finite temperatures, with a typically exponentially small gap. Increasing the size of the inference problem under consideration (and inevitably increasing the size of the quantum processor required to solve it) reduces the gap, making simulated quantum processors unsatisfactory due to the required scalability conditions.

[0130] Quantum measurements can be performed on a unique attractive steady state, which in its most general form is given by positive operator value measurement (POVM) (step 108). The measurement consequences provide solutions to hard optimization or inference problems that can be encoded into the unique attractive steady state. The measurement consequences can be in a machine-readable form and correspond to a fictitious Hamiltonian. The effective energy value of the ground state.

[0131] During the processing of 100, the quantum system can perform Hamiltonian evolution in finite time. Therefore, the ground-state fidelity may be less than unified, and the processing may need to be repeated to obtain reasonable statistics about the solution. In some implementations, the quantum system can therefore repeat the above processing to obtain the final solution to a hard optimization or inference task, or to sample the desired probability distribution.

[0132] A QSM can be trained on a set of training data to determine the system parameter values. Once trained, the QSM can accept new hard optimization or inference tasks and use the trained system parameters to process the system inputs to obtain solutions to the hard optimization or inference tasks. During the training process, the QSM can implement iterative quantum inference as well as quantum machine learning and non-learning algorithms.

[0133] Figure 2A A flowchart of an example process 200 for training a QSM with weak plasticity to obtain solutions to hard optimization or inference tasks is shown. This process is described as being executed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, the following... Figure 4A The quantum processor 400 can perform 200 operations.

[0134] Process 200 can be viewed as a self-organizing process, comprising two separate iterative processes for training the hidden node and the control node, respectively. Each iterative process includes two alternating phases of learning and non-learning. The states of the input quantum node, output quantum node, hidden quantum node, and control quantum node during the hidden node training process and the control node training process are... Figure 2B-2E The details are provided in the text and described in the table below.

[0135]

[0136] The quantum system receives training data (step 201). The training data may include input training data and output training data. In some implementations, the training data may be some known probability distribution of the input data. The QSM can be exposed to the training data to learn how to predict the statistical behavior of additional patterns not included in the training data.

[0137] The quantum system is prepared in a random quantum state (step 202), which includes the QSM density operator given in equation (1) above and the tensor product of the thermal bath degrees of freedom. In equation (1), ρ VHG (0) is a random state of the visible v, hidden h, and control g nodes, and ρ B (0) represents the thermal state of the bath at the initial time. In some implementations, ρ VHG (0) is an entangled state. During state preparation, the control node can be turned off, and the heat bath may be uncontrollable.

[0138] In some implementations, the control node is a quantum speed controller (QG) node. A QG node can represent the set of all non-information with quantum degrees of freedom and manages the interaction between the information with degrees of freedom and the bath. For time-independent Hamiltonians, using a QG node as the control node can controllably increase the interaction between the QSM system and the bath to create a robust steady state and reduce the required mixing time. For time-dependent Hamiltonians, using a QG node as the control node can be further considered as an error correction strategy. QG nodes enable the execution of dissipative quantum engineering without bath engineering.

[0139] The QSM training process can be an iterative process comprising two separate processes for training the hidden nodes and the control nodes, respectively, wherein each iterative process includes two alternating phases of learning and non-learning. The quantum system thus determines whether to enter the hidden node training phase or the control node training phase (step 203). If the previous iteration included a hidden node training phase, the quantum system can enter the control node training phase, and vice versa. For clarity, process 200 is described below as first determining whether to enter the hidden node training phase in step 203.

[0140] The quantum system enters the hidden node training phase, where the hidden nodes of the QSM are trained to iteratively capture high-level dependencies between all or a subset of the system variables in the received training dataset. During the hidden node training phase, control node coupling can be disabled, meaning the control nodes do not interact with the logic nodes. The hidden node training phase can be understood as an approximate diagonalization of a quantum Markov chain representing the dynamics of visible and hidden nodes. The hidden node training phase can also be considered a quantum correspondence to classical clustering techniques such as principal component analysis or spectral clustering.

[0141] After determining in step 203 whether to enter the hidden node training phase, the system determines whether to enter the learning phase or the non-learning phase of the hidden node (step 204). In some implementations, the quantum system may enter the learning phase if the previous iterations included a non-learning phase, and the quantum system will enter the non-learning phase if the previous iterations included a learning phase. For clarity, process 200 will be described below as first determining whether to enter the learning phase in step 204.

[0142] The quantum system performs learning processing for the hidden nodes (step 205). See below for reference. Figure 2B The learning process used to train the hidden nodes is described in more detail.

[0143] The quantum system performs non-learning processing for hiding nodes (step 206). See below for reference. Figure 2CA more detailed description of the non-learning processing used to train hidden nodes.

[0144] The quantum system can perform one or more iterations (steps 205 and 206) of learning processing and non-learning processing for the hidden nodes to temporarily train them. After temporarily training the hidden nodes, the system can determine in step 203 to enter the control node training phase.

[0145] Quantum systems can enter a control node training phase, in which the control nodes of a QSM are trained, and the processor itself can be allowed to adapt to manipulate environmental fluctuations ignored in the hidden node training phase. The control node training phase can be mathematically understood as a phase in which the control nodes adjust themselves to create optimal overlap between otherwise orthogonal, invariant subspaces that result in a frozen state outside the quantum processor.

[0146] After determining in step 203 whether to enter the control node training phase, the system determines whether to enter the control node's learning phase or non-learning phase (step 207). In some implementations, the quantum system may enter the learning phase if the previous iterations included a non-learning phase, and may enter the non-learning phase if the previous iterations included a learning phase. For clarity, process 200 will be described below as first determining whether to enter the learning phase in step 207.

[0147] The quantum system performs learning processing for controlling the nodes (step 208). See below for reference. Figure 2D The learning process used to train the control nodes is described in more detail.

[0148] The quantum system performs non-learning processing for controlling the nodes (step 209). See below for reference. Figure 2E A more detailed description of the non-learning processing used to train control nodes.

[0149] The quantum system can perform one or more iterations (steps 208 and 209) of learning processing and non-learning processing for the control nodes, for temporary training of the control nodes. After the temporary training of the control nodes, the system can determine in step 203 to enter the hidden node training phase.

[0150] Process 200 can be executed iteratively to train a QSM with weak plasticity to improve the performance of the QSM. Process 200 terminates when the quantum system exhausts its training data resources. For example, when sampling from the probability distribution function (PDF), the process can terminate when it can be determined using standard metrics such as chi-square divergence or relative entropy that the obtained sampled PDF is within a given distance from the ideal PDF.

[0151] Figure 2BA flowchart of an example learning process 210 for training hidden nodes of a QSM with weak plasticity is shown. This process is described as being executed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, below... Figure 4A The quantum processor 400 can perform processing 210.

[0152] Quantum system receives at reference Figure 2A The subset of training data provided to the system in step 201 (step 211).

[0153] The quantum system configures visible, hidden, and control nodes (step 212). Visible input and output nodes can be clamped to a subset of the training data, while hidden nodes are unclamped and allowed to adjust themselves to the data structure that allows them to interact with their environment. Control nodes are decoupled.

[0154] The quantum system allows the configured quantum states to evolve under the influence of the Hamiltonians of the visible, hidden, and QG nodes and the linear quantum dynamics mappings induced by their interactions with the heat bath (step 213). The total Hamiltonian of the QSM interacting with the heat bath can be given by equation (2) above. Typically, the Hamiltonians of the QSM, the heat bath, and their interactions can be time-dependent. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective dynamics of the QSM can be expressed as a quantum trajectory-preserving dynamical mapping, for example, given by equation (4) above.

[0155] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM can possess a unique attractive steady-state ρ. ss It can be asymptotically achieved.

[0156] The quantum system mechanically samples the hidden nodes (step 214). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state.

[0157] A quantum system can determine that the measurement consequences are within a given distance from a known result (step 215). Statistical techniques and measurements, such as the chi-square test and relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0158] The quantum system increases the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 216).

[0159] Figure 2CA flowchart of an exemplary non-learning process 220 for training hidden nodes of a QSM with weak plasticity is shown. This process is described as being performed by a classical processor, such as a classical computer / or a quantum processor / or a combination thereof. For example, the following... Figure 4A The quantum processor 400 can perform 220 operations.

[0160] The quantum system configures visible, hidden, and control nodes (step 221). Visible input and output nodes, as well as hidden nodes, can be unclamped and allowed to self-adjust to interact with data structures given their environment. This step can be viewed as the "dream" phase. Control node coupling can be decoupled.

[0161] The quantum system allows the configured quantum states to evolve under the influence of the Hamiltonians of the visible, hidden, and QG nodes and the linear quantum dynamics mappings induced by their interactions with the heat bath (step 222). The total Hamiltonian of the QSM interacting with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interaction energies depend on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective kinetic energy of the QSM is expressed as the quantum trajectory-preserving kinetic mapping, given by equation (4) above.

[0162] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM can possess a unique attractive steady-state ρ. ss It can be asymptotically achieved.

[0163] The quantum system mechanically samples the visible inputs and outputs, as well as the hidden nodes (step 223). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state.

[0164] A quantum system can determine that the measurement consequences are within a given distance from a known result (step 224). Statistical techniques and measurements, such as the chi-square test and relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0165] The quantum system reduces the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 216).

[0166] The non-learning phase of hidden node training can lead to robustness against both data noise (contamination in the data) and device noise.

[0167] Figure 2DA flowchart of an example learning process 230 for training control nodes of a QSM with weak plasticity is shown. This process is described as being executed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, the following... Figure 4A The quantum processor 400 can perform 230 operations.

[0168] Quantum system receives at reference Figure 2A The second subset of training data provided to the system in step 201 (step 231).

[0169] The quantum system configures visible, hidden, and control nodes (step 232). Visible input and output nodes are clamped to training data, and hidden nodes are clamped to values ​​learned during the hidden node training phase. Control nodes are unclamped and allowed to self-adjust to the data structure that interacts with their environment and reach a steady state, which is not achieved during the hidden node learning phase.

[0170] The quantum system allows the configured quantum states to evolve under the influence of the Hamiltonians of the visible, hidden, and QG nodes and the linear quantum dynamics mappings induced by their interactions with the heat bath (step 233). The total Hamiltonian of the QSM interacting with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interaction energies depend on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective kinetic energy of the QSM is expressed as the quantum trajectory-preserving kinetic mapping, given by equation (4) above.

[0171] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM possesses a unique attractive steady-state ρ. ss It can always be asymptotically achieved.

[0172] The quantum system mechanically samples the control node (step 234). The quantum measurement, which gives its most general form through positive operator value measurement (POVM), can be performed on a unique attractive steady state.

[0173] A quantum system can determine that the measurement consequences are within a given distance from a known result (step 235). Statistical techniques and measurements, such as the chi-square test and relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0174] The quantum system increases the coupling between the two quantum speed controller degrees of freedom that are active or turned on in steady state (step 236).

[0175] Figure 2E A flowchart of an exemplary non-learning process 240 for training hidden nodes of a QSM with weak plasticity is shown. This process is described as being performed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, the following... Figure 4A The quantum processor 400 can perform 240 operations.

[0176] The quantum system configures visible, hidden, and control nodes (step 241). Visible input and output nodes, as well as control nodes, are unclamped and allowed to self-adjust to interact with data structures given their environment. Hidden nodes are clamped to values ​​learned during the hidden node training phase.

[0177] The quantum system allows the configured quantum states to evolve under the influence of the Hamiltonians of the visible, hidden, and QG nodes and the linear quantum dynamics mappings induced by their interactions with the heat bath (step 242). The total Hamiltonian of the QSM interacting with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interaction energies depend on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective kinetic energy of the QSM is expressed as the quantum trajectory-preserving kinetic mapping, given by equation (4) above.

[0178] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM possesses a unique attractive steady-state ρ. ss It can always asymptotically reach the same level as

[0179] The quantum system mechanically samples the visible inputs and outputs, as well as the hidden nodes (step 243). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state.

[0180] A quantum system can determine that the measurement consequences are within a given distance from a known result (step 244). Statistical techniques and measurements, such as the chi-square test and relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0181] The quantum system reduces the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 225).

[0182] The non-learning phase of hidden node training can lead to robustness against both data noise (contamination in the data) and device noise.

[0183] The above reference Figure 2AThe described processing 200 (and therefore the above refer to respectively) Figure 2B , 2C The subprocesses (210, 220, 230, and 240) described in 2D and 2E lead to a form of weak plasticity because the hardware can self-adjust to adapt to new environmental conditions or new problem instances not previously encountered in the previous training dataset. As the QG degrees of freedom stabilize in a specific configuration at the steady state of the entire system during the second learning and non-learning phases, the aforementioned adjustments and their corresponding fine-tuning capabilities are facilitated via the QG degrees of freedom, and can be improved overall through several iterations of the algorithm. By fundamentally altering the architecture of the information processor to adopt new conditions and data classes, the auxiliary degrees of freedom of the QG essentially contribute to the generalization of data beyond what is assigned to typical hidden nodes.

[0184] In some implementations, strong plasticity can be achieved by enhancing the determination of all mutual and internal coupling roles between all visible and hidden qubits in the QG node.

[0185] Figure 3A A flowchart of an example process 300 for training a highly plastic QSM to obtain solutions to hard optimization or inference tasks is shown. This process is described as being executed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, the following... Figure 4B The quantum processor 401 can perform 300 operations.

[0186] Process 300 can be considered a self-organizing process, comprising two separate iterative phases: learning and non-learning, for training hidden and control nodes. Each iterative phase includes either a first learning phase and a second learning phase for hidden and control nodes, or a first non-learning phase and a second non-learning phase for hidden and control nodes. The states of the input quantum node, output quantum node, hidden quantum node, and control quantum node during the learning and non-learning phases are... Figure 3B and 3C The details are described in the text and in the table below.

[0187]

[0188]

[0189] The quantum system receives training data (step 301). The training data includes input training data and output training data. In some implementations, the training data can be some known probability distribution of the input data. The QSM can be exposed to the training data in order to learn how to predict the statistical behavior of additional patterns not included in the training data.

[0190] Prepare the quantum system with random quantum states (step 302), including the QSM density operator and the tensor product of the thermal bath degrees of freedom given in Equation (1) above. In Equation (1), ρ VHG (0) represents the random state of the visible v, hidden h, and control g nodes, and ρ B (0) represents the thermal state of the bath at the initial time. In some implementations, ρ VHG (0) is an entangled state. During state preparation, the control node and its interaction with the data node are prepared using default settings, and the heat bath may be uncontrollable.

[0191] In some implementations, the control node is a quantum speed regulator (QG) node. A QG node represents the set of all non-information with quantum degrees of freedom and manages the interaction of information with degrees of freedom with the bath. For time-independent Hamiltonians, using QG nodes as control nodes increases the interaction between the QSM system and the bath in a controlled manner to create a robust steady state and reduce the required mixing time. For time-dependent Hamiltonians, using QG nodes as control nodes can be further considered as an error correction strategy. QG nodes enable the execution of dissipative quantum engineering without bath engineering. For strong plasticity, QG nodes act as couplers for all types of data qubits—both visible and hidden.

[0192] QSM training can be an iterative process, comprising two separate processes: learning and non-learning, for training hidden nodes and control nodes. The quantum system then determines whether to enter a learning phase or a non-learning phase (step 303). In some implementations, the quantum system may enter a non-learning phase if the previous iteration included a learning phase, and vice versa. For clarity, process 300 will be described below as first determining whether to enter the learning phase in step 303.

[0193] The quantum system enters a learning phase, in which the hidden and control nodes of the QSM are trained to iteratively capture high-level dependencies between all or a subset of the system variables in the received training dataset. During the learning phase, the visible input and output nodes are clamped to the training data.

[0194] After determining the entry into the hidden node training phase in step 303, the system enters the first learning phase for the hidden nodes, and the quantum system performs the first learning process for the hidden nodes (step 304). See below for reference. Figure 3B The first learning process used to train the hidden nodes is described in more detail.

[0195] The quantum system enters the second learning phase for controlling the node, and the quantum system performs the second learning process for controlling the node (step 305). See below for reference. Figure 3BThe second learning process used to train the control nodes is described in more detail.

[0196] The quantum system can perform one or more iterations (steps 304 and 305) of the first and second learning processes for hiding and controlling nodes, for temporary training of the hiding and controlling nodes. After the temporary training of the hiding and controlling nodes, the system can determine in step 303 to enter the non-learning training phase.

[0197] The quantum system enters a non-learning phase. During the non-learning phase, the visible input and output nodes are unclamped and allowed to self-adjust to meet the data structure that interacts with its environment.

[0198] When it is determined in step 303 that the system is entering the non-learning phase, the system enters the first non-learning phase for hiding nodes, and the quantum system performs the first non-learning process for hiding nodes (step 306). See below for reference. Figure 3C The first non-learning process used to train the hidden nodes is described in more detail.

[0199] The quantum system performs a second non-learning process for controlling the nodes (step 307). See below for reference. Figure 3C The second non-learning process used to train the control nodes is described in more detail.

[0200] The quantum system can perform one or more iterations of the first and second non-learning processes for training the hidden node and the control node (steps 306 and 307). After the temporary training of the control node, the system can determine in step 203 to enter the hidden node training phase.

[0201] Process 300, used to train a highly plastic QSM, can be executed iteratively to improve the performance of the QSM. Process 300 can terminate when the quantum system has exhausted its training data resources. For example, when sampling from the probability distribution function (PDF), the process can terminate when it can be determined using standard metrics such as chi-square divergence or relative entropy that the obtained sampled PDF is within a given distance from the ideal PDF.

[0202] Figure 3B A flowchart of an example learning process 310 for training nodes with a highly plastic QSM is shown. This process is described as being executed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, the following... Figure 4B The quantum processor 401 can perform processing 310.

[0203] Quantum system receives at reference Figure 3A The subset of training data provided to the system in step 301 (step 311).

[0204] The quantum system enters the first learning phase and configures visible, hidden, and control nodes (step 312). Visible input and output nodes are clamped to a subset of the training data, while hidden nodes are unclamped and allowed to self-adjust to the data structure that interacts with their environment. Control nodes are coupled to a default value or an equilibrium state from a previous non-learning phase.

[0205] The quantum system allows the configured quantum states to evolve under the influence of the Hamiltonians of the visible, hidden, and QG nodes and the linear quantum dynamics mappings induced by their interactions with the heat bath (step 313). The total Hamiltonian of the QSM interacting with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interaction energies depend on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective dynamics of the QSM can be expressed as a quantum trajectory-preserving dynamical mapping, given by equation (4) above.

[0206] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM possesses a unique attractive steady-state ρ. ss It can always be reached gradually, just like...

[0207] The quantum system mechanically samples the hidden nodes in a quantized manner (step 314). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state. Following the quantum measurement in the steady state, the system obtains the bit string configuration of the hidden nodes, which will be used in the second learning phase.

[0208] A quantum system can determine the measurement consequences within a given distance from a known result (step 315). Statistical techniques, such as the chi-square test and measurements of relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0209] The quantum system increases the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 316).

[0210] The quantum system enters the second learning phase and configures visible, hidden, and control nodes (step 317). Visible input and output nodes are clamped to training data, hidden nodes are clamped to measurements from the first learning phase, and control nodes are allowed to self-adjust to meet data structures that interact with their environment.

[0211] The quantum system allows the configured quantum states to evolve under the influence of the Hamiltonians of the visible, hidden, and QG nodes and the linear quantum dynamics mappings induced by their interactions with the heat bath (step 318). The total Hamiltonian of the QSM interacting with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interaction energies depend on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective dynamics of the QSM can be expressed as a quantum trajectory-preserving dynamical mapping, given by equation (4) above.

[0212] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM possesses a unique attractive steady-state ρ. ss It can always be reached gradually, just like...

[0213] The quantum system mechanically samples the control node in a quantized manner (step 319). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state.

[0214] The quantum system can determine the measurement consequences within a given distance from the known result (step 320). Statistical techniques such as the chi-square test and measurements of relative entropy can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0215] The quantum system increases the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 321).

[0216] Figure 3C A flowchart of an exemplary non-learning process 320 for training nodes with a highly plastic QSM is shown. This process is described as being performed by a classical processor, such as a classical computer, or a quantum processor, or a combination thereof. For example, the following... Figure 4B The quantum processor 401 can perform 320 processing operations.

[0217] The quantum system enters the first non-learning phase and configures visible, hidden, and control nodes (step 321). Visible input and output nodes, as well as hidden nodes, are unclamped and allowed to self-adjust to interact with data structures given their environment. Control nodes are coupled to a default value or an equilibrium state from the previous learning phase.

[0218] The quantum system allows the configured quantum states to evolve under the influence of a linear quantum dynamical mapping induced by the Hamiltonians of the visible, hidden, and QG nodes and their interactions with the heat bath (step 322). The total Hamiltonian of the QSM's interaction with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interactions depends on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective kinetic energy of the QSM is expressed as the quantum trajectory-preserving dynamical mapping, given by equation (4) above.

[0219] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM possesses a unique attractive steady-state ρ. ss It can always be reached gradually, just like...

[0220] The quantum system mechanically samples the hidden and visible nodes in a quantized manner (step 323). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state. Following the quantum measurement in the steady state, the system obtains the bit string configuration of the hidden nodes, which will be used in the second learning phase.

[0221] A quantum system can determine the measurement consequences within a given distance from a known result (step 324). Statistical techniques, such as the chi-square test and measurements of relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0222] The quantum system reduces the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 325).

[0223] The quantum system enters the second non-learning phase and configures visible, hidden, and control nodes (step 326). Visible input and output nodes, as well as control nodes, are allowed to self-adjust to the data structure that allows them to interact with their environment. Hidden nodes are clamped to their previous steady state.

[0224] The quantum system allows the configured quantum states to evolve under the influence of a linear quantum dynamical mapping induced by the Hamiltonians of the visible, hidden, and QG nodes and their interactions with the heat bath (step 327). The total Hamiltonian of the QSM's interaction with the heat bath can be given by equation (2) above. Typically, the Hamiltonian of the QSM, the heat bath, and their interactions depends on time. The evolution of the quantum states of the QSM can be given by equation (3) above. The effective kinetic energy of the QSM is expressed as the quantum trajectory-preserving dynamical mapping, given by equation (4) above.

[0225] After a finite mixing time, the quantum state reaches the desired attractive steady state ρ. ss As mentioned above... Figure 1 As described in step 108, through construction, the QSM possesses a unique attractive steady-state ρ. ss It can always be reached gradually, just like...

[0226] The quantum system mechanically samples the visible and control nodes in a quantized manner (step 328). The quantum measurement, which gives its most general form via positive operator value measurement (POVM), can be performed on a unique attractive steady state.

[0227] A quantum system can determine the measurement consequences within a given distance from a known result (step 329). Statistical techniques, such as the chi-square test and measurements of relative entropy, can be used to post-process and test the measurement consequences. For example, the expected accuracy of the measurement consequences can be verified.

[0228] The quantum system reduces the coupling between two quantum degrees of freedom that are effective or enabled in steady state (step 330).

[0229] The non-learning phase 320 prevents overfitting and can be considered similar to the negative contribution in the contrastive divergence method widely used in classic deep learning algorithms.

[0230] Example quantum hardware

[0231] Figure 4 is a schematic diagram of two example quantum processors, 400 and 401, with weak and strong quantum plasticity, respectively. These two diagrams are based on superconducting qubits in chimeric graph connectivity. Quantum plasticity realized by processors is inspired by biological neural networks, such as those in the neocortex, which are known to be plastic but are still widely considered to operate according to classical physical laws. Quantum plasticity can also be considered as biologically inspired post-von Neumann architectures, known as neuromorphic computing architectures, which in principle can become plastic and completely dependent on classical physical laws because they are based on CMOS transistors.

[0232] Figure 4AThis is a schematic diagram of an exemplary quantum processor 400 for a QSM with weak plasticity, based on superconducting qubits within chimeric graph connectivity. The processor includes 16 qubits 404, represented by 2 x 3 unit cells 402. The qubits are connected via programmable inductive couplers, as shown by lines connecting different qubits. Each line can represent one or more couplers between a pair of qubits. Inter-lattice connections can be ferromagnetic (+1). Intra-lattice connections can be arbitrary. By increasing the number of qubits, the size of the processor implementing the QSM can be scalable. For example, the processor can also include a larger number of qubits represented by a larger number of unit cells, such as 4 x 6 or more.

[0233] In a processor, qubits represent different categories of degrees of freedom and play different roles in computation. A qubit labeled 'i' represents an input qubit. In this example, quantum processor 400 has four input qubits. A qubit labeled 'h' is a hidden qubit. In this example, quantum processor 400 has four hidden qubits. A qubit labeled 'o' is an output qubit. In this example, quantum processor 400 has four output qubits. A qubit labeled 'g' is a control qubit. In some implementations, the control qubit is a quantum speed controller qubit. In this example, quantum processor 400 has four quantum speed controller qubits. The input, hidden, and output qubits labeled 'i, h, and o' represent information with degrees of freedom and are logical qubits used for computations performed by the quantum processor. The qubit labeled 'g' represents non-information with degrees of freedom and is a control qubit programmed to perform the function of the quantum speed controller qubits. The control qubit does not participate in the computation of configuring the logical qubits.

[0234] The processor can be configured to allow the quantum speed controller qubits to manipulate the interaction between the data qubits (i.e., input and output) and the hidden qubits, while still allowing direct interaction between the data qubits and the hidden qubits. This results in weak quantum plasticity, which provides partial robustness with respect to environmental conditions, control interactions, and tag noise.

[0235] Figure 4BThis is a schematic diagram of an exemplary quantum processor 401 for a strongly plastic QSM based on superconducting qubits within chimeric graph connectivity. The processor includes 20 qubits 404, represented by 2x3 unit lattices 402. The qubits are connected via programmable inductive couplers, as shown by lines connecting different qubits. Each line can represent one or more couplers between a pair of qubits. Inter-lattice connections can be ferromagnetic (+1). Intra-lattice connections can be arbitrary. By increasing the number of qubits, the size of the processor implementing the QSM can be scalable. For example, the processor can also include a larger number of qubits represented by a larger number of unit lattices, such as 4x6 or more.

[0236] In a processor, qubits represent different categories of degrees of freedom and play different roles in computation. A qubit labeled 'i' represents an input qubit. In this example, quantum processor 400 has four input qubits. A qubit labeled 'h' is a hidden qubit. In this example, quantum processor 400 has four hidden qubits. A qubit labeled 'o' is an output qubit. In this example, quantum processor 400 has four output qubits. A qubit labeled 'g' is a quantum speed controller qubit. In this example, quantum processor 401 has eight fully connected quantum speed controller qubits. The input, hidden, and output qubits labeled 'i', 'h', and 'o' are logic qubits used for computations performed by the quantum processor. The qubit labeled 'g' is a control qubit programmed to perform the function of the quantum speed controller qubits. The control qubit does not participate in the computation of configuring the logic qubits. The layers of the QSM are restricted such that there is no interaction between data qubits or hidden qubits.

[0237] The processor can be configured such that the quantum speed controller qubits completely determine the interaction between the data and the hidden node, while disallowing direct interaction between the input and the hidden node. This results in strong plasticity, providing efficient learning models that are robust to environmental conditions, control interactions, and label noise.

[0238] In some implementations, the logic qubits and control qubits in quantum processors 400 and 401 have the same construction. In other implementations, the control qubits have a simpler or less precise structure than the logic qubits.

[0239] Figure 5 is a schematic diagram illustrating a one-dimensional chain of two qubits in a quantum processor, used to perform quantum inference processing to achieve strong quantum plasticity. The one-dimensional chain of qubits can be represented as... Figure 4B Two implementations of the quantum processor 401.

[0240] Figure 5AThis is a schematic diagram illustrating a one-dimensional chain of qubits in a quantum processor used to perform quantum inference processing with strong quantum plasticity without introducing auxiliary qubits. In this example, the quantum processor consists of a one-dimensional chain 502 of dual-purpose superconducting control and logic qubits 504. The qubits are numbered sequentially, with odd-numbered qubits representing logic qubits and even-numbered qubits representing control qubits or coupler qubits. In some implementations, the coupler qubits may be quantum speed controller type I qubits. The logic qubits are either data qubits or hidden qubits, and for simplicity in this example, we assume an equal distribution. In other words, each even-numbered control qubit is connected to two odd-numbered logic qubits, the one on the left labeled as visible and the one on the right labeled as hidden.

[0241] In this example, the quantum learning process can be an iterative process consisting of four stages, including two learning stages and two non-learning stages. In the first learning stage, odd-numbered qubits (i.e., logical qubits) are clamped to the input and output data, and the control qubits are clamped in some random states, as referenced above. Figure 3B As described above. In the second learning phase, the quantum system clamps the hidden qubits to their steady-state values, keeps the visible qubits fixed, and allows even-numbered coupler qubits to self-adjust to meet specific input / output data structures, as described above. Figure 3B Essentially, this phase can be conceived as the physical execution of the Herbie learning rule, which dictates that nodes ignited together are wired together. In the first non-learning phase, the control node is fixed, and the visible node is not clamped. Given an initial state and other factors such as environmental interactions, the processor can be allowed to reach a new steady state. The hidden qubit is then fixed, allowing the control and visible qubits to reconfigure themselves to a new equilibrium. The above four phases can be repeated for all training data. In some implementations, the quantum system can sample from a probability distribution function (PDF). In such implementations, the algorithm terminates when it is determined that the sampled PDF obtained from the measurement consequences is within a given distance from the ideal PDF.

[0242] In the contrastive divergence method, widely used in traditional deep learning algorithms, the non-learning phase can be considered similar to the negative term. The non-learning phase prevents overfitting. Quantum inference algorithms have many advantages; for example, they avoid the extremely difficult computation of the gradient of the log-likelihood function with complexity #P.

[0243] Figure 5BThis is a schematic diagram illustrating a one-dimensional chain of qubits in a quantum processor for performing quantum inference processing with strong quantum plasticity. In this example, the quantum processor consists of a one-dimensional chain 506 of superconducting logic qubits 510 and control qubits 508. The algorithm and architecture are similar. Figure 5A The algorithm and architecture, except that the logic and control qubits act as pure qubits rather than couplers and have independent tensor product structures, interact with each other through conventional couplers such as those used for superconducting flux qubits. In some implementations, these coupler qubits can be quantum speed regulator type II qubits. Here, strong quantum plasticity can be explicitly encoded into the adaptive states of the control qubits when a unique attractive steady state is reached. Given certain fixed interactions between the logic and control qubits, the state of the control qubits determines the interactions of the logic qubits in either equilibrium or non-equilibrium steady states.

[0244] Figure 6 shows two example layouts for constructing coupled qubits with strong quantum plasticity in one dimension. Figure 6A and 6B Each provides for Figure 6A and Figure 6B The diagram shows an example layout of coupled qubits.

[0245] Figure 6A It is shown that in the same quantum processor (e.g., Figure 4A An example sequence of three coupled qubits 601, 602, and 603 in a quantum processor 400. Qubits 601, 602, and 603 can correspond to any combination of three logic qubits, three control qubits, or logic and control qubits. In this example, each qubit can be a superconducting qubit and includes a Josephson box 604. Each Josephson box can include a Josephson junction 605 connected to a capacitor. The sequence of coupled qubits can also include a greater number of coupled qubits. The qubits are subjected to an external magnetic field B, which is applied along the e3 direction perpendicular to the surface of the paper, on which a pattern is shown; the B field is represented by the symbol... mark.

[0246] In some implementations, the control qubit is a quantum speed controller type I qubit. Logical qubits can be constructed with higher precision than control qubits. Then, the lower-precision constructed control qubits can perform the functions of quantum speed controller qubits at a reduced cost. In other implementations, control qubits can be constructed using structures other than Josephson boxes, such as quantum harmonic oscillators.

[0247] Figure 6B It is shown that in the same quantum processor (e.g., Figure 4B An example sequence of three coupled qubits 606, 607, and 608 in a quantum processor 401 is shown. Qubits 606 and 608 are logic qubits used for computations performed by the quantum processor. Qubit 607 may be a control qubit. Each qubit 606, 607, and 608 may be a superconducting qubit and includes a Josephson box 609. Each Josephson box may include a Josephson junction 610. The sequence of qubits may also include a larger number of coupled qubits. A larger number of coupled qubits will alternate sequentially between control qubits and logic qubits. The qubits are acted upon by an external magnetic field B, which is applied along the e3 direction perpendicular to the surface of the paper on which the pattern is shown; the field B is denoted by the symbol... Label. A set of inductive couplers are connected between the qubits, so that the qubits are coupled along the e3-e3 direction.

[0248] In some implementations, the control qubit is a quantum speed controller type II qubit. The logic qubit can be constructed with higher precision than the control qubit. Then, the lower-precision control qubit can perform the function of a quantum speed controller qubit at a reduced cost. In other implementations, control qubits can be constructed using structures other than Josephson boxes, such as quantum harmonic oscillators.

[0249] The digital and / or quantum themes described in this specification, as well as the implementations of digital functional operations and quantum operations, can be implemented in digital electronic circuits, suitable quantum circuits, or more generally, quantum computing 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 these. The term "quantum computing system" can include, but is not limited to, a quantum computer, a quantum information processing system, a quantum encryption system, or a quantum simulator.

[0250] The digital and / or quantum themes 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-transient storage medium, for execution by a data processing device or for controlling the operation of a data processing device. 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 storage device, one or more qubits, or a combination of one or more of these. Alternatively or additionally, the program instructions can be encoded on an artificially generated propagation signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) capable of encoding digital and / or quantum information, which is generated to encode digital and / or quantum information for transmission to a suitable receiver device for execution by the data processing device.

[0251] The terms quantum information and quantum data refer to information or data carried, held, or stored in quantum systems, the smallest nontrivial system being a qubit, i.e., a system that defines the unit of quantum information. It should be understood that the term "qubit" includes all quantum systems that can be appropriately approximated as a two-level system in the appropriate context. Such quantum systems can include multi-level systems, for example, having two or more levels. For example, such systems can include atomic, electron, photon, ionic, or superconducting qubits. In many implementations, the fundamental states of computation are identified by ground and first excited states; however, it should be understood that other settings in which computational states are identified by higher-level excited states are possible. The term "data processing device" refers to digital and / or quantum data processing hardware and includes various devices, apparatuses, and machines for processing digital and / or quantum data, including, for example, programmable digital processors, programmable quantum processors, digital computers, quantum computers, multiple digital and quantum processors or computers, and combinations thereof. The device may also or further include application-specific logic circuitry, such as FPGAs (Field-Programmable Gate Arrays), ASICs (Application-Specific Integrated Circuits), or quantum simulators, i.e., quantum data processing devices designed to simulate or generate information about a particular quantum system. In particular, a quantum simulator is a purpose-specific quantum computer and does not have the capability to perform general-purpose quantum computing. In addition to the hardware, the device may optionally include code that creates an execution environment for digital and / or quantum computer programs, such as code constituting processor firmware, protocol stack, database management system, operating system, or a combination of one or more of these.

[0252] A digital computer program, which can also be referred to or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages. It can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a digital computing environment. A quantum computer program, which can also be referred to or described as a program, software, software application, module, software module, 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 such as QCL or Quipper.

[0253] Digital and / or quantum computer programs may, but do not necessarily, correspond to files in a file system. Programs may be stored as a portion of a file containing other programs or data (e.g., one or more scripts stored in a markup language document), a single file dedicated to the program in question, or multiple coordination files (e.g., files storing one or more modules, subroutines, or code sections). Digital and / or quantum computer programs can be deployed to execute on a single digital or quantum computer, or on multiple digital and / or quantum computers located at one site or distributed across multiple sites and interconnected via digital and / or quantum data communication networks. A quantum data communication network is understood as a network that can transmit quantum data using quantum systems (e.g., qubits). Typically, digital data communication networks cannot transmit quantum data, but quantum data communication networks can transmit both quantum data and digital data.

[0254] The processing and logic flows described in this specification can be executed by one or more programmable digital and / or quantum computers, which operate in conjunction with one or more digital and / or quantum processors to execute one or more digital and / or quantum computer programs, where appropriate, to perform functions by manipulating input digital and quantum data and generating outputs. The processing and logic flows can also be executed by a combination of dedicated logic circuitry (e.g., FPGA or ASIC) or a quantum simulator, or a combination of dedicated logic circuitry or a quantum simulator and one or more programmable digital and / or quantum computers, and the device can also be implemented as a combination of dedicated logic circuitry (e.g., FPGA or ASIC) or a quantum simulator, or a combination of dedicated logic circuitry or a quantum simulator and one or more programmable digital and / or quantum computers.

[0255] For a system of one or more digital and / or quantum computers “configured” to perform a specific operation or action, it means that the system has software, firmware, hardware, or a combination thereof installed thereon that causes the system to perform the operation or action in operation. For one or more digital and / or quantum computer programs to be configured to perform a specific operation or action, it means that the one or more programs include instructions that, when executed by a digital and / or quantum data processing device, cause that device to perform the operation or action. A quantum computer can receive instructions from a digital computer that, when executed by a quantum computing device, cause that device to perform the operation or action.

[0256] Digital and / or quantum computers suitable for executing digital and / or quantum computer programs can be based on general-purpose or special-purpose digital and / or quantum processors, or both, or any other type of central digital and / or quantum processing unit. Typically, the central digital and / or quantum processing unit receives instructions and digital and / or quantum data from read-only memory, random access memory, or a quantum system suitable for transmitting quantum data (e.g., photons), or a combination thereof.

[0257] The essential components of a digital and / or quantum computer are a central processing unit (CPU) for executing or running instructions, and one or more storage devices for storing instructions and digital and / or quantum data. The CPU and memory can be supplemented or incorporated into dedicated logic circuitry or a quantum simulator. Typically, a digital and / or quantum computer will also include, or be operatively coupled to, receiving, or transferring digital and / or quantum data, or both, from one or more mass storage devices (e.g., magnetic disks, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information). However, a digital and / or quantum computer does not require such a device.

[0258] 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 memories, media, and storage devices, including, for example: semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks or removable disks; magneto-optical disks; CD-ROM and DVD-ROM disks; and quantum systems such as trapped atoms or electrons. It is understood that quantum memory is a device capable of storing quantum data for long periods with high fidelity and efficiency, for example, an optical-matter interface where light is used for transmission and matter is used for storing and maintaining the quantum characteristics of the quantum data, such as superposition or quantum coherence.

[0259] Control of the various systems or portions thereof described in this specification can be implemented in a digital and / or quantum computer program product, which includes instructions stored on one or more non-transitory machine-readable storage media and executable on one or more digital and / or quantum processing devices. Each of the systems or portions thereof described in this specification can be implemented as an apparatus, method, or system that may include one or more digital and / or quantum processing devices and a memory storing executable instructions to perform the operations described in this specification.

[0260] Although this specification contains many specific implementation details, these should not be construed as limiting the scope that can be claimed, but rather as a description of features that may be specific to particular embodiments. Some features described herein in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments. Furthermore, although features may be described above as operating in certain combinations and even initially claimed in this way, in some cases one or more features from the claimed combination may be removed from the combination, and the claimed combination may be for sub-combinations or variations thereof.

[0261] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or to perform all the shown operations to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of the various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or encapsulated in multiple software products.

[0262] Specific embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in different orders and still achieve the desired result. As an example, the processing depicted in the figures does not necessarily require the specific order or sequential order shown to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of the computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and a control quantum node, and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; and iteratively determining whether to enter a hidden quantum node training phase or a control quantum node training phase, and for each iteration in which it is determined to enter the hidden quantum node training phase, setting the control quantum node to a non-interacting state and iteratively changing learning and non-learning phases of the quantum nodes; and outputting a solution to the computational task.

2. The method of claim 1, wherein, the solution to the computational task is encoded into an attractive fixed point of the quantum processor.

3. The method of claim 1, wherein, iteratively changing learning and non-learning phases of the quantum nodes comprises, for each iteration until an event completion occurs: switching learning and non-learning of the quantum nodes; evolving the quantum state under a dissipative quantum map until a steady state is reached, wherein a solution to the computational task is encoded at the steady state; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that the event completion occurs. the evolution of the quantum state under the dissipative quantum map causes the quantum state to reach a steady state, wherein the steady state is a unique steady state or a non-equilibrium steady state.

4. The method of claim 3, wherein, the non-equilibrium steady state has a corresponding fictitious Hamiltonian, wherein an energy spectrum of the fictitious Hamiltonian encodes a solution to the computational task.

5. The method of claim 4, wherein, the evolution of the quantum state is designed by a quantum metronome without requiring access to any degree of freedom of the bath.

6. The method of claim 3, wherein, the steady state substantially converges to a desired state, and the desired state gives a result that substantially approaches a desired result.

7. The method of claim 3, wherein, 8. The method of claim 1, further comprising, for each iteration in which it is determined to enter the control quantum node training phase: setting the control quantum node to a solution pinning state; iteratively changing learning and non-learning phases of the quantum nodes. iteratively changing learning and non-learning phases of the quantum nodes comprises, for each iteration until an event completion occurs:

9. The method of claim 8, wherein, switching learning and non-learning phases of the quantum nodes; evolving the quantum state under a dissipative quantum map until a steady state is reached, wherein a solution to the computational task is encoded at the steady state; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that the event completion occurs. ​ 10. The method of claim 8, wherein, For each iteration in which it is determined to enter the hidden quantum node training phase, the method further comprises setting the hidden quantum nodes to an unclamped state during the learning phase and the non-learning phase.

11. The method of claim 10, further comprising: setting the input and output quantum nodes to a clamped state during the learning phase and to an unclamped state during the non-learning phase, wherein setting the input and output quantum nodes to a clamped state during the learning phase comprises clamping the input and output quantum nodes to the training data.

12. The method of claim 10, wherein, setting the hidden quantum nodes to the clamped state comprises clamping the hidden quantum nodes to learning values of the hidden quantum node training phase.

13. The method of claim 10, further comprising: setting the input and output quantum nodes to a clamped state during the learning phase and to an unclamped state during the non-learning phase, wherein setting the input and output quantum nodes to a clamped state during the learning phase comprises clamping the input and output quantum nodes to the training data.

14. The method of claim 1, wherein, For each iteration in which it is determined to enter the hidden quantum node training phase, the method further comprises setting the hidden quantum nodes to an unclamped state during the learning phase and the non-learning phase.

15. A quantum processor comprising: a plurality of logical quantum nodes, the logical quantum nodes comprising input quantum nodes, hidden quantum nodes, and output quantum nodes; a plurality of control quantum nodes; and a plurality of quantum node couplers, each coupler configured to couple a pair of quantum nodes, wherein the couplers at least couple an input quantum node and a hidden quantum node to a first control quantum node, and the couplers at least couple a hidden quantum node and an output quantum node to a second control quantum node; wherein the quantum processor is configured to perform operations comprising: receiving data representative of a computational task; processing the data, wherein the quantum processor has been trained on training data to process input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising the plurality of logical quantum nodes and control quantum nodes and a state of a bath; and iteratively determining whether to enter a hidden quantum node training phase or a control quantum node training phase, and for each iteration in which it is determined to enter the hidden quantum node training phase: setting control quantum nodes to a non-interacting state and iteratively changing learning and non-learning phases of the quantum nodes; and outputting the solution to the computational task.

16. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and a control quantum node, and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; and iteratively determining whether to enter a first learning phase or a first non-learning phase, including, for each iteration in which it is determined to enter the first learning phase: setting the control quantum node to a pinning state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the computational task is encoded at the steady state; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that a completion event occurs; and outputting the solution to the computational task.

17. The method of claim 16, further comprising: entering a second learning phase, including setting the control quantum node to a solution pinning state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the computational task is encoded at the steady state; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that a completion event occurs.

18. The method of claim 16, further comprising, for each iteration in which it is determined to enter the first non-learning phase: setting the control quantum node to a pinning state; encoding a solution to the computational task at the steady state; evolving the quantum state under a dissipative quantum map until a steady state is reached, wherein, performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that a completion event occurs.

19. The method of claim 18, further comprising: entering a second non-learning phase, including setting the control quantum node to a solution pinning state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the computational task is encoded at the steady state; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that a completion event occurs. The method further comprises, for each iteration in which it is determined to enter the first learning phase and for each iteration in which it is determined to enter the first non-learning phase, setting the hidden quantum nodes to a solution pinning state. setting the input and output quantum nodes to a pinning state for each iteration in which it is determined to enter the first learning phase and to a solution pinning state for each iteration in which it is determined to enter the first non-learning phase, wherein setting the input and output quantum nodes to a pinning state for each iteration in which it is determined to enter the first learning phase comprises pinning the input and output quantum nodes to the training data. ​ 20. The method of claim 18, wherein, ​ 21. The method of claim 18, further comprising: ​ 22. The method of claim 18, wherein, The method further includes setting the hidden quantum nodes to a clamped state for each iteration in which the second learning phase is entered and for each iteration in which the second non-learning phase is entered.

23. The method of claim 21, further comprising: setting the input and output quantum nodes to a clamped state for each iteration in which the second learning phase is entered and to an unclamped state for each iteration in which the second non-learning phase is entered, wherein setting the input and output quantum nodes to a clamped state for each iteration in which the second learning phase is entered includes clamping the input and output quantum nodes to the training data.

24. The method of claim 18, wherein, setting the control quantum nodes to a clamped state for each iteration in which it is determined to enter the first non-learning phase further includes clamping the control quantum nodes to an equilibrium state of a second learning phase.

25. The method of claim 18, wherein, setting the control quantum nodes to a clamped state for each iteration in which it is determined to enter the first learning phase after the second non-learning phase has been completed further includes clamping the control quantum nodes to an equilibrium state of the second non-learning phase.

26. The method of claim 16, wherein, The evolution of the quantum state under the dissipative quantum graph causes the quantum state to reach a steady state, wherein the steady state is a unique steady state or a non-equilibrium steady state.

27. The method of claim 26, wherein, The non-equilibrium steady state has a corresponding fictitious Hamiltonian, wherein the energy spectrum of the fictitious Hamiltonian encodes a solution to the computational task.

28. The method of claim 16, wherein, The evolution of the quantum state is designed by a quantum governor without requiring access to any bath degrees of freedom.

29. The method of claim 16, wherein, The steady state substantially converges to a desired state and the desired state gives a result that substantially approaches a desired result.

30. A quantum processor, comprising: a plurality of logical quantum nodes including input quantum nodes, hidden quantum nodes, and output quantum nodes, wherein each of the plurality of logical quantum nodes is configured to switch between a clamped state and an unclamped state; a plurality of control quantum nodes, each of the plurality of control quantum nodes configured to switch between a clamped state, an unclamped state, or an initial default state; a plurality of quantum node couplers, each coupler configured to couple a pair of quantum nodes, wherein the couplers at least couple an input quantum node and a hidden quantum node to a first control quantum node and the couplers at least couple a hidden quantum node and an output quantum node to a second control quantum node; wherein the quantum processor is configured to perform operations comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training including determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor including the plurality of logical quantum nodes and control quantum nodes and a state of a bath; and iteratively determining whether to enter a first learning phase or a first non-learning phase, including, for each iteration in which it is determined to enter the first learning phase: setting a control qubit to a pinched state; evolving the quantum state under a dissipative quantum map until a steady state is reached, wherein a solution to the computational task is encoded at the steady state; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result; and outputting the solution to the computational task.

31. A method for training a quantum processor to solve a machine learning inference problem, comprising: receiving a set of training data; preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical qubits and control qubits and a state of a bath, wherein the logical qubits comprise input qubits, hidden qubits, and output qubits; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting a control qubit to a pinched state; evolving the quantum state under a dissipative quantum map until a steady state is reached, wherein a solution to the machine learning inference problem is encoded at the steady state, and wherein the control qubit increases an interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

32. A quantum processor, comprising: a plurality of logical qubits comprising input qubits, hidden qubits, and output qubits, wherein each of the plurality of logical qubits is configured to switch between a pinched state and an unpinched state; a plurality of control qubits, each of the plurality of control qubits configured to switch between a pinched state, an unpinched state, or an initial default state; a plurality of qubit couplers, each coupler configured to couple a pair of qubits, wherein the couplers at least couple an input qubit and a hidden qubit to a first control qubit, and the couplers at least couple a hidden qubit and an output qubit to a second control qubit; wherein the quantum processor is trained according to operations comprising: receiving a set of training data; preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical qubits and control qubits and a state of a bath; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting a control qubit to a pinched state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

33. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a clamped state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

33. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a clamped state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

33. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a clamped state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

33. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a clamped state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

33. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a clamped state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

33. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a clamped state; evolving a quantum state under a dissipative quantum map until a steady state is reached, wherein, at the steady state, a solution to the computational task is encoded, and wherein the control quantum nodes increase the interaction between the quantum processor and the bath to reach the steady state in a target finite mixing time without bath engineering; performing a quantum measurement on the steady state; determining whether a measurement outcome is within a given distance from a known result; and determining that a completion event occurs when the measurement outcome is within the given distance from the known result.

35. A method for solving a computational task, the computational task comprising an optimization task or an inference task, the method comprising: receiving data representative of a computational task; processing the data using a quantum processor, wherein the quantum processor has been trained on training data to process an input representing the computational task to output a solution to the computational task, the training comprising determining training values of system parameters by: preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath, wherein the logical quantum nodes comprise input quantum nodes, hidden quantum nodes, and output quantum nodes; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a pinched state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the computational task is encoded at the steady state, and wherein the steady state comprises a ground state of an imaginary Hamiltonian; performing a quantum measurement on the steady state to sample from the ground state of the imaginary Hamiltonian; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that a completion event occurs; and outputting the solution to the computational task.

36. A quantum processor comprising: a plurality of logical quantum nodes, the logical quantum nodes comprising input quantum nodes, hidden quantum nodes, and output quantum nodes, wherein each of the plurality of logical quantum nodes is configured to switch between a pinched state and an unpinched state; a plurality of control quantum nodes, each of the plurality of control quantum nodes configured to switch between a pinched state, an unpinched state, or an initial default state; a plurality of quantum node couplers, each coupler configured to couple a pair of quantum nodes, wherein the couplers at least couple an input quantum node and a hidden quantum node to a first control quantum node, and the couplers at least couple a hidden quantum node and an output quantum node to a second control quantum node; wherein the quantum processor is trained according to operations comprising: receiving a set of training data; preparing an initial quantum state, wherein the initial quantum state is a tensor product of an initial state of the quantum processor comprising a plurality of logical quantum nodes and control quantum nodes and a state of a bath; iteratively determining whether to enter a first learning phase or a first non-learning phase; for each iteration in which it is determined to enter the first learning phase: setting control quantum nodes to a pinched state; evolving the quantum state under a dissipative quantum graph until a steady state is reached, wherein a solution to the computational task is encoded at the steady state, and wherein the steady state comprises a ground state of an imaginary Hamiltonian; performing a quantum measurement on the steady state to sample from the ground state of the imaginary Hamiltonian; determining whether a measurement outcome is within a given distance from a known result; and when the measurement outcome is within the given distance from the known result, determining that a completion event occurs.

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