Artificial Intelligence-Driven Quantum Computing

Abstract

The present disclosure provides methods and systems for using one or more artificial intelligence (AI) procedures (such as one or more machine learning (ML) or reinforcement learning (RL) procedures) implemented on a classical computer to execute heuristics through interaction with computations performed using a classical computer or a non-classical computer (such as a quantum computer).

Description

Technical Field

[0001] Cross-reference This application claims the benefit of U.S. Provisional Application No. 62 / 776,183, filed Dec. 6, 2018, and U.S. Provisional Application No. 62 / 872,601, filed Jul. 10, 2019, each of which is hereby incorporated by reference in its entirety for all purposes.

Background Art

[0002] Many challenging problems can be solved by heuristics implemented using classical computers. Thus, it can be important to use heuristic strategies in the field of non-classical computing (e.g., quantum computing) to extend the computing power of non-classical devices (e.g., quantum devices) and to extend the applicability of such devices to real-world computing problems. Non-classical computing (e.g., quantum computing) procedures, in principle, include adjustable parameters (such as the strength of the transverse magnetic field in the transverse-field Ising model of quantum annealing, the strength of XX, XY, and other couplers in quantum annealing, adiabatic quantum computing of various quantum systems, recovery operations in quantum error correction, fault-tolerant quantum computing and quantum memory (QRAM), the navigator Hamiltonian of VanQver, etc.), while the heuristics of non-classical computing may face challenges.

[0003] In classical computing, adjustable parameters of classical heuristics can be initiated, computed, and updated according to a path taken by procedures (such as historical information stored in memory, current methods, user-defined schedules, and previous values of adjustable parameters). However, attempting to apply such principles to non-classical computers (e.g., quantum computers), the measurement (reading) of non-classical information (e.g., quantum information) under the operation of non-classical computing procedures may result in the so-called collapse of the wave function, which may be harmful to non-classical information and may prevent non-classical procedures from continuing or converging. As a result, the instantaneous state or history of a non-classical computing register may not be available during the implementation of non-classical or quantum heuristics.

[0004] Many procedures inspired by classical physics, including procedures such as simulated annealing, simulated quantum annealing, parallel tempering, parallel tempering with equal energy cluster moves, diffusion Monte Carlo methods, population annealing, and quantum Monte Carlo methods, can also benefit from the methods and systems described herein. SUMMARY OF THE INVENTION

[0005] In this specification, there is a recognized need for methods and systems for overcoming limitations of heuristics and / or other computational procedures in non-classical or quantum computing. For example, in this specification, systems and methods are provided for improving the computational efficiency and / or accuracy of non-classical computing (e.g., quantum computing). The systems and methods provided herein utilize a non-classical computer (e.g., a quantum computer) that includes a first non-classical or quantum subsystem (referred to herein as a "computation subsystem") for performing non-classical or quantum computing, and a second non-classical or quantum subsystem (referred to herein as a "syndrome subsystem") that is quantum-entangled with the computation subsystem. During non-classical or quantum computing, the syndrome subsystem may be measured, and at the same time, the computation subsystem may be advanced to perform non-classical or quantum computing. The systems and methods provided herein may further enable measurement of the syndrome subsystem during the execution of non-classical or quantum computing to provide a partial observation about the computation subsystem. Such an observation may then be provided to an artificial intelligence (AI) module, such as a machine learning (ML) module or a reinforcement learning (RL) module, that may be trained during or prior to the computation, to determine the next best selection for adjustable parameters during or prior to non-classical or quantum computing. The selection of adjustable parameters may be related to an initial segment, an intermediate segment, or a final segment of non-classical or quantum computing.

[0006] The systems and methods provided herein thus enable an AI module to change the course of a computation as it occurs. For example, adjustable parameters may represent quantum gates applied to a circuit model quantum computation, and changes to them during the execution time of a non-classical computation would change the gates. In another example, adjustable parameters may represent the evolution path of an adiabatic quantum computation or a quantum annealing procedure. Changes by the AI module to adjustable parameters may change the evolution path of a non-classical computation as the computation is performed.

[0007] In one aspect, a system for performing calculations using artificial intelligence (AI) includes: (a) at least one computer configured to perform a calculation that includes one or more adjustable parameters and one or more non-adjustable parameters and output a report indicating the calculation, the computer including: (i) one or more registers configured to perform the calculation; and (ii) a measurement unit configured to measure at least one state of the one or more registers and determine a representation of the state of the one or more registers, thereby determining a representation of the calculation; and (b) at least one AI control unit configured to control the calculation, execute at least one AI procedure to determine one or more adjustable parameters corresponding to the calculation, and instruct the computer with the adjustable parameters, where the at least one artificial intelligence (AI) control unit may include at least one AI control unit including one or more AI control unit parameters. The computer may include a hybrid computing system, the hybrid computing system including: (a) at least one non-classical computer configured to perform the calculation, the at least one non-classical computer including: (i) one or more registers; and (ii) a measurement unit; and (b) an AI control unit. The at least one non-classical computer may include at least one quantum computer, where the one or more registers include one or more qubits configured to perform the calculation, and the measurement unit is configured to measure at least one state of the one or more qubits and determine a representation of the at least one state of the one or more qubits, thereby determining a representation of the calculation, and the measurement unit is further configured to provide the representation of the calculation to the AI control unit.The measurement unit may be configured to measure the state of at least one of one or more qubits, obtain syndrome data representing partial information about the current state of the calculation, and provide the syndrome data to the AI control unit. One or more registers may include a calculation register and a syndrome register, where the calculation register includes one or more calculation qubits configured to perform a calculation, and where the syndrome register includes one or more syndrome qubits different from the one or more calculation qubits, where the one or more syndrome qubits are quantum mechanically entangled with the one or more calculation qubits, and where the one or more syndrome qubits are not for performing a calculation, and where the measurement unit is configured to measure the state of the one or more syndrome qubits to determine a representation of the state of the one or more calculation qubits, thereby determining a representation of the calculation. The calculation may include quantum calculation. The quantum calculation may include adiabatic quantum calculation. The quantum calculation may include the Quantum Approximate Optimization Algorithm (QAOA). The quantum calculation may include a variational quantum algorithm. The quantum calculation may include error correction on a quantum register. The quantum calculation may include a fault-tolerant quantum computing gadget. The calculation may include classical calculation. The calculation may include at least one member selected from the group consisting of simulated annealing, simulated quantum annealing, parallel tempering, parallel tempering with equal energy cluster moves, diffusion Monte Carlo method, population annealing, and quantum Monte Carlo method. At least one quantum computer may be configured to perform one or more quantum operations including at least one member selected from the group consisting of preparation of an initial state of one or more qubits, implementation of one or more single-qubit quantum gates on one or more qubits, implementation of one or more multi-qubit quantum gates on one or more qubits, and adiabatic evolution from an initial Hamiltonian to a final Hamiltonian using one or more qubits. The representation of the state of the one or more calculation qubits may be correlated with the state of the one or more syndrome qubits.The measurement unit may be configured to measure the state of one or more syndrome qubits during the evolution of one or more computational qubits during computation. At least one non-classical computer may include an integrated photonic coherent ising machine computer. At least one non-classical computer may include a network of optical parametric pulses. At least one AI procedure may include at least one machine learning (ML) procedure. At least one ML procedure may include at least one ML training procedure. At least one ML procedure may include at least one ML inference procedure. At least one AI procedure may include at least one reinforcement learning (RL) procedure. At least one AI procedure may be configured to modify adjustable parameters during computation, thereby providing one or more modified adjustable parameters. One or more modified adjustable parameters may be configured to modify the computation during the course of the computation. At least one AI control unit may include one or more members selected from the group consisting of a tensor processing unit (TPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC). At least one computer may include one or more members selected from the group consisting of a field programmable gate array (FPGA) and an application specific integrated circuit (ASIC). At least one AI control unit may communicate with at least one computer on a network. At least one AI control unit may communicate with at least one computer on a cloud network. At least one AI control unit may be integrated as a classical processing system operating at extremely low temperatures within a cryogenic system. One or more adjustable parameters and one or more non-adjustable parameters may define the next segment of the computation, including the instruction set from the current representation of the computation. One or more adjustable parameters may include the initial temperature of the computation. One or more adjustable parameters may include the temperature schedule of the computation. One or more adjustable parameters may include the final temperature of the computation.The adjustable parameter(s) of 1 or more may include a schedule of pumping energy of the network. The adjustable parameter(s) of 1 or more may include an instruction of a quantum gate for a segment of quantum computing. The adjustable parameter(s) of 1 or more may include an instruction of a local operation and classical communication (LOCC) channel for a segment of quantum computing. The AI control unit may include a neural network, where the AI control unit parameter(s) of 1 or more include neural network weights corresponding to the neural network.

[0008] In another aspect, a method for training an artificial intelligence (AI) control unit, the method comprising: (a) obtaining one or more instances of one or more non-adjustable parameters, and obtaining one or more adjustable parameters and AI control unit parameters; (b) configuring the AI control unit using the AI control unit parameters; (c) selecting at least one instance of the one or more non-adjustable parameters; (d) configuring a computer using at least one instance of the one or more non-adjustable parameters and the one or more adjustable parameters, wherein the values of the one or more adjustable parameters are directed by the AI control unit, and wherein the computer includes one or more registers; (e) executing a segment of computation using the one or more registers of the computer; (f) performing at least one measurement of at least one of the one or more registers, thereby obtaining a representation of the segment of computation; (g) repeating (c)-(f) a plurality of times; (h) outputting a report indicating each computation performed a plurality of times; (i) reconfiguring the AI control unit by modifying the AI control unit parameters based on the report; (j) repeating (c)-(i) until a stop criterion is satisfied. The AI control unit and the computer may include a system for performing computations, where the system further includes a system in any aspect or embodiment. The step of performing at least one measurement of at least one of the one or more registers, thereby obtaining a representation of the segment of computation, may include: (a) when the segment is not the last segment for computation, the at least one measurement includes syndrome data; (b) when the segment is the last segment for computation, the at least one measurement includes computation data.

[0009] In another aspect, a method for performing calculations using a system including a computer and an artificial intelligence (AI) control unit, the method comprising: (a) obtaining one or more non-adjustable parameters; (b) configuring the computer using the one or more non-adjustable parameters; (c) configuring the computer using one or more adjustable parameters, wherein the one or more adjustable parameters are directed by the AI control unit; (d) performing a segment of the calculation using one or more registers of the computer; (e) performing one or more measurements of at least one of the one or more registers, thereby obtaining a representation of the segment of the calculation; (f) repeating (c), (d), and (e) until a stop criterion is satisfied; and (g) outputting a report indicating the calculation. The AI control unit and the computer may include a system for performing the calculation, where the system further includes a system of any aspect or embodiment.

[0010] In another aspect, a method for performing calculations, the method comprising: (a) obtaining one or more non-adjustable parameters from a user; (b) using an artificial intelligence (AI) control unit to direct values of one or more adjustable parameters to a computer, wherein the computer includes one or more registers; (c) using one or more registers for performing the calculation, the calculation including using the one or more non-adjustable parameters and the one or more adjustable parameters; (d) performing one or more measurements of the one or more registers to obtain a representation of the calculation; and (e) outputting a report indicating the calculation. The AI control unit and the computer may include a system for performing the calculation, where the system further includes a system of any aspect or embodiment.

[0011] In another aspect, a method for training a hybrid computer including at least one artificial intelligence (AI) control unit and at least one non-classical computer to perform computations, the method comprising: (a) using the AI control unit, thereby: (i) obtaining a training set including a plurality of instances of computations; (ii) obtaining and initializing AI control unit parameters and one or more adjustable parameters; (iii) selecting one instance of the plurality of instances; (iv) initializing at least one non-classical computer; and (v) obtaining and initializing a state-action epoch schedule including a plurality of state-action epochs; (b) using at least one non-classical computer, thereby: (i) executing the instance up to the next state-action epoch of the plurality of state-action epochs; (ii) performing one or more measurements of a syndrome register to obtain an immediate reward corresponding to the selected instance; and (iii) providing an indication of the immediate reward to the AI control unit, thereby updating the AI control unit parameters based on the immediate reward; (c) using the AI control unit to provide a set of adjustable parameters from the one or more adjustable parameters; (d) repeating (b) until a first stopping criterion is satisfied; and (e) repeating (a)(iii)-(d) until a second stopping criterion is satisfied.

[0012] In another aspect, a method for performing calculations using a hybrid computer including at least one artificial intelligence (AI) control unit and at least one non-classical computer, the method comprising: (a) using the AI control unit, thereby (i) obtaining a set of instructions representing the calculations, the instructions including an adjustable instruction set including a plurality of adjustable instructions, (ii) obtaining a trained policy and a state-action epoch schedule including a plurality of state-action epochs, (iii) initializing at least one non-classical computer, and (iv) initializing a plurality of state-action epochs and the adjustable instruction set; (b) using at least one quantum computer, thereby (i) performing calculations up to the next state-action epoch of the plurality of state-action epochs, (ii) performing one or more measurements of one or more registers to obtain a representation of the calculations, and (iii) obtaining the next plurality of adjustable instructions; and (c) repeating (a)-(b) until a stop criterion is satisfied.

[0013] In another aspect, a method for training an AI control unit, the method comprising: (a) obtaining one or more non-adjustable parameters, one or more adjustable parameters, and AI control unit parameters; (b) configuring the AI control unit using the AI control unit parameters; (c) configuring a computer using the one or more non-adjustable parameters and the one or more adjustable parameters, wherein the values of the one or more adjustable parameters are directed by the AI control unit; (d) performing calculations using the computer; (e) performing one or more measurements to obtain a representation of the calculations; (f) outputting a report indicating the calculations; and (g) reconfiguring the AI control unit by modifying the AI control unit parameters based on the report.

[0014] In another aspect, a system for performing calculations using artificial intelligence (AI) includes: (a) a computer configured to perform calculations and output a report indicating the calculations, the computer including: (i) one or more computing registers, where the one or more computing qubits are configured to perform calculations; (ii) one or more syndrome registers; and (iii) a measurement unit configured to measure one or more states of the one or more syndrome registers to determine a representation of one or more states of the one or more computing registers, thereby determining a representation of the calculations; and (b) at least one AI control unit configured to control the calculations, execute at least one AI procedure to determine one or more adjustable parameters corresponding to the calculations, and instruct the computer with the adjustable parameters, where the at least one artificial intelligence (AI) control unit may include at least one AI control unit including one or more AI control unit parameters. The computer may include a hybrid computing system, the hybrid computing system including: (a) at least one non-classical computer configured to perform calculations, the at least one non-classical computer including: (i) one or more computing registers; (ii) one or more syndrome registers; and (iii) a measurement unit; and (b) an AI control unit. The at least one non-classical computer may include at least one quantum computer, where the computing register includes one or more computing qubits configured to perform calculations, the syndrome register includes one or more syndrome qubits different from the one or more computing qubits, the one or more syndrome qubits are quantum entangled with the one or more computing qubits, and the one or more syndrome qubits are not for performing calculations, and the measurement unit is configured to measure one or more states of the one or more syndrome qubits to determine a representation of one or more states of the one or more computing qubits, thereby determining a representation of the calculations.The computation may include quantum computation. The computation may include quantum-classical computation. The computation may include classical computation. At least one quantum computer may further include a control unit configured to perform one or more quantum operations on computational qubits or syndrome qubits. The one or more quantum operations may include at least one member selected from the group consisting of preparation of an initial state of one or more computational qubits or one or more syndrome qubits, implementation of one or more single-qubit quantum gates on one or more computational qubits or one or more syndrome qubits, implementation of one or more multi-qubit quantum gates on one or more computational qubits or one or more syndrome qubits, and adiabatic evolution on one or more computational qubits or one or more syndrome qubits. The control unit may be configured to perform one or more quantum operations based on one or more adjustable parameters. At least one quantum computer may include a greater number of computational qubits than syndrome qubits. At least one quantum computer may include a smaller number of computational qubits than syndrome qubits. At least one quantum computer may include an equal number of computational qubits and syndrome qubits. The representation of one or more states of one or more computational qubits may be correlated with one or more states of one or more syndrome qubits. The measurement unit may be configured to measure one or more states of one or more syndrome qubits during the evolution of one or more computational qubits during the computation. The measurement unit may be further configured to measure one or more states of one or more computational qubits after the evolution of one or more computational qubits. At least one non-classical computer may include an integrated photonic coherent Ising machine computer. One or more syndrome registers may be further configured to perform the computation. At least one AI procedure may include at least one machine learning (ML) procedure. At least one ML procedure may include at least one ML training procedure. At least one ML procedure may include at least one ML inference procedure. At least one AI procedure may include at least one reinforcement learning (RL) procedure.At least one AI procedure may be configured to modify adjustable parameters during a calculation, thereby obtaining one or more modified adjustable parameters. The one or more modified adjustable parameters may be configured to modify the calculation during the course of the calculation. At least one AI control unit may include at least one member selected from the group consisting of a tensor processing unit (TPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC). At least one computer may include at least one member selected from the group consisting of a field programmable gate array (FPGA) and an application specific integrated circuit (ASIC). The calculation may include at least one member selected from the group consisting of simulated annealing, simulated quantum annealing, parallel tempering, and the quantum Monte Carlo method. At least one AI control unit may communicate with at least one computer on a network. At least one AI control unit may communicate with at least one computer on a cloud network. At least one AI control unit may be located within a distance of up to about 1 centimeter (cm) from a computer. The one or more adjustable parameters may include an initial temperature of the calculation. The one or more adjustable parameters may include a temperature schedule of the calculation. The one or more adjustable parameters may include a final temperature of the calculation. The AI control unit may include a neural network, and the one or more AI control unit parameters may include neural network weights corresponding to the neural network. The step of reconfiguring the AI control unit based on the representation may include modifying adjustable parameters.

[0015] In another aspect, a method for training an AI control unit, the method comprising: (a) obtaining adjustable parameters and AI control unit parameters; (b) configuring the AI control unit using the AI control unit parameters; (c) using a computer to perform calculations, where the adjustable parameters are instructed to the computer by the AI control unit; (d) performing one or more measurements of a syndrome register to obtain an expression of the calculations; (e) repeating (c)-(d) a plurality of times; (f) outputting a report indicating the expression; (g) reconfiguring the AI control unit by modifying the AI control unit parameters based on the expression; and (h) repeating (c)-(g) until a stop criterion is met.

[0016] In another aspect, a method for performing calculations using a system, the method comprising: (a) obtaining non-adjustable parameters from a user; (b) instructing adjustable parameters to a computer; (c) using a computer that uses non-adjustable parameters and adjustable parameters to perform calculations; (d) performing one or more measurements of a calculation register to obtain the calculations; and (e) outputting a report indicating the calculations.

[0017] In another aspect, a method for training a hybrid computer including at least one artificial intelligence (AI) control unit and at least one quantum computer to perform calculations includes: (a) using the AI control unit, thereby: (i) obtaining a training set including a plurality of instances of the calculation; (ii) obtaining and initializing AI control unit parameters and adjustable parameters; (iii) selecting one instance of the plurality of instances; (iv) initializing at least one quantum computer; and (v) initializing at least one quantum computer; (b) using at least one quantum computer, thereby: (i) executing the instance up to the next state-action epoch of the plurality of state-action epochs; (ii) performing one or more measurements of the syndrome register to obtain an immediate reward corresponding to the selected instance; and (iii) providing an indication of the immediate reward to the artificial AI control unit, thereby updating the AI control unit parameters based on the immediate reward; (c) using the AI control unit to provide a set of adjustable parameters from the plurality of adjustable parameters; (d) repeating (b) until a first stopping criterion is met; and (e) repeating (a)(iii)-(d) until a second stopping criterion is met.

[0018] In another aspect, a method for performing calculations using a hybrid computer including at least one artificial intelligence (AI) control unit and at least one quantum computer, the method comprising: (a) using the AI control unit, thereby: (i) obtaining a set of instructions representing a calculation, the instructions including an adjustable instruction set including a plurality of adjustable instructions; (ii) obtaining a trained policy and a state-action epoch schedule including a plurality of state-action epochs; (iii) initializing at least one quantum computer; and (iv) initializing a plurality of state-action epochs and the adjustable instruction set; (b) using at least one quantum computer, thereby: (i) performing calculations up to the next state-action epoch of the plurality of state-action epochs; (ii) performing one or more measurements of a syndrome register to obtain a representation of the calculation; and (iii) obtaining a new sequence of adjustable instructions; and (c) repeating (a)-(b) until a stop criterion is satisfied.

[0019] Additional aspects and advantages of the present disclosure will be readily apparent to those of ordinary skill in the art from the following detailed description, wherein only exemplary embodiments of the present disclosure are shown and described. As will be understood from the following description, the present disclosure may be other and different embodiments and its several details may be modified in various respects without departing from the present disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive.

[0020] Incorporation by reference All publications, patents, and patent applications mentioned in this specification are hereby incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent that the incorporated publications, patents, or patent applications conflict with the disclosure contained herein, the specification is intended to supersede and / or take precedence over any such conflicting subject matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The novel features of the present invention are described, among other things, in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description, which describes exemplary embodiments in which the principles of the present invention are utilized, and the accompanying drawings (or "Figures and FIGS." herein).

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Best Mode for Carrying Out the Invention

[0022] While various embodiments of the present invention are shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many variations, changes, and substitutions may be envisioned by those skilled in the art without departing from the present invention. It should be understood that various alternatives to the embodiments of the present invention described herein may be utilized.

[0023] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art belonging to the present invention. When used in the specification and the appended claims, the singular forms "a", "an", and "the" include plural references unless the context clearly dictates otherwise. Any reference to "or" is intended to encompass "and / or" unless otherwise specified.

[0024] The terms "at least", "greater than", "greater than or equal to", when preceding the first of a series of two or more numerical values, always apply to each of the numerical values within that series of numerical values. For example, 1, 2, or 3 or more is greater than or equal to 1, greater than or equal to 2, greater than or equal to 3.

[0025] The terms "no more than", "less than", "less than or equal to", or "at most", when preceding the first of a series of two or more numerical values, always apply to each of the numerical values within that series of numerical values. For example, 3, 2, or 1 or less is less than or equal to 3, less than or equal to 2, less than or equal to 1.

[0026] In the following detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, like reference numerals generally identify like components unless the content indicates otherwise. The exemplary embodiments, drawings, and claims described in the detailed description are not intended to be limiting. Other embodiments may be utilized and other changes may be made without departing from the scope of the subject matter presented herein. As is normally described herein and shown in the drawings, aspects of the present disclosure are arranged, replaced, combined, separated, and designed in a variety of different configurations, all of which are clearly contemplated herein and will be readily understood.

[0027] As used herein, the term "heuristic" generally refers to any computational procedure (such as non-classical (e.g., quantum mechanical) computations) that may not have the best-known value, may have a best value that may not be efficiently computable, or is inherently probabilistic, and may depend on the selection of "tunable parameters" (such as weights in a neural network) that can produce different results when the heuristic is implemented with different initial values. Examples of heuristics include, but are not limited to, local heuristic search methods in optimization, simulated annealing, genetic algorithms, particle swarm optimization, gradient-based methods, gradient-free methods, artificial intelligence (AI), machine learning (ML), reinforcement learning (RL), neural information processing, statistical learning, representational learning, and the like.

[0028] As used herein, the terms "artificial intelligence", "artificial intelligence procedure", and "artificial intelligence operation" generally refer to any system, or computational procedure, that can take one or more actions that may enhance or maximize the chance of successfully achieving a goal. The term "artificial intelligence" may include "machine learning" (mL) and / or "reinforcement learning" (RL).

[0029] As used herein, the terms "machine learning", "machine learning procedure", and "machine learning operation" generally refer to any system, or analytical and / or statistical procedure, that gradually improves a computer's performance with respect to a task. Machine learning may include machine learning algorithms. A machine learning algorithm may be a trained algorithm. Machine learning (ML) may include one or more supervised, semi-supervised, or unsupervised machine learning techniques. For example, an ML algorithm may be a trained algorithm that is trained through supervised learning (e.g., and various parameters are determined as weighting coefficients or scaling coefficients). ML may include one or more of regression analysis, regularization, classification, dimensionality reduction, ensemble learning, meta-learning, association rule learning, clustering analysis, anomaly detection, deep learning, or ultra-deep learning. ML may include k-means, k-means clustering, k-nearest neighbor, learning vector quantization, linear regression, non-linear regression, least squares regression, partial least squares regression, logistic regression, stepwise regression, multivariate adaptive regression spline, ridge regression, principal component regression, least absolute shrinkage and selection operator, least angle regression, canonical correlation analysis, factor analysis, independent component analysis, linear discriminant analysis, multidimensional scaling, non-negative matrix factorization, principal component analysis, principal coordinate analysis, projection pursuit, Sammon mapping, t-distributed stochastic neighbor embedding, AdaBoosting, boosting, gradient boosting, bootstrap aggregation, ensemble averaging, decision tree, conditional decision tree, boosted decisiona tree, a gradient boosted decision tree, a random forest, stacked generalization, a Bayesian network, a Bayesian belief network, naive Bayes, Gaussian naive Bayes, multinomial naive Bayes, a hidden Markov model, a hierarchical hidden Markov model, a support vector machine, an encoder, a decoder, an autoencoder, a stacked autoencoder, a perceptron, a multi-layer perceptron, an artificial neural network, a feedforward neural network, a convolutional neural network, a recurrent neural network, long short-term memory, a deep belief network, a deep Boltzmann machine, a deep convolutional neural network, a deep recurrent neural network, or an adversarial generative network, including but not limited to these.

[0030] As used herein, "reinforcement learning", "reinforcement learning procedure", and "reinforcement learning operation" generally refer to any system, or computational procedure, that takes one or more actions in order to reinforce or maximize some notion of cumulative reward for interaction with an environment. An agent that executes a reinforcement learning (RL) procedure (classical, non-classical, or on a quantum computer, etc.) takes one or more actions within an environment, thereby placing itself and the environment in various new states, and can receive positive or negative reinforcement, called "immediate reward".

[0031] The goal of the agent may be to enhance or maximize some notion of cumulative reward. For example, the goal of the agent may be to enhance or maximize a "discounted reward function" or an "average reward function". The "Q-function" may represent the maximum cumulative reward obtainable from a state and the action taken in that state. The "value function" and the "generalized advantage estimator" may represent the maximum cumulative reward obtainable from a state given a choice of optimal or best action. RL may utilize any one or more of such notions for cumulative reward. As used herein, any such function may be referred to as a "cumulative reward function". Thus, calculating the best or optimal cumulative reward function may be equivalent to finding the best or optimal policy for the agent. The goal of the calculation may be to decrease the value of one or more eigenvalues of a Hamiltonian implemented on a non-classical computer. The goal of the calculation may be to find the global minimum value of the value of one or more eigenvalues of a Hamiltonian implemented on a non-classical computer. The goal of the agent may be to find an optimal policy for the calculation. The optimal policy may include finding the values of adjustable parameters to select for the process of the calculation.

[0032] The agent, and its interaction with its environment, may be formulated as one or more Markov Decision Processes (MDPs). The RL procedure may not assume knowledge of the exact mathematical model of the MDP. The MDP may be completely unknown, partially known, or completely known to the agent. The RL procedure may exist on a spectrum between two ranges, "model-based" or "model-free", with respect to prior knowledge of the MDP. Therefore, the RL procedure may be applicable to large-scale MDPs, in which case, due to the unknown or probabilistic nature of the MDP, an exact method may be infeasible or unavailable.

[0033] The learning procedure may be implemented using a digital processing unit, such as any classical computer described herein. The learning procedure may include the RL procedure. The RL procedure may be implemented using a digital processing unit, such as any classical computer described herein. The digital processing unit may utilize an agent that trains, stores, and later deploys a "policy" to enhance or maximize the cumulative reward. The policy may be sought (e.g., searched) for as long as possible or for a desired period. Such optimization problems may be solved by preserving an approximation of the optimal policy, preserving an approximation of the cumulative reward function, or both. In some cases, the RL procedure may store one or more tables of approximate values for such functions. In other cases, the RL procedure may utilize one or more "function approximators".

[0034] Examples of function approximators may include neural networks (such as deep neural networks) and probabilistic graphical models (e.g., Boltzmann machines, Helmholtz machines, and Hopfield networks). A function approximator may create a parameterization of the approximation of the cumulative reward function. The optimization of the function approximator with respect to the parameterization may move the parameters in a direction that enhances or maximizes the cumulative reward, and thus may enhance or optimize the policy (such as by a policy gradient method) or configure the function approximator to satisfy Bellman's optimality criteria (such as by a temporal difference method).

[0035] During training, the agent may take actions in the environment and obtain additional information regarding the environment and the appropriate or best selection of a policy for survival or better utility. The actions of the agent may be generated randomly (e.g., especially in the initial stages of training), or may be defined by another machine learning paradigm (such as supervised learning, imitation learning, or other machine learning procedures described herein). The actions of the agent may become better by selecting actions closer to the agent's recognition of what the enhanced or optimal policy is. Various training strategies may exist on a spectrum between two ranges of off-policy and on-policy methods with respect to the choice between exploration and exploitation.

[0036] In some cases, the policy may include a path of one or more adjustable parameters in the optimization space of non-classical computing. In a simple example, the policy may include a temperature schedule for the computation. The policy may include a schedule for the pumping energy of a network of optical parameter pulses. The policy may include a schedule for the instructions of quantum gates for segments of quantum computing. For example, the policy may include the order of the gates. For example, the policy may include the speed of rotation of one or more rotation gates. The policy may include the evolution of the phase of one or more gates. The policy may solve control problems for a quantum computer. The policy may include a schedule for the instructions of local operations and classical communication (LOCC) channels for segments of quantum computing.

[0037] The RL procedure may include deep reinforcement learning (DRL), such as those disclosed in [Mnih et al., Playing Atari with Deep Reinforcement Learning, arXiv: 1312.5602 (2013)], [Schulman et al., Proximal Policy Optimization Algorithms, arXiv:1707.06347 (2017)], [Konda et al., Actor-Critic Algorithms, in Advances in Neural Information Processing Systems, pp. 1008-1014 (2000)], and [Mihn et al., Asynchronous Methods for Deep Reinforcement Learning, in International Conference on Machine Learning, pp. 1928-1937 (2016)], each of which is incorporated herein by reference in its entirety.

[0038] The RL procedure may also be referred to as "approximate dynamic programming" or "neuro-dynamic programming".

[0039] The present disclosure provides methods and systems for overcoming limitations of heuristics and / or other computational procedures in non-classical or quantum computing. For example, provided herein are systems and methods for improving the computational efficiency and / or accuracy of non-classical or quantum computing. The systems and methods provided herein may utilize a non-classical or quantum computer including a first non-classical or quantum subsystem (referred to herein as a "computation subsystem") for performing non-classical or quantum computing, and a second non-classical or quantum subsystem (referred to herein as a "syndrome subsystem") that is quantumly entangled with the computation subsystem. During non-classical or quantum computing, the syndrome subsystem may be measured, and at the same time, the computation subsystem may be evolved to perform non-classical or quantum computing. The systems and methods provided herein may further enable measurement of the syndrome subsystem during the implementation of non-classical or quantum computing to provide a partial observation about the computation subsystem. Such an observation may then be provided to an artificial intelligence (AI) control unit, such as a machine learning (ML) module or a reinforcement learning (RL) module, that may be trained during or prior to the computation, to determine a next-best selection for adjustable parameters during or prior to non-classical or quantum computing. The selection of adjustable parameters may be related to an initial segment, an intermediate segment, or a final segment of non-classical or quantum computing.

[0040] AI-Enabled Quantum Computing When applied to non-classical computing such as quantum computing, the environment may be the total Hilbert space including any possible instantaneous state of the quantum computer. The classical AI control unit may be trained by some executions of segments of quantum computing for some instances of the problem. Measurements in a subsystem of the Hilbert space may describe a partially observable environment for the AI control unit. In the language of deep learning, each measurement may be observed as feature extraction from the state of the quantum system. In some examples, each syndrome measurement may be observed as feature extraction from the state of the quantum subsystem, but in other examples, any measurement may be used.

[0041] Hybrid computing In some embodiments, the classical computer may be configured to execute one or more classical algorithms. A classical algorithm (or classical computing task) may include an algorithm (or computing task) that can be executed by one or more classical computers without using a quantum computer, a quantum-ready computing service, or a quantum-enabled computing service. Classical algorithms may include non-quantum algorithms. The classical computer may include a computer that does not include a quantum computer, a quantum-ready computing service, or a quantum-enabled computer. The classical computer may process or store data represented by digital bits (e.g., zero ("0") and one ("1")) rather than quantum bits (qubits). Examples of classical computers include, but are not limited to, server computers, desktop computers, laptop computers, notebook computers, subnotebook computers, netbook computers, netpad computers, set-top computers, media streaming devices, handheld computers, Internet appliances, mobile smartphones, tablet computers, personal digital assistants, video game consoles, and media.

[0042] A hybrid computing system may include a classical computer and a quantum computer. The quantum computer may be configured to execute one or more quantum algorithms to solve computational problems. The one or more quantum algorithms may be executed using a quantum computer, a quantum-enabled computing service, or a quantum-ready computing service. For example, the one or more quantum algorithms may be executed using a system or method described in U.S. Patent Publication No. 2018 / 0107526, titled "METHODS AND SYSTEMS FOR QUANTUM READY AND QUANTUM ENABLED COMPUTATIONS," which is hereby incorporated by reference in its entirety. The classical computer may include at least one classical processor and computer memory and may be configured to execute one or more classical algorithms to solve computational problems (e.g., at least a portion of a quantum chemistry simulation). A digital computer may include at least one computer processor and computer memory, where the digital computer may include a computer program with instructions executable by at least one computer processor to render an application. The application may assist a user in using the quantum computer and / or the classical computer.

[0043] In some implementations, a quantum computer may be used in conjunction with a classical computer that operates on bits, such as a personal desktop, laptop, supercomputer, distributed computing, cluster, cloud-based computing resources, smartphone, or tablet.

[0044] The system may include an interface for the user. In some embodiments, the interface may include an application programming interface (API). The interface may provide a program - following model that removes (e.g., by hiding from the user) the internal details of the quantum computer (e.g., architecture and operations). In some embodiments, the interface may minimize the need to update application programs in response to changes in the quantum hardware. In some embodiments, the interface may remain unchanged even when the quantum computer has changes in its internal structure.

[0045] This disclosure provides systems and methods that may include quantum computing or the use of quantum computing. A quantum computer may be able to solve a certain class of computational tasks more efficiently than a classical computer. However, quantum computing resources may be scarce and expensive, and may require a certain level of expertise to be used efficiently or effectively (e.g., to increase cost - efficiency or cost - effectiveness). Multiple parameters may be adjusted for the quantum computer to fulfill its potential computing power.

[0046] A quantum computer (or other type of non-classical computer) may sometimes be operated in parallel with a classical computer as a coprocessor. A hybrid architecture (e.g., a computing system) that includes a classical computer and a quantum computer can be very efficient when tackling complex computational tasks. Although this disclosure has referred to quantum computers, the methods and systems of this disclosure may be utilized for use with other types of computers that may be non-classical computers. Such non-classical computers may include quantum computers, hybrid quantum computers, quantum-like computers, or other computers that are not classical computers. Examples of non-classical computers include, but are not limited to, Hitachi's Ising solver, an optical parametric-based coherent Ising machine, and other solvers that utilize different physical phenomena to obtain more efficiency when solving certain classification problems.

[0047] Non-Classical Computers and Computing Non-classical computing (e.g., quantum computing) may involve performing certain quantum operations (such as unitary transformations or completely positive trace-preserving (CPTP) maps on quantum channels) on a Hilbert space represented by a quantum device. Thus, quantum computing and classical (or digital) computing may be similar in the following aspects. That is, both computations may include a sequence of instructions executed on input information, followed by providing an output. Various paradigms of quantum computing may decompose quantum operations into a sequence of basic quantum operations that simultaneously affect a subset of the qubits of the quantum device. The quantum operations may be selected, for example, based on their locality or the ease of their physical implementation. At that time, a quantum procedure or quantum computation may consist of a sequence of instructions that can represent different quantum evolutions of the quantum device in various applications. For example, a procedure for computing a quantum chemistry simulation may represent quantum states and electron spin-orbit pair annihilation and creation operators through a so-called Jordan-Wigner transformation [Wigner, E.P, & Jordan, P, Ueber das Paulische Aequivalenzverbot, Zeitschri fuer Physik 5, 11 (1928)], or Bravyi-Kitaev transformation [Bravyi, S. B., & Kitaev, A.Yu., Fermionic quantum computation, arXiv:quant-ph / 0003137], using qubits (such as two-level quantum systems) and a universal quantum gate set (such as Hadamard, controlled-NOT (CNOT), and π / 8 rotation), each of the above references being incorporated herein by reference in its entirety.

[0048] Additional examples of quantum procedures or computations may include procedures for optimization such as the Quantum Approximate Optimization Algorithm (QAOA), [Farhi et al., A Quantum Approximate Optimization Algorithm, arXiv:1411.4028 (2014)], or Quantum Minimum Finding [Durr et al., A Quantum Algorithm for Finding the Minimum, arXiv:quant-ph / 9607014 (1996)], each of which is hereby incorporated by reference in its entirety. QAOA may include performing single qubit rotations and entangling multi-qubit gates. In quantum adiabatic computing, the instructions may be conveyed along a stochastic or non-stochastic path of the evolution from an initial quantum system to a final quantum system.

[0049] Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solver, Monte Carlo procedures, and the like.

[0050] Quantum-classical algorithms or hybrid algorithms may include procedures such as the variational quantum eigensolver (VQE) [Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L., A variational eigenvalue solver on a quantum processor, arXiv:1304.3061], and the variational and adiabatically navigated quantum eigensolver (VanQver) [Matsuura et al., VanQver: The Variational and Adiabatically Navigated Quantum Eigensolver, arXiv:1810.11511 (2018)], each of the above documents being incorporated herein by reference in its entirety. Quantum-classical algorithms or hybrid algorithms may include simulated quantum annealing or quantum Monte Carlo methods. Such hybrid algorithms may be particularly suitable for near-term noisy quantum devices, which may have limitations (and in some cases severe limitations) on the available quantum computing power due to short coherence times and / or limitations in the number of available qubits.

[0051] A quantum computer includes one or more adiabatic quantum computers, quantum gate arrays, one-way quantum computers, topological quantum computers, quantum Turing machines, superconductor-based quantum computers, trapped ion quantum computers, trapped neutral atom quantum computers, trapped atom quantum computers, optical lattices, quantum dot computers, spin-based quantum computers, spatial-based quantum computers, Loss-DiVincenzo quantum computers, nuclear magnetic resonance (NMR)-based quantum computers, solution-state NMR quantum computers, solid-state NMR quantum computers, solid-state NMR Kane quantum computers, electrons-on-helium quantum computers, cavity-quantum-electrodynamics based quantum computers, molecular magnet quantum computers, fullerene-based quantum computers, linear optical quantum computers (linearoptical quantum computer), diamond-based quantum computer, nitrogen vacancy (NV) diamond-based quantum computer, Bose-Einstein condensate-based quantum computer, transistor-based quantum computer, and rare-earth-metal-ion-doped inorganic crystal based quantum computer. The quantum computer may include one or more of a quantum annealer and a gate model of quantum computing. The non-classical computer may include one or more of an Ising solver and an optical parametric oscillator (OPO).

[0052] In some cases, a classical simulator of a quantum circuit that can be executed on a classical computer, such as a MacBook Pro laptop, a Windows laptop, or a Linux® laptop, may be used. In some embodiments, the classical simulator may be executed on a cloud computing platform that has access to multiple compute nodes in a parallel or distributed manner. In some embodiments, the total quantum mechanical energy and / or electronic structure calculations for a subset of the fragments can be performed using a classical simulator, and the total quantum mechanical energy and / or electronic structure calculations for the remaining fragments can be performed using quantum hardware.

[0053] Classical computer In some embodiments, the systems, media, networks, and methods described herein include, or their use involves, classical computers. For example, the systems, media, networks, and methods described herein may include, or their use involves, the computers described herein with respect to FIG. 6. In some embodiments, a classical computer includes one or more hardware central processing units (CPUs) that perform functions of the classical computer. In some embodiments, a classical computer further includes an operating system (OS) configured to execute executable instructions. In some embodiments, a classical computer is connected to a computer network. In some embodiments, a classical computer is connected to the Internet to access the World Wide Web. In some embodiments, a classical computer is connected to a cloud computing infrastructure. In some embodiments, a classical computer is connected to an intranet. In some embodiments, a classical computer is connected to a data storage device.

[0054] According to the description herein, suitable classical computers may include, by way of non-limiting example, server computers, desktop computers, laptop computers, notebook computers, subnotebook computers, netbook computers, netpad computers, set-top computers, media streaming devices, handheld computers, Internet appliances, mobile smartphones, tablet computers, personal digital assistants, video game consoles, and media. Smartphones may be suitable for use with the methods and systems described herein. Some select televisions, video players, and digital music players may in some cases be connected to a computer network and may be suitable for use in the systems and methods described herein. Suitable tablet computers may include those with a booklet, slate, and convertible configuration.

[0055] In some embodiments, a classical computer includes an operating system configured to execute executable instructions. The operating system is software that includes programs and data that manage, for example, the hardware of the device and provide services for the execution of applications. Suitable server operating systems include, by way of non-limiting example, FreeBSD, OpenBSD, NetBSDR, Linux®, Apple® Mac OS X Server®, Oracle® Solaris®, Windows Server®, and Novell® NetWare®. Suitable personal computer operating systems may include, by way of non-limiting example, Microsoft® Windows®, Apple® Mac OS X®, UNIX®, and UNIX®-like operating systems such as GNU / Linux®. In some embodiments, the operating system is provided by cloud computing. Suitable mobile smartphone operating systems may include, by way of non-limiting example, Nokia® Symbian® OS, Apple® iOS®, Research In Motion® BlackBerry OS®, Google® Android®, Microsoft® Windows Phone® OS, Microsoft® Windows Mobile® OS, Linux®, and Palm® WebOS®. Suitable media streaming device operating systems may include, by way of non-limiting example, Apple TV®, Roku®, Boxee®, Google TV®, Google Chromecast®, Amazon Fire®, and Samsung® HomeSync®.Suitable operating systems for video game machines may include, by way of non-limiting example, Sony® PS3®, Sony® PS4®, Microsoft® Xbox 360®, Microsoft Xbox One, Nintendo® Wii®, Nintendo® Wii U®, and Ouya®.

[0056] In some embodiments, the classical computer includes a storage device and / or a memory device. In some embodiments, the storage device and / or the memory device are one or more physical devices used to store data or programs, either temporarily or permanently. In some embodiments, the device is volatile memory and requires power to maintain the stored information. In some embodiments, the device is non-volatile memory and retains the stored information when the classical computer is not powered. In some embodiments, the non-volatile memory includes flash memory. In some embodiments, the non-volatile memory includes dynamic random access memory (DRAM). In some embodiments, the non-volatile memory includes ferroelectric random access memory (FRAM). In some embodiments, the non-volatile memory includes phase change random access memory (PRAM). In other embodiments, the device is a storage device including, by way of non-limiting example, CD-ROMs, DVDs, flash memory devices, magnetic disk drives, magnetic tape drives, optical disk drives, and cloud computing-based storage devices. In some embodiments, the storage device and / or the memory device are a combination of devices such as those disclosed herein.

[0057] In some embodiments, the classical computer includes a display for sending visual information to the user. In some embodiments, the display is a cathode ray tube (CRT). In some embodiments, the display is a liquid crystal display (LCD). In some embodiments, the display is a thin film transistor liquid crystal display (TFT-LCD). In some embodiments, the display is an organic light emitting diode (OLED) display. In some embodiments, in the OLED display, it is a passive matrix OLED (PMOLED) or an active matrix OLED (AMOLED) display. In some embodiments, the display is a plasma display. In some embodiments, the display is a video projector. In some embodiments, the display is a combination of devices such as those disclosed herein.

[0058] In some embodiments, the classical computer includes an input device for receiving information from the user. In some embodiments, the input device is a keyboard. In some embodiments, the input device is, by way of non-limiting example, a pointing device including a mouse, trackball, trackpad, joystick, game controller, or stylus. In some embodiments, the input device is a touch screen or a multi-touch screen. In some embodiments, the input device is a microphone for capturing voice or other audio input. In some embodiments, the input device is a video camera or other sensor for capturing motion input or visual input. In some embodiments, the input device is a Kinect, Leap Motion, etc. In some embodiments, the input device is a combination of devices such as those disclosed herein.

[0059] Classical computers may include classical processing units. In some embodiments, a classical computer may include dedicated hardware configured to implement AI procedures such as any of the AI procedures described herein. A classical computer may include any semiconductor device configured to implement AI procedures. For example, a classical computer may include one or more members selected from the group consisting of tensor processing units (TPUs), graphics processing units (GPUs), field programmable gate arrays (FPGAs), and application specific integrated circuits (ASICs). A classical computer may include any one or more of a TPU, GPU, FPGA, or ASIC, either wholly or in part.

[0060] Non-transitory computer-readable storage medium In some embodiments, the systems and methods described herein include one or more non-transitory computer-readable storage media encoded with a program comprising instructions executable by an operating system of optionally networked digital processing units. In some embodiments, the computer-readable storage medium is a tangible component of a classical computer. In some embodiments, the computer-readable storage medium is optionally removable from the classical computer. In some embodiments, the computer-readable storage medium includes, by way of non-limiting example, CD-ROMs, DVDs, flash memory devices, solid state memories, magnetic disk drives, magnetic tape drives, optical disk drives, cloud computing systems, and services, etc. In some cases, the program and instructions are encoded permanently, substantially permanently, semi-permanently, or non-transitorily on the medium.

[0061] Embodiments of the disclosed systems and methods for performing computations are described below.

[0062] Systems and methods for performing computations In one aspect, the present disclosure provides a system for performing calculations using artificial intelligence (AI). The system includes at least one computer configured to perform a calculation including one or more adjustable parameters and one or more non-adjustable parameters and output a report indicating the calculation, and at least an AI control unit. The computer may include (i) one or more registers, where the one or more registers are configured to perform the calculation, and (ii) a measurement unit configured to measure at least one state of the one or more registers and determine a representation of the state of the one or more registers, thereby determining a representation of the calculation. The AI control unit may be configured to control the calculation, execute at least one AI procedure to determine one or more adjustable parameters corresponding to the calculation, and instruct the computer with the one or more adjustable parameters. The AI control unit may include one or more AI control unit parameters.

[0063] FIG. 1 shows a schematic diagram of an example of a system (100) for performing calculations using AI. The system may be a hybrid computing system. The hybrid computing system may include at least one classical computing system and at least one non-classical computing system. The non-classical computing system may include a quantum computer. The calculation may include quantum computing. The quantum computing may include adiabatic quantum computing. The quantum computing may further include a quantum approximate optimization algorithm (QAOA). The quantum computing may further include a variational quantum algorithm. The quantum computing may further include error correction on a quantum register. The quantum computing may further include a fault-tolerant quantum computing gadget. The calculation may include classical computing. The calculation may further include at least one member selected from the group consisting of simulated annealing, simulated quantum annealing, parallel tempering with energy class cluster moves such as parallel tempering, diffusion Monte Carlo method, population annealing, and quantum Monte Carlo method.

[0064] The calculation may include one or more adjustable parameters and one or more non - adjustable parameters. The non - adjustable parameters may include parameters that define a family of instances of the calculation. In one embodiment, the non - adjustable parameters may include the form of the problem Hamiltonian. The adjustable parameters may include parameters that define an instance of the calculation. The adjustable parameters may include the initial temperature of the calculation. The adjustable parameters may include the temperature schedule of the calculation. The adjustable parameters may include the final temperature of the calculation. The adjustable parameters may include the schedule of the pumping energy of the network of optical parameter pulses. The adjustable parameters may include instructions for quantum gates for segments of the quantum calculation. The adjustable parameters may include instructions for local operations and classical communication (LOCC) channels for segments of the quantum calculation. The one or more adjustable parameters and the one or more non - adjustable parameters may define the next segment of the calculation, including an instruction set from the current representation of the calculation.

[0065] As shown in FIG. 1, the computing system may include at least one computer (110) and at least one AI control unit (120). The computer (110) may be configured to execute computations and output a report indicating the computations. The computer (110) may include a classical computer. The computer (110) may include a non-classical computer. The computer (110) may include any non-classical computer. The computer (110) may include at least one member selected from the group consisting of a field programmable gate array (FPGA) and an application specific integrated circuit (ASIC). The computer (110) may include any non-classical computer described herein. In some embodiments, the non-classical computer may include an integrated photonic coherent ising machine computer. U.S. Publication No. 20180267937 is hereby incorporated by reference in its entirety. In another embodiment, the non-classical computer may include a network of optical parametric pulses. See U.S. Patent No. 10139703, which is hereby incorporated by reference in its entirety. In yet another embodiment, the non-classical computer may include a quantum computer.

[0066] The computer may include one or more registers. The computer may include a first register (111). The one or more registers may be configured to perform calculations. The computer (110) may include a second register (113), a third register (117), a fourth register (119), and a fifth register (121). In FIG. 1, it is depicted as including five registers, but the computer (110) may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, or more registers, or any number of registers such as a maximum of about 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 register, or a plurality of registers within a range defined by any two of the aforementioned values.

[0067] The register may include one or more qubits. For example, the register may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, or more qubits, or any number of qubits such as up to about 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 register, or a plurality of qubits within a range defined by any two of the foregoing values. In some embodiments, the register (111) may include a first qubit (112a), a second qubit (112b), a third qubit (112c), and a fourth qubit (112d). The register may be configured to perform calculations using one or more qubits. The register may be configured to function as a syndrome register using one or more qubits. The one or more qubits may be entangled with each other as indicated by the double-headed arrows between the qubits (112a), (112b), (112c), and (112d) of FIG. 1. The register may be configured to function as a syndrome register.

[0068] The number of registers configured to perform calculations, or registers that function as syndrome registers, may be changed according to the requirements of a particular calculation or during the execution of different operations within a particular calculation.

[0069] In some embodiments, a register configured to perform calculations may be different from a register configured to function as a syndrome register. The qubits included in the syndrome register may be quantum mechanically entangled with the qubits included in the calculation register.

[0070] The measurement unit (115) may be configured to measure one or more states of one or more registers to determine the representation of the computation. In one embodiment, the measurement unit may be configured to measure at least one state of one or more qubits to obtain syndrome data representing partial information about the current state of the computation and provide the syndrome data to the AI control unit (120).

[0071] In one embodiment, the measurement unit (115) may be configured to measure the states of one or more first registers to obtain syndrome data and determine the representation of the states of one or more second registers, thereby determining the representation of the computation. The first register may include a syndrome subsystem. The second register may include a computation subsystem. The syndrome subsystem may include one or more registers. The computation subsystem may include one or more registers. In some cases, the measurement unit (115) may be configured to measure the states of one or more qubits to determine the representation of the computation. The measurement unit may be configured to measure the states of one or more qubits using any type of measurement such as von Neumann measurement, projective value measurement (PVM), positive operator value measure (POVM), weak continuous measurement, etc.

[0072] The representation of the state of the second register or registers greater than or equal to 1 may be correlated with the state of the first register or registers greater than or equal to 1. The representation of the state of the second register or registers greater than or equal to 1 may be correlated with the state of the first register or registers greater than or equal to 1 with a correlation coefficient of at least about 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 0.99 or more. The representation of the state of the second register or registers greater than or equal to 1 may be correlated with the state of the first register or registers greater than or equal to 1 with a correlation coefficient of at most about 0.99, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, or less. The representation of the state of the second register or registers greater than or equal to 1 may be correlated with the state of the first register or registers greater than or equal to 1 with a correlation coefficient within the range defined by any two of the foregoing values.

[0073] Since the measurement of the first register or registers does not affect a computing subsystem that may include one or more second registers different from the first register or registers, the first register or registers may be prepared, entangled with the second register or registers, and measurement may be repeatedly performed thereon during computation. Each repetition of the measurement may allow an AI control unit (120), such as an agent of the RL procedure described herein, to obtain new knowledge about the state of the quantum information stored in the computational qubits of the computing subsystem and to define a new set of adjustable parameters for the computation. In the language of RL, a new schedule for the adjustable parameters may be referred to as an action taken by the agent in the environment. Thus, each measurement of the syndrome subsystem may include a new state-action epoch for RL.

[0074] The measurement unit may be configured to measure the state of one or more registers of the syndrome subsystem during the evolution of one or more registers of the computing system during computation. The measurement unit may further be configured to measure the state of one or more registers of the computing subsystem after the evolution of one or more registers of the computing system.

[0075] In some cases, the non-classical computer described in this specification may further include a control unit (116). The control unit may be configured to perform one or more quantum operations on one or more qubits. The quantum operations may include at least one member selected from the group consisting of preparation of an initial state of one or more qubits, implementation of one or more single-qubit quantum gates on one or more qubits, implementation of one or more multi-qubit quantum gates on one or more qubits, and adiabatic evolution from an initial Hamiltonian to a final Hamiltonian using one or more qubits.

[0076] The quantum operations may be dynamic. For example, the quantum operations may be changed according to specific computational requirements or during the execution of different operations within a specific computation. The control unit may be configured to perform one or more quantum operations based on one or more adjustable parameters.

[0077] The AI control (120) may include a classical computer, such as any classical computer described herein or any one or more components of a classical computer. For example, the classical computer may include a digital processing unit. The classical computer may include one or more members selected from the group consisting of a TPU, a GPU, an FPGA, and an ASIC. The AI control unit may be integrated as a classical processing system operating at extremely low temperatures within the refrigerator system. For example, see An FPGA-based Instrumentation Platform for use at Deep Cryogenic Temperatures by I. D. Conway Lamb, J. I. Colless, J. M. Hornibrook, S. J, Pauka, S. J. Waddy, M. K. Frechtling, and D. J. Reilly, arxiv.org / abs / 1509.06809, which is incorporated herein by reference. The AI control unit may be configured to execute at least one artificial intelligence (AI) procedure to determine one or more adjustable parameters for computing. The AI control unit may be configured to instruct one or more adjustable parameters to a non-classical computer. The AI procedure may include any AI procedure described herein. The AI procedure may include at least one machine learning (ML) procedure. The ML procedure may include any ML procedure described herein. The ML procedure may include at least one ML training procedure. The ML procedure may include at least one ML inference procedure. The AI procedure may include at least one reinforcement learning (RL) procedure. The RL procedure may include any RL procedure described herein. For example, the AI procedure may include a training procedure described herein with respect to the method (1400) of FIG. 14. In some embodiments, the AI procedure may include a training procedure described herein with respect to the method (400) of FIG. 4. The AI procedure may include an inference procedure described herein with respect to the method (500) of FIG. 5. The AI procedure may change adjustable parameters of the computing.Changes to adjustable parameters may change the calculation during the calculation process. The AI control unit may be configured to save or execute the AI procedure. The AI control unit may be configured to modify the AI procedure during the calculation. The AI control unit may be configured to modify the adjustable parameters of the calculation. Modification of the adjustable parameters may change the calculation during the calculation process. The AI control unit may be configured to instruct the computer to adjust the parameters. The AI control unit may include one or more AI control unit parameters. The AI control unit may include a neural network including a plurality of neural network weights. In this embodiment, the AI control unit parameters include neural network weights. The neural network may include at least one layer, at least one node in each layer, and neural network weights associated with each edge. The neural network may include any number of layers and any number of nodes in each layer. For example, the neural network may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, or more layers, up to about 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 layer, or a plurality of layers within a range defined by any of the foregoing values. The neural network may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, or more nodes, up to about 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 node, or a plurality of nodes within a range defined by any of the foregoing values in each layer.The neural network may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000 or more neural network weights, up to 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 neural network weight, or a plurality of neural network weights within a range defined by any of the foregoing values.

[0078] The AI control unit (120) may communicate with the computer (110). The AI control unit may communicate with the computer over a network. The AI control unit may communicate with the computer over a cloud network. The AI control unit may be in proximity to the computer. The AI control unit (120) may be located remotely from the computer (110) (e.g., the AI control unit (120) may be at least 0.5 miles, 1 mile, 10 miles, or 100 miles away from the computer (110)). In some examples, the AI control unit may be within a distance of at least about 1 micrometer (μm), 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 200 μm, 300 μm, 400 μm, 500 μm, 600 μm, 700 μm, 800 μm, 900 μm, 1 centimeter (cm), 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, 8 cm, 9 cm, 10 cm, 100 cm, 200 cm, 300 cm, 400 cm, 500 cm, 600 cm, 700 cm, 800 cm, 900 cm, 1,000 cm, or more from the computer. The AI control unit may be within a distance of up to about 1,000 cm, 900 cm, 800 cm, 700 cm, 600 cm, 500 cm, 400 cm, 300 cm, 200 cm, 100 cm, 90 cm, 80 cm, 70 cm, 60 cm, 50 cm, 40 cm, 30 cm, 20 cm, 10 cm, 9 cm, 8 cm, 7 cm, 6 cm, 5 cm, 4 cm, 3 cm, 2 cm, 1 cm, 900 μm, 800 μm, 700 μm, 600 μm, 500 μm, 400 μm, 300 μm, 200 μm, 100 μm, 90 μm, 80 μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, or less from the computer. The AI control unit may be within the distance of the computer defined by any two of the foregoing values.The AI control unit may be located in proximity to the computer in a manner that reduces or minimizes the communication delay between the AI control unit and the non-classical computer during the execution of the calculation. An arrangement with the AI control unit in proximity to the computer may be particularly advantageous for state-of-the-art non-classical computers characterized by significant noise and / or short quantum coherence times.

[0079] The AI control unit (120) may further include a memory. The memory may include instructions for executing at least one AI procedure.

[0080] The system (100) may be used to implement any one or more of the methods described herein, such as any one or more of the methods (200), (300), (400), (500), (1300), and (1400) described herein with respect to FIGS. 2, 3, 4, 5, 13, and 14, respectively.

[0081] In one aspect, the present disclosure provides a method for performing a calculation using a trained artificial control unit. The method includes obtaining one or more non-adjustable parameters, configuring a computer using the one or more non-adjustable parameters and adjustable parameters directed by an AI control unit, performing a next segment of the calculation using the computer, performing one or more measurements of one or more registers to obtain an expression of the calculation, repeating the steps of performing a next segment of the calculation using the computer and performing one or more measurements of one or more registers to obtain an expression of the calculation until the end of the calculation, and outputting a report indicating the calculation.

[0082] Figure 2 shows a flowchart of an example of a method (200) for performing calculations using AI. In a first operation (210), the method (200) may include obtaining one or more non-adjustable parameters and one or more adjustable parameters. The operation (210) may additionally include configuring a computer using the parameters directed by an AI control unit. The AI control unit may be any AI control unit described herein, such as any AI control unit described herein with respect to the system (100) of FIG. 1. The AI procedure may be any AI procedure described herein, such as any AI procedure described herein with respect to the system (100) of FIG. 1. For example, the AI procedure may include a training procedure as described herein with respect to the method (1400) of FIG. 14. In some embodiments, the AI procedure may include a training procedure as described herein with respect to the method (400) of FIG. 4. The AI procedure may include an inference procedure as described herein with respect to the method (500) of FIG. 5.

[0083] In a second operation (220), the method (200) may include performing a segment of the calculation using the computer.

[0084] In a third operation (230), the method (200) may include performing one or more measurements of one or more registers to obtain a representation of the calculation. The representation may be any representation described herein, such as any representation described herein with respect to the system (100) of FIG. 1.

[0085] In a fourth operation (240), the method (200) may include electronically outputting a report indicating the representation of the calculation.

[0086] The method (200) may further include using an AI procedure to change adjustable parameters during the calculation. The step of using an AI procedure to change adjustable parameters may change the calculation during the process of the calculation. The method (200) may further include using an AI control unit to save or execute the AI procedure. The method may further change the AI procedure during the calculation. The method may further include using an AI control unit to change adjustable parameters during the calculation. The change of the adjustable parameters may change the calculation during the process of the calculation.

[0087] In one aspect, the present disclosure provides a method for using a hybrid computing system including at least one non-classical computer and at least one classical computer to perform a calculation. The method includes using at least one classical computer to execute at least one artificial intelligence (AI) procedure to determine one or more adjustable parameters for a calculation performed by the non-classical computer. Next, the at least one non-classical computer may be used to perform the calculation with the one or more adjustable parameters to generate a result. Thereafter, the method may include electronically outputting the result.

[0088] FIG. 3 shows a flowchart of an example of a method (300) for using a hybrid computing system including at least one non-classical computer and at least one classical computer to perform a calculation.

[0089] In the first operation (310), the method (300) includes using at least one classical computer to execute at least one artificial intelligence (AI) procedure to determine one or more adjustable parameters for calculations to be performed by a non-classical computer. The classical computer may be any classical computer described herein, such as any classical computer described herein with respect to the system (100) of FIG. 1. The AI procedure may be any AI procedure described herein, such as any AI procedure described herein with respect to the system (100) of FIG. 1.

[0090] For example, the AI procedure may include a training procedure as described herein with respect to the method (1400) of FIG. 14. In some embodiments, the AI procedure may include a training procedure as described herein with respect to the method (400) of FIG. 4. The AI procedure may include an inference procedure as described herein with respect to the method (500) of FIG. 5. The non-classical computer may be any non-classical computer described herein, such as any non-classical computer described herein with respect to the system (100) of FIG. 1.

[0091] In the second operation (320), the method (300) may include using at least one non-classical computer to execute a calculation with one or more adjustable parameters to generate a result.

[0092] In the third operation (330), the method (300) may include electronically outputting the result.

[0093] The method (300) may include any operation as described herein with respect to the method (200) of FIG. 2.

[0094] Training of the AI control unit In the training mode, the AI control unit can improve its recognition of the optimal adjustable parameters. To train the AI control unit on a specific calculation (such as a specific quantum calculation, quantum-classical calculation, or classical calculation), a number of instances of the input represented by non-adjustable parameters may be provided to the computer (e.g., by various initializations of the calculation registers, reprogramming the quantum oracle, etc.). In each execution of each instance of the algorithm, initialization and measurement of the registers may be performed in multiple segments of the calculation. The AI control unit may receive an indication of the display of the calculation from the executed measurement. In an embodiment where the computer is a quantum computer, the AI control unit may receive syndrome data representing partial information about the current state of the calculation. At the end of each execution of each instance of the algorithm, the registers may be measured. In an embodiment where the computer is a quantum computer, at the end of each execution of each instance of the algorithm, the calculation registers are measured. The resulting information (such as classical information) may indicate how well the procedure or heuristic solved the desired problem, or how well it performed the calculation. Thus, the most important segment of the calculation for the AI control unit may be at the end of the execution of the calculation registers.

[0095] In one aspect, the present disclosure provides a method for training an AI control unit using the systems described herein, the method comprising at least one computer for performing calculations and at least one AI control unit configured to control the calculations. The method includes obtaining one or more instances of one or more non-adjustable parameters, obtaining adjustable parameters and AI control unit parameters, configuring the AI control unit using the AI control unit parameters, selecting at least one instance of one or more non-adjustable parameters, and configuring the computer using at least one instance of the non-adjustable parameters and the adjustable parameters, where the adjustable parameters are directed by the AI control unit, using the computer to perform the next segment of the calculation, performing at least one measurement of at least one of one or more registers to obtain a representation of the calculation, selecting at least one instance of one or more non-adjustable parameters, and configuring the computer using at least one instance of the non-adjustable parameters and the adjustable parameters, where the adjustable parameters are directed by the AI control unit, using the computer to perform the next segment of the calculation, and performing at least one measurement of at least one of one or more registers to obtain representations of the calculation multiple times, repeating the steps of performing the next segment of the calculation, and performing at least one measurement of at least one of one or more registers to obtain representations of the calculation multiple times, outputting a report indicating the calculations performed multiple times, reconfiguring the AI control unit by modifying the AI control unit parameters based on the report, and repeating the above processing steps until a stop criterion is met.

[0096] In one aspect, a method of training an AI control unit includes: (a) obtaining one or more non-adjustable parameters, one or more adjustable parameters, and AI control unit parameters; (b) configuring the AI control unit using the AI control unit parameters; (c) configuring a computer using the one or more non-adjustable parameters and the one or more adjustable parameters, where the values of the one or more adjustable parameters are directed by the AI control unit; (d) executing calculations using the computer; (e) performing one or more measurements to obtain an expression of the calculations; (f) outputting a report indicating the calculations; and (g) reconfiguring the AI control unit by modifying the AI control unit parameters based on the report.

[0097] The AI control unit and the computer may include a system for executing calculations, where the system further includes a system of any aspect or embodiment. The step of performing one or more measurements on at least one of one or more registers to obtain an expression of a segment of the calculations may include: (a) when the segment is not the last segment for the calculations, the one or more measurements include syndrome data; and (b) when the segment is the last segment for the calculations, the one or more measurements include calculation data.

[0098] FIG. 14 shows a flowchart of an example of a method (1400) for training an AI control unit using a system described herein, such as any of the systems described herein with respect to the system (100) of FIG. 1.

[0099] In a first operation (1402), the method (1400) may include obtaining one or more instances of one or more non-adjustable parameters. The computer may be any computer disclosed herein, such as any computer described herein with respect to the system (100) of FIG. 1. In some embodiments, the computer is a non-classical computer. For example, the computer may be any quantum computer described herein. The computer may include a control unit. The AI control unit may be any AI control unit described herein, such as any AI control unit described herein with respect to the system (100) of FIG. 1. The AI control unit is trained. The AI procedure may be any AI procedure described herein, such as any AI procedure described herein with respect to the system (100) of FIG. 1. For example, the AI procedure may include the training procedure described herein with respect to the method (1400) of FIG. 14. In some embodiments, the AI procedure may include the training procedure described herein with respect to the method (400) of FIG. 4. The AI procedure may include the inference procedure described herein with respect to the method (500) of FIG. 5. The AI control unit may be configured to direct one or more adjustable parameters to the computer. The computer may include one or more registers and a measurement unit.

[0100] The measurement unit may be configured to measure at least one state of one or more registers to determine a representation of the state of the one or more registers, thereby determining a representation of the computation. The measurement unit may be any measurement unit described herein, such as any measurement unit described herein with respect to the system (100) of FIG. 1.

[0101] In a second operation (1404), the method (1400) may include obtaining adjustable parameters and AI control unit parameters.

[0102] In the third operation (1406), the method (1400) may include configuring the AI unit using the AI control unit parameters.

[0103] In the fourth operation (1408), the method (1400) may include selecting at least one instance of one or more non - adjustable parameters.

[0104] In the fifth operation (1410), the method (1400) may include configuring a computer using at least one instance of a non - adjustable parameter and an adjustable parameter, where the adjustable parameter is directed by the AI control unit. In one embodiment, the AI control unit includes a feed - forward neural network. In this embodiment, the step of directing the adjustable parameter by the AI control unit includes performing a feed - forward calculation on the neural network and providing a value of the adjustable parameter.

[0105] In the sixth operation (1412), the method (1400) may include executing the next segment of the calculation using the computer.

[0106] In the seventh operation (1414), the method (1400) may include performing at least one measurement of one or more registers to obtain an expression of the calculation. If the measurement is performed after the last segment calculation, the measurement includes calculation data. If the measurement is performed before the last segment calculation and in an embodiment where the computer is a quantum computer, the measurement includes syndrome data. The syndrome data may be an expression of partial information about the current state of the calculation.

[0107] In the eighth operation (1416), the method (1400) may include repeating operations (1408), (1410), (1412), and (1414) a plurality of times.

[0108] In the ninth operation (1418), the method (1400) may include the step of outputting a report indicating the calculations performed in the previous operation.

[0109] In the tenth operation (1420), the method (1400) may include the step of reconfiguring the AI control unit by modifying the AI control unit parameters based on the report. In one embodiment, the AI control unit includes a neural network. In this embodiment, the AI control unit parameters are neural network weights. As used herein, modifying the AI control unit parameters includes updating the neural network weights. Modifying the AI control unit parameters based on the report may follow any machine learning protocol such as supervised machine learning. Modifying the AI control unit parameters based on the report may include performing backpropagation calculations executed on the neural network.

[0110] In the eleventh operation (1422), the method (1400) may include the step of repeating operations (1408), (1410), (1412), (1414), (1416), (1418), and (1420) until the stop criterion is satisfied. The stop criterion may be the convergence of the AI control unit parameters. The stop criterion may be the end of a list of instances of one or more non-adjustable parameters.

[0111] Implementation of AI-Driven Calculations When using the system described herein to perform calculations with a trained AI control unit, the AI control unit provides the values of the adjustable parameters for each segment of the calculation without updating its AI control unit parameters. As a result, the adjustable parameters are not updated during the calculation. The AI control unit instructs the computer to make the best selection of the adjustable parameters for each segment of the calculation in order to perform the calculation. The course of the calculation is changed based on the values of the adjustable parameters directed by the trained AI control unit for each segment of the calculation.

[0112] In one aspect, the present disclosure provides a method for use using the systems described herein, the method comprising at least one computer for performing calculations and at least one AI control unit configured to control the calculations. The method may include obtaining one or more non-adjustable parameters, configuring a computer using the obtained non-adjustable parameters and adjustable parameters as directed by a trained AI control unit, using the computer to execute a next segment of the calculation, performing one or more measurements to obtain a representation of the calculation, using the computer to execute a next segment of the calculation, performing one or more measurements to obtain a representation of the calculation, repeating, and outputting a report indicating the calculation.

[0113] FIG. 13 shows a flowchart of an example of a method (1300) for performing calculations using a computer, as described herein.

[0114] In the first operation (1302), the method (1300) may include the step of obtaining one or more non-adjustable parameters. The computer may be any computer disclosed herein, such as any computer described herein with respect to the system (100) of FIG. 1. In some embodiments, the computer is a non-classical computer. For example, the computer may be any quantum computer described herein. The computer may include a control unit. The AI control unit may be any AI control unit described herein, such as any AI control unit described herein with respect to the system (100) of FIG. 1. The AI control unit is trained. The AI procedure may be any AI procedure described herein, such as any AI procedure described herein with respect to the system (100) of FIG. 1. For example, the AI procedure may include the training procedure described herein with respect to the method (1700) of FIG. 17. In some embodiments, the AI procedure may include the training procedure described herein with respect to the method (400) of FIG. 4. The AI procedure may include the inference procedure described herein with respect to the method (500) of FIG. 5. The AI control unit may be configured to instruct the computer with one or more adjustable parameters. The computer may include one or more registers and a measurement unit.

[0115] The measurement unit may be configured to measure the state of at least one or more registers in order to determine the representation of the state of the one or more registers, thereby determining the representation of the calculation. The measurement unit may be any measurement unit described herein, such as any measurement unit described herein with respect to the system (100) of FIG. 1.

[0116] In the second operation (1304), the method (1300) may include the step of configuring the computer using the non-adjustable parameters and the adjustable parameters, where the adjustable parameters are instructed by the trained AI control unit.

[0117] In the third operation (1306), the method (1300) may include using a computer to perform the next segment of the calculation. In the initial segment, the next segment may be the initial segment.

[0118] In the fourth operation (1308), the method (1300) may include performing one or more measurements of a register to obtain a representation of the calculation. The representation may be any representation described herein, such as any of the representations described herein with respect to the system (100) of FIG. 1.

[0119] In the fifth operation (1310), the method (1300) may include determining whether a stop criterion is satisfied.

[0120] In the sixth operation (1312), the method (1300) may include electronically outputting a report indicating the representation of the calculation.

[0121] Training of RL-driven quantum computing In the training mode, the AI control unit can improve its recognition of the optimal strategy. To train the AI control unit for a specific calculation (such as a specific quantum calculation, quantum-classical calculation, or classical calculation), many instances of the input of the procedure may be provided to the calculation subsystem (for example, by various initializations of the calculation register, reprogramming the quantum oracle, etc.). In each execution of each instance of the algorithm, the initialization, entanglement, and measurement of the syndrome subsystem may be performed in a plurality of state-action epochs. The AI control unit may receive an immediate reward from the performed measurement. At the end of each execution of each instance of the quantum algorithm, the calculation subsystem may be measured. The resulting information (such as classical information) may indicate how well the procedure or heuristic solved the desired problem, or how well it performed the calculation. Thus, the most important state-action epoch of the AI control unit may be at the end of the execution of the instance of the calculation, where the immediate reward may be obtained in relation to the usefulness of the result of the calculation.

[0122] In one aspect, the present disclosure provides a method for training a hybrid computer, the hybrid computer including at least one classical computer and at least one non-classical computer for performing calculations. The method may include the steps of: (i) obtaining a training set including a plurality of instances of calculations; (ii) obtaining and initializing an artificial intelligence (AI) module; (iii) selecting an instance of the plurality of instances, the instance including a plurality of adjustable parameters; (iv) initializing the non-classical computer; and (v) using the classical computer to initialize a state-action epoch schedule including a plurality of state-action epochs. The non-classical computer may include: (1) at least one computational register including one or more computational qubits, where the computational register is configured to perform calculations using one or more computational qubits; (2) at least one syndrome register including one or more syndrome qubits different from the one or more computational qubits, where the one or more syndrome qubits are quantum-entangled with the one or more computational qubits and the one or more syndrome qubits are not for performing calculations; and (3) at least one measurement unit configured to measure one or more states of the one or more syndrome qubits to determine one or more states of the one or more computational qubits, thereby determining the representation of the calculation. Next, the method may include the steps of: (i) executing example instances up to the next state-action epoch of the plurality of state-action epochs; (ii) performing one or more measurements of the syndrome register to obtain an immediate reward corresponding to the selected instance; and (iii) providing the display of the immediate reward to the classical computer, thereby using the non-classical computer to train the AI module based on the immediate reward. Next, the AI module may be used to provide a set of adjustable parameters from the plurality of adjustable parameters. Thereafter, the operation of the non-classical computer may be repeated until a first stop criterion is satisfied.Finally, the operations of the classical and non-classical computers may be repeated until a second stopping criterion is satisfied.

[0123] In one aspect, a method for training a hybrid computer including at least one artificial intelligence (AI) control unit and at least one non-classical computer for performing a calculation may include: (a) causing the AI control unit to: (i) obtain a training set including a plurality of instances of the calculation; (ii) obtain and initialize AI control unit parameters and adjustable parameters; (iii) select an instance of the plurality of instances; (iv) initialize at least one non-classical computer; and (v) obtain and initialize a state-action epoch schedule including a plurality of state-action epochs; (b) causing the at least one non-classical computer to: (i) execute the instance up to a next state-action epoch of the plurality of state-action epochs; (ii) perform one or more measurements of a syndrome register to obtain an immediate reward corresponding to the selected instance; and (iii) provide an indication of the immediate reward to a classical computer, thereby using the immediate reward to update the AI control unit parameters; (c) using the AI control unit to provide a set of adjustable parameters from the plurality of adjustable parameters; (d) repeating (b) until a first stopping criterion is satisfied; and (e) repeating (a)(iii)-(d) until a second stopping criterion is satisfied.

[0124] FIG. 4 shows a flowchart of an example of a method (400) for training an AI module for performing a calculation.

[0125] In a first operation (402), the method (400) may include obtaining a training set of instances of a computation. The computation may be any computation described herein, such as quantum computing, quantum-classical computing, or classical computing. Each instance of the computation in the training set may include a set of adjustable and non-adjustable (or static) instructions representing the computation, as well as a reward function representing intermediate and terminal state-action epochs.

[0126] In a second operation (404), the method (400) may include obtaining and initializing an AI module that includes a trainable policy and a state-action epoch schedule. The AI module may include any AI module described herein, such as an ML module or an RL module.

[0127] In a third operation (406), the method (400) may include selecting a new instance of a computation from the training set. The new instance of the computation may include a new instance of a quantum computation, a quantum-classical computing example, or an instance of a classical computation.

[0128] In a fourth operation (408), the method (400) may include initializing a non-classical device. The non-classical device may include a syndrome subsystem and a computation subsystem. The non-classical device may include any quantum device described herein (e.g., with respect to the system (100) of FIG. 1). The syndrome subsystem may include any syndrome subsystem described herein (e.g., with respect to the system (100) of FIG. 1). The computation subsystem may include any computation subsystem described herein (e.g., with respect to the system (100) of FIG. 1).

[0129] In a fifth operation (410), the method (400) may include initializing a state-action epoch schedule.

[0130] In the sixth operation (412), the method (400) may include the step of executing a segment of instructions of the computational instance until the next state-action epoch.

[0131] In the seventh operation (414), the method (400) may include the step of performing syndrome subsystem measurements and the step of obtaining an immediate reward. The seventh operation (414) may be performed as soon as the next state-action epoch of the sixth operation (412) is reached.

[0132] In the eighth operation (416), the method (400) may include the step of further training the AI module. The AI module may be trained based on the measurement results of the syndrome subsystem, the immediate reward, and the current policy of the AI module.

[0133] Unless the next state-action epoch of the current instance of the computation is a terminal state-action epoch, any, at least a subset, or all of the sixth, seventh, and eighth operations (412), (414), and (416) may be repeated at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, or more times.

[0134] In the ninth operation (418), the method (400) may include the step of using the AI module to provide a new set of adjustable parameters for the computation.

[0135] In the tenth operation (420), the method (400) may include the step of using the new set of adjustable parameters to provide a new set of adjustable instructions.

[0136] In the 11th operation (422), the method (400) may include a step of determining whether the stopping criterion for the current instance of the calculation is satisfied. If the stopping criterion is not satisfied, any, at least a subset, or all of the 6th, 7th, 8th, 9th, and 10th operations (412), (414), (416), (418), and (420) may be repeated at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, or more times each until the stopping criterion for the current instance of the calculation is satisfied. If the stopping criterion is satisfied, the method (400) may proceed to the 12th operation (424).

[0137] In the 12th operation (424), the method (400) may include a step of performing measurements of the computing subsystem to obtain information (such as classical information) and the reward of the terminal state action epoch of the current instance of the calculation.

[0138] In the 13th operation (426), the method (400) may include a step of training the AI module in the terminal state action epoch.

[0139] In the 14th operation (428), the method (400) may include a step of determining whether the stopping criterion for the training of the AI module is satisfied. If the stopping criterion is not satisfied, any, at least a subset, or all of the 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, and 13th operations (406), (408), (410), (412), (414), (416), (418), (420), (422), (424), and (426) may be repeated at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, or more times each until the stopping criterion is satisfied. If the stopping criterion is satisfied, the method for training the AI module may end.

[0140] Implementation of RL-driven quantum computing In the estimation mode, the agent may not be obligated to pursue improvements in the policies it discovers. Instead, it may simply provide the best choice of arcs as a function of the measurements of the syndrome subsystem. In some embodiments, one or more classical neural networks may be used as function approximators to store the optimal policies. The estimation may then include performing a feed-forward calculation on the neural network and providing the best arc suggested by the activation of the output layer of the neural network.

[0141] In one aspect, the present disclosure provides a method of performing calculations using a hybrid computer that includes at least one classical computer and at least one non-classical computer. The method may include causing the classical computer to (i) obtain a set of instructions representing the calculations, the set of instructions including an adjustable set of instructions that includes a plurality of adjustable instructions and at least one non-adjustable set of instructions, (ii) obtain a trained artificial intelligence (AI) module that includes a trained policy and a state-action epoch schedule that includes a plurality of state-action epochs, (iii) initialize the non-classical computer, and (iv) utilize the plurality of state-action epochs and the adjustable set of instructions for initialization.

[0142] In one aspect, a method for performing a computation using a hybrid computer including at least one artificial intelligence (AI) control unit and at least one non-classical computer may include: (a) causing the AI control unit to: (i) obtain an instruction set representing a computation, the instruction set including an adjustable instruction set including a plurality of adjustable instructions; (ii) obtain a trained policy and a state-action epoch schedule including a plurality of state-action epochs; (iii) initialize at least one non-classical computer; and (iv) use the plurality of state-action epochs and the adjustable instruction set for initialization; (b) causing the at least one quantum computer to: (i) perform a computation up to a next state-action epoch of the plurality of state-action epochs; (ii) perform one or more measurements of one or more registers to obtain a representation of the computation; and (iii) use the representation to obtain a next plurality of adjustable instructions; and (c) repeating (a)-(b) until a stop criterion is satisfied.

[0143] FIG. 5 shows a flowchart of an example of a method (500) for providing an estimate from an AI module for performing a computation.

[0144] In a first operation (502), the method (500) may include obtaining an instruction set representing a computation. The computation may be any computation described herein, such as quantum computation, quantum-classical computation, or classical computation. The computation may include an adjustable and non-adjustable (or static) instruction set.

[0145] In a second operation (504), the method (500) may include obtaining a trained AI module. The trained AI module may include any AI module described herein, such as an ML module or an RL module. For example, the trained AI module may include an AI module obtained from the method (400) described herein with respect to FIG. 4. The trained AI module may include a trained policy and an action epoch schedule (such as the trained policy and action epoch schedule described herein with respect to the method (400) of FIG. 4).

[0146] In a third operation (506), the method (500) may include initializing a non-classical device. The non-classical device may include a syndrome subsystem and a computation subsystem. The non-classical device may include any quantum device described herein (e.g., with respect to the system (100) of FIG. 1). The syndrome subsystem may include any syndrome subsystem described herein (e.g., with respect to the system (100) of FIG. 1). The computation subsystem may include any computation subsystem described herein (e.g., with respect to the system (100) of FIG. 1).

[0147] In a fourth operation (508), the method (500) may include initializing a state-action epoch and adjustable parameters of a state-action epoch schedule.

[0148] In a fifth operation (510), the method (500) may include executing a segment of computational instructions from a current state-action epoch to a next state-action epoch. The computational instructions may include adjustable and non-adjustable (or static) instructions. The adjustable instructions may be obtained from adjustable parameters.

[0149] In a sixth operation (512), the method (500) may include performing measurements of one or more registers. The one or more registers may include syndrome subsystem measurements.

[0150] In the seventh operation (514), the method (500) may include using the trained policy of the measured and trained AI module to provide a new sequence of adjustable parameters.

[0151] In the eighth operation (516), the method (500) may include obtaining a new sequence of adjustable instructions for calculation.

[0152] In the ninth operation (518), the method (500) may include determining whether a stop criterion is satisfied. If the stop criterion is not satisfied, any, at least a subset, or all of the fifth, sixth, seventh, and eighth operations (510), (512), (514), and (516) may be repeated at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, or more times until the stop criterion is satisfied. If the stop criterion is satisfied, the tenth operation (520) may be performed.

[0153] In the tenth operation (520), the method (500) may include performing measurements to obtain information (such as classical information) and ending the calculation.

[0154] Numerous variations, modifications, and adaptations are possible based on the methods (200), (300), (400), (500), (1300), and (1400) provided herein. For example, the order of operations of the methods (100), (200), (300), (400), (500), (1300), and (1400) may be changed, some operations may be deleted, some operations may be replicated, and additional operations may be added as needed. Some of the operations may be executed sequentially. Some of the operations may be executed in parallel. Some of the operations may be executed once. Some of the operations may be executed more than once. Some of the operations may include sub-operations. Some of the operations may be automated, and some of the operations may be manual.

[0155] Computer system The present disclosure provides a computer system programmed to implement the methods of the present disclosure. FIG. 6 shows a computer system (601) programmed or configured to implement the methods of the present disclosure. The computer system (601) can adjust various aspects of the methods and systems of the present disclosure.

[0156] A computer system (601) is an electronic device of a user or the computer system, and the user or the computer system is positioned remotely with respect to the electronic device. The electronic device can be a mobile electronic device. The computer system (601) includes a central processing unit (CPU, referred to herein as "processor" and "computer processor") (605) that can be a single-core or multi-core processor, or multiple processors for parallel processing. The computer system (601) also includes a memory or storage location (610) (e.g., random access memory, read-only memory, flash memory), an electronic storage device (615) (e.g., hard disk), a communication interface (620) (e.g., network adapter) for communicating with one or more other systems, and peripheral devices (625), such as cache, other memory, data storage devices, and / or an electronic display adapter. The memory (610), storage device (615), interface (620), and peripheral devices (625) communicate with the CPU (605) via a communication bus (solid line), such as a motherboard. The storage device (615) can be a data storage device (or data repository) for storing data. The computer system (601) can be operably connected to a computer network ("network") (630) with the aid of the communication interface (620). The network (630) can be the Internet and / or an extranet, an intranet and / or an extranet in communication with the Internet.

[0157] In some cases, the network (630) is a telecommunications and / or data network. The network (630) can include one or more computer servers, which can enable distributed computing such as cloud computing. For example, one or more computer servers can enable cloud computing on the network (630) (the "cloud") to perform various aspects of the analysis, calculation, and generation of the present disclosure. Such cloud computing can be provided, for example, by cloud computing platforms such as Amazon (registered trademark) Web Services (AWS), Microsoft Azure, Google (registered trademark) Cloud Platform, and IBM Cloud. The network (630) can, in some cases, implement a peer-to-peer network with the help of the computer system (601), which can enable devices connected to the computer system (601) to act as clients or servers. "Cloud" services (including one or more of the above cloud platforms) may also be used to provide data storage.

[0158] The CPU (605) can execute a sequence of machine-readable instructions that can be embodied in a program or software. These instructions can be stored in a memory location such as the memory (610). These instructions can be directed to the CPU (605), which can later program or configure the CPU (605) to implement the methods of the present disclosure. Examples of operations performed by the CPU (605) can include fetch, decode, execute, and write-back.

[0159] The CPU (605) can be part of a circuit such as an integrated circuit. One or more other components of the system (601) can be included in the circuit. In some cases, the circuit is an application-specific integrated circuit (ASIC). The CPU (605) can include one or more general-purpose processors, one or more graphics processing units (GPUs), or a combination thereof.

[0160] The memory device (615) can store files such as drivers, libraries, and saved programs. The memory device (615) can store user data. The computer system (601) may include one or more additional data storage devices outside of the computer system (601), such as being located on a remote server in communication with the computer system (601) via an intranet or the Internet in some cases.

[0161] The computer system (601) can communicate with one or more remote computer systems via the network (630). For example, the computer system (601) can communicate with a user's remote computer system. Examples of remote computer systems include personal computers (e.g., portable PCs), slates or tablet PCs (e.g., Apple® iPad®, Samsung® Galaxy Tab), phones, smartphones (e.g., Apple® iPhone®, Android-enabled devices, Blackberry®), or personal digital assistants. A user can access the computer system (601) via the network (630). The user can control or adjust various aspects of the methods and systems of the present disclosure.

[0162] A method as described herein can be executed as machine (e.g., computer processor) executable code stored on an electronic storage location of a computer system (601), such as, for example, in a memory (610) or an electronic storage device (615). In some embodiments, the machine executable or machine readable code can be provided in the form of software. In use, the code can be executed by a processor (605). Optionally, the code can be retrieved from the storage device (615) and stored in the memory (610) for immediate access by the processor (605). In some situations, the electronic storage device (615) can be excluded and the machine executable instructions can be stored in the memory (610).

[0163] The code can be pre-compiled and configured for use with a machine having a processor adapted to execute the code, or can be compiled at run-time. The code can be provided in a programming language that can be selected to render the code executable in a pre-compiled form, or in a form that remains compiled.

[0164] Aspects of the systems and methods provided herein, such as computer system (601), can be embodied in programming. Various aspects of this technology can typically be considered as a "product" or "manufactured article" in the form of machine (or processor) executable code and / or associated data that is carried on or embedded in a type of machine-readable medium. The machine executable code can be stored in an electronic storage device such as a memory (e.g., read-only memory, random access memory, flash memory solid state memory) or a hard disk. A "storage" type medium can include any or all of various semiconductor memories, tape drives, disk drives, etc., which are tangible memories of a computer or processor, or related modules thereof, and which can provide non-transitory storage at any time for the programming of software. All or part of the software is sometimes communicated via the Internet or various other electrical communication networks. Such communication can enable, for example, the loading of software from one computer or processor to another, such as from a management server or host computer to an application server computer platform. Thus, another type of medium that can hold software elements includes optical, electrical, and electromagnetic waves such as those used via various air links, as well as wired and optical terrestrial communication line networks between local devices. Physical elements that carry such waves, such as wired or wireless links, optical links, etc., can also be considered as media that hold software. As used herein, the term "readable medium" of a computer or machine refers to any medium that participates in providing instructions to a processor for execution, unless limited to non-transitory tangible "storage" media.

[0165] Accordingly, machine-readable media such as computer-executable code can take many forms, including but not limited to tangible storage media, carrier wave media, or physical transmission media. Non-volatile storage media can include, for example, optical disks or magnetic disks such as any of the storage devices in any computer(s) that might be used to implement, for example, a database shown in the drawings. Volatile storage media can include dynamic memory such as the main memory of such a computer platform. Tangible transmission media include coaxial cables; wires including the buses within a computer system, including copper wire and fiber optic cable. Carrier wave transmission media can take the form of electrical signals or electromagnetic signals, such as those generated during radio frequency (RF) and infrared (IR) data communications, or in the form of sound waves or light waves. Thus, common forms of computer-readable media include, for example: floppy disks, flexible disks, hard disks, magnetic tape, other magnetic media, CD-ROM, DVD or DVD-ROM, other optical media, punch cards, paper tape, other physical storage media with patterns of holes, RAM, ROM, PROM and EPROM, FLASH-EPROM, other memory chips or cartridges, carrier waves carrying data or instructions, cables or links that transmit such carrier waves, or other media that a computer can read programming code and / or data from. Many of these forms of computer-readable media can be involved in carrying one or more sequences of one or more instructions to a processor for execution.

[0166] A computer system (601) can include, or be communicable with, an electronic display (635) that includes a user interface (UI) (640). Examples of UIs include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0167] The computer system (601) can include or communicate with, for example, a non - classical computer (e.g., a quantum computer) (645) for executing a quantum algorithm (e.g., quantum mechanical energy and / or electronic structure calculations). The non - classical computer (1045) may be operatively coupled to a central processing unit (605) and / or a network (630) (e.g., the cloud).

[0168] The computer systems of the present disclosure may be, for example, as described in International Application PCT / CA2017 / 050709, U.S. Application No. 15 / 486,960, U.S. Patent No. 9,537,953, and U.S. Patent No. 9,660,859, each of which is hereby incorporated by reference in its entirety herein.

[0169] The methods and systems of the present disclosure can be implemented by one or more algorithms. When executed by a central processing unit (605), the algorithms can be implemented by software.

[0170] Although described herein with respect to hybrid or quantum - classical computing, or specific systems such as computing hardware, the problems of the present disclosure may be solved using various types of computing systems, such as, for example, one or more classical computers, one or more non - classical computers (such as one or more quantum computers), or a combination of one or more classical computers and one or more non - classical computers.

Example

[0171] Example 1: AI - Driven QAOA When using QAOA to solve the combinatorial optimization problems described herein, each instance of the combinatorial optimization problem may be provided by an oracle that computes the objective function. The Hamiltonian representation of the objective function may be programmed within the quantum oracle and coherently computed by any query to the oracle via the computation. In some embodiments, there may only be two state-action epochs: one during the QAOA computation (which may be referred to as the intermediate state-action epoch), and one at the end of one execution of the QAOA computation (which may be referred to as the terminal state-action epoch).

[0172] In each state-action epoch, the rotation angles β and γ may then be confirmed to be used to perform exp(-iyH) on some computational registers and then exp(-iβX) on each qubit of the computational register. In some embodiments, the immediate reward is not provided to the AI module in the intermediate state-action epoch, but the reward is provided in the terminal state-action epoch in response to the measurement of the computational register. In some embodiments, this reward is proportional to <γ, β|H|γ, β>, e.g., energy, eigenvalue, etc., such that the size of the reward received by the agent corresponds to the increase in the readout of the objective function.

[0173] Example 2: AI-Driven Variational Quantum Eigensolver In an embodiment, the variational quantum eigenvalue solver (VQE) introduced above is a method for using a quantum device to find the low-energy state (e.g., the ground state) of a quantum Hamiltonian. In quantum chemistry applications, the Hamiltonian is constructed from its molecule or a type of material and may then be transformed into a Hamiltonian written from the perspective of multiple qubits in various ways (e.g., Jordan-Wigner transformation or Bravyi-Kitaev transformation). In some examples, VQE may use the power of a quantum computer (even a small one) to prepare highly entangled quantum states. On the one hand, VQE may use a classical optimization module that varies the gate set executed by VQE to achieve a more desirable quantum state by the end of the calculation. VQE may assume that it is easy to solve classical optimization problems; however, the landscape of optimizing the objective function that specifies the angles and amplitudes of single and multi-qubit gates for the observation of quantum states (e.g., energy) can be very complex. In some aspects, the methods disclosed herein provide a way to use an AI module (e.g., reinforcement learning) to train an approximate mechanical programming scheme that can achieve the goals of VQE (e.g., finding the angles and amplitudes of single and multi-qubit gates associated with the observation of a quantum state).

[0174] In some examples, the application of AI-driven quantum computing (including use cases in QAOA and VQE) can be considered a technique for inducing a quantum simulation process. One goal of quantum simulation may be to prepare a quantum state containing information about a hard calculation. In QAOA, the final state to be prepared may represent one or more of the optimal or next-optimal solutions to an optimization problem. In VQE, the final state to be prepared may represent the ground or low-energy state of a molecular Hamiltonian. For example, quantum simulation may start from either a state that is considered a good guess for the problem to be solved, or, for example, the ground state of a Hamiltonian that is easy to handle or well-understood for preparation. The transition from the initial state to the final state is performed by a quantum device through a quantum algorithm that includes several quantum gates. The path taken by the quantum algorithm from the initial state to the final state affects how well the final state approaches a solution to the computational task being performed. However, the choice of path is not a trivial matter. The AI-driven quantum computing method disclosed herein provides a way to overcome this problem.

[0175] Compared to methods such as gradient-based optimization, the methods disclosed herein for QAOA and VQE may have the advantage of not necessarily requiring the calculation or approximation of the partial derivative of an observable (e.g., the energy of the prepared state). Calculating the gradient for this landscape requires resources and may also require extensive repetition of various similar quantum circuits and can be plagued by noisy measurements.

[0176] Example 3: AI-Driven Adiabatic Quantum Computing Adiabatic quantum computing is universal quantum computing, and its computational objective is to obtain the ground state of a target computational subsystem Hamiltonian. To achieve this, adiabatic quantum computing may start with an initial computational subsystem Hamiltonian whose ground state is easy to prepare, and then adiabatically change the computational subsystem Hamiltonian to a final computational subsystem Hamiltonian.

[0177] To efficiently obtain the correct answer, it may be important to maintain the energy gap between the instantaneous ground state and the excited state that is widely open during the calculation. The energy gap may prevent the quantum state from non-adiabatic transitions and thermal excitations, each of which may cause computational errors. The energy gap may depend on the path through which the computational subsystem Hamiltonian is changed from the initial Hamiltonian to the final one during the calculation.

[0178] Therefore, it may be desirable to identify a path for the energy gap to remain as open as possible during the calculation. In some cases, the use of non-stochastic paths or inhomogeneous transverse magnetic fields may prevent the energy gap from closing exponentially fast in relation to the size of the computational register. The computational subsystem Hamiltonian includes adjustable parameters, which are defined by the AI module.

[0179] In some embodiments, the computational subsystem and the syndrome subsystem may be entangled via a two-qubit coupling such as a controlled-X gate. In each state-action epoch, the syndrome subsystem may be measured. By using the measurement results, the strategy of the AI module may provide the next iteration of the schedule for the adjustable parameters of the computational subsystem until the next state-action epoch.

[0180] Example 4: Reinforcement Learning of a Simulated Annealing Temperature Schedule Optimization procedures for calculations such as simulated annealing may typically require careful selection and fine-tuning of parameters (such as temperature schedules), and may require multiple repeated executions until the optimization procedure converges to a solution. Limited choices of parameters may result in fast execution of the optimization procedure but an inaccurate solution, an accurate solution but slow execution of the optimization procedure, or an inaccurate solution and slow execution of the optimization procedure. Disclosed herein are systems and methods that utilize AI procedures to select parameters in order to obtain an accurate solution and fast execution of the optimization procedure.

[0181] Reinforcement learning (RL) was applied to learn the temperature schedule of simulated annealing in order to always check the ground state. A weak-strong cluster model was applied. The weak-strong cluster model is a small 16-node bipartite graph that includes two fully connected 8-node graphs. Negative bias was applied to the first graph (h = -0.44), and a stronger positive bias was applied to the second graph (h = 1.0). The four outermost nodes of one cluster were coupled to the four outermost nodes of the second cluster by ferromagnetic (J = 1) couplings. All couplings, including the intra-cluster couplings between nodes of each graph and the inter-cluster couplings between the first and second clusters, were set to unit strength (J = 1). In this configuration, the global minimum was achieved when the spin values of both clusters satisfied and aligned with the inter-cluster coupling.

[0182] Figure 7 shows an example of a weak-strong cluster model. As shown in Figure 7, the graph includes two fully connected 8-node graphs in configuration (700). The first graph may include nodes (701a), (701b), (701c), (701d), (701e), (701f), (701g), and (701h). The second graph may include nodes (702a), (702b), (702c), (702d), (702e), (702f), (702g), and (702h). A negative bias was applied to the first graph (h = -0.44), and a stronger positive bias was applied to the second graph (h = 1.0). Figure 7 shows the nodes interacting within each graph (703). Figure 7 shows the nodes interacting between the graphs (704). The model shown in Figure 7 may include nodes representing, for example, spins, atoms, electrons, etc.

[0183] Figure 8 shows an example of a 16-spin distribution of energy. As shown, the weak-strong cluster model includes a local minimum of -2.47 represented by configuration (810). The local minimum aligned the nodes in the first 8-node graph and, in a single-node graph, the nodes not aligned with the first 8-node graph. The global minimum was confirmed in configuration (700) where all 16 nodes were aligned. The global maximum was confirmed in configurations (840) and (845) where half of the spins were aligned in each 8-node graph. Configurations (820) and (830) are other intermediate energy configurations.

[0184] Figure 9 shows an example of an energy landscape associated with the weak-strong cluster model. Eight spin flips are required to move along the landscape from local minima and global minima. As shown, the solver has to cross large uphill sections of the energy landscape to confirm the global minimum. For the annealer to confirm the global minimum, the annealer would need to start at a higher initial temperature to sample the entire energy landscape. Thereafter, the temperature is lowered to confirm the minimum. The temperature of the system may be changed out of time. The temperature schedule is a representative case of a policy and it may be learned by a reinforcement learning algorithm.

[0185] Figure 10 shows an example of observations during the development of the weak-strong cluster model. Here, N spin refers to the number of aligned nodes (or spins) in the graph, N steps refers to the number of steps per episode, N sweeps refers to the number of sweeps per episode, N read and N rep refers to the number of simultaneous annealers, N buffer refers to the buffer size (or how many steps should be taken between updates), and o refers to the observations of the weak-strong cluster model.

[0186] A neural network was implemented to learn the optimal policy. One set of (512) kernels slid along the Rep dimension while another set of (512) kernels slid along the spin dimension. These kernels operated in parallel over the spin values. Their outputs were flattened, concatenated, and sent to a dense layer.

[0187] A neural network was implemented to learn to observe the state of the system and suggest changes to the system temperature.

[0188] Figure 11 shows an example of the excellent convergence possibility of simulated annealing assuming various initial temperatures and final temperatures. As shown, higher initial temperatures (lower beta) had a higher success probability than lower initial temperatures (higher beta).

[0189] The reward was implemented to train the neural network to minimize energy. The sparse reward was implemented to give the agent the negative average final energy of the episode. The dense reward was implemented to give the agent the negative average energy difference between the previous state and the new state during each step of the process. Figure 12 shows the temperature schedule for increasing N steps for each example. The insets (1210), (1220), and (1230) show the temperature schedule (top) and the energy evolution (bottom) along the temperature schedule.

[0190] Figure 12 shows an example of the excellent convergence possibility of simulated annealing assuming random initial and final temperatures. Moving from (1210) to (1220) and then to (1230), the number of steps N steps in the temperature sweep (policy) increased. The number of upward steps in the energy landscape has increased, thus having the possibility of checking for the global minimum. As shown, the learning algorithm learned a temperature sweep with a higher possibility of checking for the global minimum. In particular, the policy of taking upward steps in the energy landscape has been confirmed to be a policy with a high possibility of discovering the global minimum.

[0191] Preferred embodiments of the present invention have been shown and described herein, but it will be apparent to those skilled in the art that such embodiments are provided by way of example only. It is not intended that the present invention be limited by the specific examples provided within this specification. While the present invention has been described with reference to the foregoing specification, the description and illustration of the embodiments herein are not intended to be construed in a limiting sense. Those skilled in the art will envision many changes, variations, and substitutions without departing from the present invention. Further, it will be understood that all aspects of the present invention are not limited to the specific depictions, configurations, or relative ratios described herein, which depend on various conditions and variables. It should be understood that various alternatives to the embodiments of the present invention described herein may be utilized in practicing the present invention. Therefore, the present invention is intended to cover any such alternatives, modifications, variations, or equivalents. The following claims define the scope of the present invention, and it is intended that methods and structures within the scope of these claims and their equivalents be covered thereby.

Claims

1. A hybrid computing system for performing calculations using artificial intelligence (AI), the system comprising: (a) at least one quantum computer configured to perform a calculation including one or more adjustable parameters and one or more non-adjustable parameters and output a report indicating the calculation, the computer comprising: (i) one or more registers, the one or more registers including one or more qubits, wherein the one or more qubits are configured to perform the calculation, one or more registers; (ii) a measurement unit configured to measure at least one state of the one or more qubits to determine a representation of the state of the one or more qubits, thereby determining the representation of the calculation, a measurement unit; and a computer including; (b) at least one artificial intelligence (AI) control unit, the at least one artificial intelligence (AI) control unit configured to (1) control the calculation, (2) execute at least one AI procedure to determine one or more adjustable parameters corresponding to the calculation, and (3) instruct the computer with the one or more adjustable parameters, wherein the at least one artificial intelligence (AI) control unit includes one or more AI control unit parameters, the at least one AI procedure is configured to improve the calculation, the at least one AI procedure is different from the calculation, at least one artificial intelligence (AI) control unit; and The system is configured such that the measurement unit measures at least one of the states of the one or more qubits to obtain syndrome data representing partial information regarding the current state of the calculation and provides the syndrome data to the AI control unit.

2. The register(s) with a value of 1 or more includes a calculation register and a syndrome register, where the calculation register includes one or more calculation qubits, the one or more calculation qubits are configured to perform the calculation, where the syndrome register includes one or more syndrome qubits different from the one or more calculation qubits, where the one or more syndrome qubits are quantum-mechanically entangled with the one or more calculation qubits, and where the one or more syndrome qubits are not for performing the calculation, and where the measurement unit is configured to measure the state of the one or more syndrome qubits to determine a representation of the state of the one or more calculation qubits, thereby determining the representation of the calculation, the system according to claim 1.

3. The system according to claim 1, wherein the calculation includes quantum calculation.

4. The system according to claim 3, wherein the quantum calculation includes adiabatic quantum calculation.

5. The system according to claim 3, wherein the quantum calculation includes a quantum approximate optimization algorithm (QAOA).

6. The system according to claim 3, wherein the quantum calculation includes a variational quantum algorithm.

7. The system according to claim 3, wherein the quantum calculation includes error correction on a quantum register.

8. The system according to claim 3, wherein the quantum calculation includes a fault-tolerant quantum computing gadget.

9. The system according to claim 1, wherein the calculation includes classical calculation.

10. The system according to claim 1, wherein the calculation includes at least one member selected from the group consisting of simulated annealing, simulated quantum annealing, parallel tempering, parallel tempering with equal-energy cluster moves, diffusion Monte Carlo method, population annealing, and quantum Monte Carlo method.

11. The system according to claim 1, wherein the at least one quantum computer is configured to perform one or more quantum operations including at least one member selected from the group consisting of preparation of an initial state of the one or more qubits, implementation of one or more single-qubit quantum gates on the one or more qubits, implementation of one or more multi-qubit quantum gates on the one or more qubits, and adiabatic evolution from an initial Hamiltonian to a final Hamiltonian using one or more qubits.

12. The system according to claim 2, wherein the representation of the state of the one or more computational qubits is mathematically correlated with the state of the one or more syndrome qubits.

13. The system according to claim 2, wherein the measurement unit is configured to measure the state of the one or more syndrome qubits during the evolution of the one or more computational qubits during the computation.

14. The system according to claim 1, wherein the at least one AI procedure includes at least one machine learning (ML) procedure.

15. The system according to claim 14, wherein the at least one ML procedure includes at least one ML training procedure.

16. The system according to claim 14, wherein the at least one ML procedure includes at least one ML inference procedure.

17. The system according to claim 1, wherein the at least one AI procedure includes at least one reinforcement learning (RL) procedure.

18. The system according to claim 1, wherein the at least one AI procedure is configured to modify the adjustable parameter during the computation, thereby providing one or more modified adjustable parameters.

19. The system according to claim 1, wherein the one or more modified adjustable parameters are configured to modify the computation during the process of the computation.

20. The system according to claim 1, wherein the at least one AI control unit includes at least one member selected from the group consisting of a tensor processing unit (TPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC).

21. The system of claim 1, wherein the at least one computer includes at least one member selected from the group consisting of a field programmable gate array (FPGA) and an application specific integrated circuit (ASIC).

22. The system of claim 1, wherein the at least one AI control unit communicates with the at least one computer on a network.

23. The system of claim 1, wherein the at least one AI control unit communicates with the at least one computer on a cloud network.

24. The system of claim 1, wherein the at least one AI control unit is integrated as a classical processing system operating at extremely low temperatures within a refrigeration system.

25. The system of claim 1, wherein the one or more adjustable parameters and the one or more non - adjustable parameters define the next segment of the calculation including an instruction set from the current representation of the calculation.

26. The system of claim 1, wherein the one or more adjustable parameters include an initial temperature of the calculation.

27. The system of claim 1, wherein the one or more adjustable parameters include a temperature schedule of the calculation.

28. The system of claim 1, wherein the one or more adjustable parameters include a final temperature of the calculation.

29. The system of claim 1, wherein the one or more adjustable parameters include a schedule of pumping energy of a network.

30. The system of claim 1 or claim 2, wherein the one or more adjustable parameters include an instruction of quantum gates for a segment of the calculation.

31. The system of claim 1 or claim 2, wherein the one or more adjustable parameters include an instruction of a local operation and classical communication (LOCC) channel for a segment of the calculation.

32. The system of claim 1, wherein the AI control unit includes a neural network, and wherein the one or more AI control unit parameters include neural network weights corresponding to the neural network.

33. A method for training an artificial intelligence (AI) control unit, the method comprising Step of obtaining: (a) one or more instances of one or more non-adjustable parameters of 1 or more, and (2) one or more adjustable parameters and AI control unit parameters; Step of configuring the AI control unit using the AI control unit parameters; Step of selecting at least one instance of the one or more non-adjustable parameters; Step of configuring a computer using the at least one instance of the one or more non-adjustable parameters and the one or more adjustable parameters, wherein the values of the one or more adjustable parameters are directed by the AI control unit, and wherein the computer includes one or more registers; Step of executing a segment of a calculation using the one or more registers of the computer; Step of performing at least one measurement of at least one of the one or more registers, thereby obtaining a representation of the segment of the calculation, wherein if the segment is not the last segment for the calculation, the at least one measurement includes syndrome data, and if the segment is the last segment for the calculation, the at least one measurement includes calculation data; Step of repeating (c)-(f) a plurality of times; Step of outputting a report indicating each of the plurality of executed calculations; Step of reconfiguring the AI control unit by modifying the AI control unit parameters based on the report, wherein the reconfiguration of the AI control unit is configured to improve the calculation, and the AI procedure executed by the AI control unit is different from the calculation; Step of repeating (c)-(i) until a stop criterion is satisfied, the method comprising:

34. The method according to claim 33, wherein the AI control unit and the computer include a system for executing the calculation, and wherein the system includes the system according to any one of claims 1-32.

35. A method for training a hybrid computer including at least one artificial intelligence (AI) control unit and at least one non-classical computer for executing a calculation, the method comprising: Step of using the AI control unit, thereby: (i) Obtain a training set including a plurality of instances of the calculation, (ii) Obtain and initialize AI control unit parameters and one or more adjustable parameters, (iii) Select one instance of the plurality of instances, (iv) Initialize the at least one non-classical computer, and (v) Obtain and initialize a state-action epoch schedule including a plurality of state-action epochs, (b) A step of using the at least one non-classical computer, whereby (i) Execute the instance until the next state-action epoch of the plurality of state-action epochs, (ii) Perform one or more measurements of the syndrome register to obtain an immediate reward corresponding to the selected instance, and (iii) Provide an indication of the immediate reward to the AI control unit, thereby updating the AI control unit parameters based on the immediate reward, and the AI control unit parameters updated based on the immediate reward are configured to improve the calculation, (c) A step of using the AI control unit to provide a set of adjustable parameters from the one or more adjustable parameters, (d) Repeating (b) until a first stop criterion is satisfied, (e) Repeating (a)(iii)-(d) until a second stop criterion is satisfied, a method comprising.

36. A method for executing a calculation using a hybrid computer including at least one artificial intelligence (AI) control unit and at least one non-classical computer, the method comprising: (a) A step of using the AI control unit, whereby (i) Obtain a set of instructions representing the calculation, the instructions including an adjustable set of instructions including a plurality of adjustable instructions, (ii) Obtain a trained policy and a state-action epoch schedule including a plurality of state-action epochs, (iii) Initialize the at least one non-classical computer, and (iv) Initialize the plurality of state-action epochs and the adjustable set of instructions, (b) A step of using the at least one quantum computer, whereby (i) Execute the calculation until the next state-action epoch of the plurality of state-action epochs, (ii) performing one or more measurements of the one or more registers to obtain an expression of the calculation, and (iii) obtaining a plurality of adjustable instructions next, and (c) repeating (a)-(b) until a stop criterion is satisfied. A method comprising the steps of

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