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WO2024232909A2 - Amélioration de l'optimisation avec un algorithme génératif évolutif utilisant des modèles génératifs quantiques ou classiques - Google Patents

Amélioration de l'optimisation avec un algorithme génératif évolutif utilisant des modèles génératifs quantiques ou classiques Download PDF

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WO2024232909A2
WO2024232909A2 PCT/US2023/036429 US2023036429W WO2024232909A2 WO 2024232909 A2 WO2024232909 A2 WO 2024232909A2 US 2023036429 W US2023036429 W US 2023036429W WO 2024232909 A2 WO2024232909 A2 WO 2024232909A2
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quantum
samples
bit string
generative model
computer
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Collin Farquhar
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Zapata Computing Inc
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/60—Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/044—Recurrent networks, e.g. Hopfield networks
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/047—Probabilistic or stochastic networks
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/0475—Generative networks
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/088—Non-supervised learning, e.g. competitive learning
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/094—Adversarial learning
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic

Definitions

  • the field of the invention is enhanced optimization using quantum or classical models.
  • Quantum-assisted or quantum-inspired algorithms may outperform traditional classical algorithms in a real-world application having a commercial or scientific value.
  • a number of techniques have been developed to address optimization problems with quantum subroutines, including algorithms tailored for quantum annealers and gate-based quantum computers.
  • these various approaches have drawbacks.
  • PUBO polynomial unconstrained binary optimization
  • QEOs quantum enhanced optimizers
  • quantum generative models which can generate a sample with lower minima wthan those found by means of classical or known optimizers, including stand-alone, state-of-the-art classical solvers or optimizers.
  • optimizer and solver are used synonymously for purposes of the following disclosure.
  • Quantum-Enhanced Optimizers QEO may also be referred to as Generator-Enhanced Optimization (GEO), which encompasses the use of machine learning models known as generative models to solve optimization problems.
  • GEO Generator-Enhanced Optimization
  • the disclosed technology includes at least two embodiments for quantum-enhanced optimization (QEO).
  • QEO quantum-enhanced optimization
  • the first embodiment boosts the performance of classical and known optimizers by using a quantum generative model.
  • the QEO operates as a booster to enhance the performance of known stand-alone optimizers in complex instances where known optimizers have limitations and are incapable of providing the desired results in a stand- alone mode.
  • the quantum generative model is based on unsupervised machine learning methods.
  • the second embodiment operates as a stand-alone QEO optimizer.
  • the stand-alone optimizer exhibits improved performance when the purpose of the optimizer is to find the best minimum within the least number of cost function evaluations.
  • the disclosed quantum enhanced optimization methods outperform classical and known optimizers, including Bayesian optimizers which are known to be one of the best competing solvers in such tasks.
  • the generative models may be quantum-based or quantum-inspired, using tensor networks (TN).
  • TN tensor networks
  • the quantum generati ve model s are capable of generating new “unseen” soluti on candidates which have the potential for a lower value for the objective function then those already “seen” and used as the training step in training the generative model. This is a desirable feature of any practical machine learning (ML) model.
  • Another advantage of the present technology is that it can utilize available observations obtained from prior attempts to solve the optimization problem. These initial evaluations may originate from random searches or from classical optimizers tailored to solve specific problems.
  • Embodiments of the present invention implement a generative model based on Matrix Product States (MPS) to learn target distributions.
  • MPS is a type of Tensor Network (TN) where the tensors are arranged in a one-dimensional geometry. Despite its simple structure, MPS can represent a large number of quantum states extremely well.
  • TN Tensor Network
  • MPS can represent a large number of quantum states extremely well.
  • learning can be achieved by adjusting parameters of the wavefunction such that the distribution represented by Born’s rule is as close as possible to the data distribution.
  • MPS uses a direct sampling method that is more efficient than other Machine Learning (ML) methods, for instance, Boltzmann machines, which require Markov Chain Monte Carlo (MCMC) methods for data generation.
  • ML Machine Learning
  • MCMC Markov Chain Monte Carlo
  • a first data set is generated comprising a plurality of bit string data elements from a prior probability distribution.
  • Unsupervised training is performed, using the first data set to generate a quantum generative model.
  • new bit string samples are generated and filtered according to properties of the bit string samples.
  • the bit string samples are evaluated and selected based on the cost function values of the new bit string samples.
  • the first data set is merged with the selected bit string samples to create a second data set.
  • the steps are repeated iteratively so that the second data set is used to update the quantum generative model until a limiting number of iterations is reached.
  • the number of iterations may also be a predetermined number.
  • the properties of the bit string samples may include cardinality constraints. Also, the properties of the bit string samples may include frequency of appearance.
  • the prior probability distribution comprises initial observations and cost function values. The initial observations may be drawn from randomly selected data elements in the first dataset.
  • matrix product states MMS
  • MRS matrix product states
  • the quantum generative model may be implemented as a tensor network (TN).
  • the quantum generative model is a quantum-assisted generative adversarial network (GAN).
  • GAN quantum-assisted generative adversarial network
  • the bit string samples are evaluated based on minimizing cost function values.
  • the method and system may be practiced in a stand-alone mode (i.e., the initial dataset is not received from a first optimizer) and the required number of cost function evaluations are reduced over classical and other known optimizers.
  • a booster mode the initial dataset is provided by the output of a first optimizer and the method, practiced as a second optimizer, boosts the performance of the first optimizer.
  • the method and system of the second optimizer achieve lower minima than the first optimizer.
  • the first optimizer may be a classical optimizer.
  • a hybrid quantum-classical computer system for performing a method for solving combinatorial optimization problems.
  • the system includes a quantum computer, which comprises a plurality of qubits.
  • the system includes a classical computer having a processor, a non-transitory computer-readable medium, and computer instructions stored in the non-transitory computer-readable medium.
  • the computer instructions when executed by the processor of the hybrid quantum-classical computer, execute a method for solving combinatorial optimization problems.
  • a first data set is generated comprising a plurality of bit string data elements from a prior probability distribution.
  • Unsupervised training is performed, using the first data set to generate a quantum generative model.
  • new bit string samples are generated and filtered according to properties of the bit string samples.
  • bit string samples are evaluated and selected based on the cost function values of the new bit string samples.
  • the first data set is merged with the selected bit string samples to create a second data set.
  • the steps are repeated iteratively so that the second data set is used to update the quantum generative until a limiting number of iterations is reached.
  • the number of iterations may also be a predetermined number.
  • the system further includes a Quantum Circuit Associative Adversarial Network (QC-AAN).
  • the system further includes a Quantum Circuit Born Machines (QCBM).
  • the quantum generative model may be implemented using gate-based quantum circuits.
  • the generative model may also be a quantum-assisted generative adversarial network (GAN).
  • the disclosed technology uses an evolutionary generative algorithm (EGA) method.
  • EGA evolutionary generative algorithm
  • the EGA method is a variation of the generator-enhanced optimization (GEO) disclosed herein, with the steps rearranged, as will be described.
  • Booster Mode a starting set of samples is created using a classical optimizer, and the starting samples are used as a dataset to pre-train a generative model.
  • a quantum or classical generative model is used to generate a set of new samples according to an exploration strategy.
  • a selection criterion may be used to filter a subset of the new samples, thereby producing filtered samples.
  • the cost of the filteredsamples is evaluated according to a cost or fitness function associated with the problem to be optimized, and a final selection of evaluated samples is made, typically by choosing, from the filtered samples, a plurality of samples having lowest cost.
  • the evaluated samples are added to the data set.
  • the generative model is trained on the new dataset.
  • the disclosed EGA method performs the following steps:
  • the EGA method has similarities to an evolutionary/genetic algorithm framework where selection occurs after the cost (or fitness) is evaluated. Instead of using GEO in standalone mode (with no optimizer) or in booster mode (initialized with samples from an optimizer), the disclosed EGA method alternates between using a generative model and a traditional optimizer.
  • the EGA method provides an improved method for generating sample populations, without relying on undirected randomness to create new samples.
  • the EGA method may use an exploration strategy in conjunction with a generative model.
  • the exploration strategy ensures that the generated solutions are not confined to localized area of the solution space.
  • the generative model provides a more sophisticated method for generating new samples, as the generative model can learn the underlying structure of an optimization landscape to then generate high-quality samples.
  • the EGA method combines generation and optimization steps to find better solutions. Evolutionary algorithms are not typically combined with an optimizer.
  • FIG. 1 is a diagram of a quantum computer according to one embodiment of the present invention.
  • FIG. 2A is a flowchart of a method performed by the quantum computer of FIG. 1 according to one embodiment of the present invention
  • FIG. 2B is a diagram of a hybrid quantum-classical computer which performs quantum annealing according to one embodiment of the present invention.
  • FIG. 3 is a diagram of a hybrid quantum-classical computer according to one embodiment of the present invention.
  • FIG. 4 illustrates in block diagram form the general data flow for using QEO
  • FIG. 5 illustrates the structure and data flow of the disclosed the quantum enhanced optimizer (QEO);
  • FIG. 6 illustrates the pseudocode for the first embodiment of the quantum enhanced optimization (QEO) algorithm for a stand-alone optimizer
  • FIG. 7 illustrates the pseudocode for the second embodiment of the quantum enhanced optimization (QEO) algorithm used as an enhancer or boost optimizer;
  • QEO quantum enhanced optimization
  • FIG. 8 illustrates the block diagram showing the process steps for the disclosed evolutionary generative algorithm (EGA) method.
  • FIG. 9 illustrates the pseudo-code for the disclosed evolutionary generative algorithm method.
  • the present technology uses a quantum generative model based on tensor networks (TNs) to lest and scale the disclosed QEO method with a set of vari bles commensurate with those found in industrial-scale scenarios.
  • TNs tensor networks
  • MPS Matrix Product States
  • a quantum generative model may be implemented (e.g., trained, stored, and/or executed) on a classical computer or a quantum computer.
  • the disclosed technology may, for example, operate in either of two modes: a boosted mode, or stand-alone mode.
  • boosted mode past observations are derived from classical and known solvers.
  • stand-alone mode all initial cost function evaluations are decided entirely by the quantum-inspired generative model, and a random prior is constructed to give support to the target probability distribution the MPS model is aiming to capture.
  • a first data set is generated comprising a plurality of bit string data elements from a prior probability distribution.
  • Unsupervised training is performed, using the first data set to generate a quantum generative model.
  • new bit string samples are generated and filtered according to properties of the bit string samples.
  • the new bit string samples are evaluated and selected based on the cost function values of the new bit string samples.
  • the first data set is merged with the selected bit string samples to create a second data set.
  • the steps are repeated iteratively so that the second data set is used to update the quantum generative until a limiting number of iterations is reached.
  • the number of iterations may also be a predetermined number.
  • a hybrid quantum-classical computer system for performing a method for solving combinatorial optimization problems.
  • the system includes a quantum computer comprises a plurality of qubits.
  • the system includes a classical computer having a processor, a non-transitory computer-readable medium, and computer instructions stored in the non-transitory computer-readable medium.
  • the computer instructions when executed by the processor, perform, on the hybrid quantum-classical computer, execute a method for solving combinatorial optimization problems.
  • a first data set is generated comprising a plurality of bit string data elements from a prior probability distribution.
  • Unsupervised training is performed, using the first data set to generate a quantum generative model.
  • new bit string samples are generated and filtered according to properties of the bit string samples.
  • the new bit string samples are evaluated and selected based on the cost function values of the new bit string samples.
  • the first data set is merged with the selected bit string samples to create a second data set.
  • the steps are repeated iteratively so that the second data set is used to update the quantum generative until a limiting number of iterations is reached.
  • the number of iterations may also be a predetermined number.
  • MPS is a type of Tensor Network (TN) where the tensors are arranged in a one- dimensional geometry. Despise its simple structure, MPS can represent a large number of quantum states extremely well. Once the MPS form of the wavefunction ⁇ is chosen, learning can be achieved by adjusting parameters of the wavefunction such that the distribution represented by Bom's rule is as close as possible to the data distribution. MPS enjoys a direct sampling method that is more efficient than other Machine Learning techniques, for instance, Boltzmann machines, which require which require a Markov Chain Monte Carlo (MCMC) process for data generation.
  • MCMC Markov Chain Monte Carlo
  • the method for training the MPS includes adjusting the value of the tensors composing the MPS as well as the bond dimension among them, via the minimization of the negative log- likelihood function defined over the training dataset sampled from the target distribution:
  • FIG. 4 illustrates in block diagram form the general data flow of a quantum enhanced optimizer QEO.
  • the illustration highlights the available strategies the user might explore a user might explore when solving a combinatorial optimization problem with a suite of classical optimizers such as simulated annealing (SA), parallel tempering (PT), generic algorithms (GA), among others.
  • SA simulated annealing
  • PT parallel tempering
  • GA generic algorithms
  • the user would use its computational budget with a preferred solver.
  • strategies 1-2 the user would inspect intermediate results and decide whether to keep trying with the same solver (strategy 1).
  • the user may try a new solver or a new setting of the same solver used to obtain the intermediate results (strategy 2).
  • acquired data will be used to train a quantum enhanced generative model within a QEO framework such as TN-QEO (strategy 3).
  • FIG. 5 provides an overview of the algorithm methodology for the quantum enhanced optimization method according to one embodiment of the present invention.
  • the QEO framework leverages generative models to utilize previous samples coming from any classical or quantum solver to propose candidate solutions which might be out of reach for conventional solvers.
  • the prior initial observations and cost function values serves as a prior distribution from which the training set samples are withdrawn to train the generative model (steps 1-3).
  • a tensor- network (TN) based generative model is central to one embodiment of the method referred hereafter as TN-QEO.
  • TN-QEO tensor- network
  • Other families of generative models from classical, quantum, or hybrid quantum-classical may also be used.
  • the quantum-enhanced generative model is used to capture the main features in training set and propose new solution candidates which are subsequently post selected before their costs are evaluated (steps 4-6).
  • the new dataset is then merged with the first dataset (step 7) to form an updated (second) dataset (step 8) which is to be used in the next iteration of the algorithm.
  • This section presents an algorithm for the Tensor Network Quantum Enhanced Optimizer scheme (TN-QEO) according to one embodiment of the present invention.
  • TN-QEO Tensor Network Quantum Enhanced Optimizer scheme
  • the new candidates go through a selection criterion before these are evaluated and subsequently appended to the original dataset from which a Boltzmann posterior is constructed and from which samples are taken as the training for the new algorithmic cycle.
  • FIG. 6 illustrates the pseudo-code for a full algorithm implemented according to1 one embodiment of the present invention.
  • the algorithm of FIG. 6 is illustrative only and does not constitute a limitation of the present invention.
  • the steps in the algorithm are broken down as follows:
  • step (2) Repeat the process from step (2) to (8), inclusive, with the output from step (8) as new input for step (2) every for new iteration after the initial one until reaching the predetermined maximum number of observations.
  • the goal is to use it as an enhancer or boost optimizer.
  • it may be considered a variant of the two-steps previous algorithm, where the first step, the prior construction, is now substituted for the result from another classical optimizer — in the case here studied it corresponds to Simulating Annealing — and the second step is understood as a continuation in the search for a lower minimum, now guided by the MPS update step.
  • the cost of evaluating the objective function is not high, and consequently there is no practical limitations in the number of observations, the number of cost evaluation of the Boltzmann distribution, to be taken.
  • FTG. 7 illustrates the pseudo-code for a full algorithm implemented according to one embodiment of the present invention. The algorithm of FIG.
  • FIG. 7 is illustrative only and does not constitute a limitation of the present invention.
  • the method of FIG. 7 follows fundamentally the same procedure as the prior method 1, with the only two differences.
  • the prior is constructed via Simulated Annealing instead of the Random procedure explained above.
  • the acquisition stage differs in that the new bit string candidates corresponds simply to sample a predetermined number of them from the trained MPS.
  • the steps in the algorithm are broken down as follows.
  • the computer system includes a classical computer.
  • the classical computer includes a processor, a non-transitory computer- readable medium, and computer instructions stored in the non-transitory computer-readable medium.
  • the computer program instructions are executable by the processor to perform the method.
  • the method includes: (a) generating a first dataset, the first dataset comprising a plurality of bit string samples from a prior probability distribution, (b) performing unsupervised training using the first dataset to generate a quantum generative model; (c) using the quantum generative model to generate a plurality of new bit string samples; (d) filtering the new bit string samples according to properties of the plurality of new bit string samples to produce a plurality of filtered bit string samples; (e) applying a cost function to the plurality of filtered bit string samples to produce a plurality of cost function values of the plurality of filtered bit string samples; (f) evaluating the plurality of new bit string samples based on the plurality of cost function values of the plurality of filtered bit string samples; (g) selecting a subset of the plurality of filtered bit string samples based on the evaluation; (h) merging the first dataset with the subset of the plurality of filtered bit string samples to generate a second dataset; and (g) iteratively repeating (c) through (h), where
  • the properties of the plurality of new bit string samples may include cardinality constraints.
  • the properties of the plurality of new bit string samples may include frequency of appearance.
  • the prior probability distribution may include initial observations and cost function values.
  • the method may further include drawing the initial observations from randomly selected data elements in the first dataset.
  • Operation (b) may include using matrix product states (MPS) to generate the quantum generative model.
  • the quantum generative model may be implemented as a tensor network (TN).
  • the quantum generative model may include a generative adversarial network (GAN).
  • the evaluating may include evaluating the plurality of new bit string samples based on minimizing cost function values.
  • the method may be practiced in a stand-alone mode.
  • the required number of cost function evaluations may be smaller than that of classical optimizers.
  • Operation (a) may include receiving the first dataset from an output of a first optimizer, and the method may boost performance of the first optimizer.
  • the method may achieve lower minima of the cost function than the first optimizer.
  • the first optimizer may be a classical optimizer.
  • the computer system may further include a quantum computer, which includes a plurality of qubits.
  • Performing unsupervised training using the first dataset to generate the quantum generative model may include performing the unsupervised training on the quantum computer.
  • the quantum generative model may include a quantum-assisted generative adversarial network (qa-GAN).
  • the computer system may include: a classical computer including a processor, a non-transitory computer-readable medium, and computer program instructions stored in the non-transitory computer-readable medium.
  • the computer program instructions when executed by the processor, perform, on the computer system, the method.
  • the method includes: (a) generating a first dataset, the first dataset comprising a plurality of bit string samples from a prior probability distribution, (b) performing unsupervised training using the first dataset to generate a quantum generative model; (c) using the quantum generative model to generate a plurality of new bit string samples; (d) filtering the new bit string samples according to properties of the plurality of new bit string samples to produce a plurality of filtered bit string samples; (e) applying a cost function to the plurality of filtered bit string samples to produce a plurality of cost function values of the plurality of filtered bit string samples; (f) evaluating the plurality of new bit string samples based on the plurality of cost function values of the plurality of filtered bit string samples; (g) selecting a subset of the plurality of filtered bit string samples based on the evaluation; (h) merging the first dataset with the subset of the plurality of filtered bit string samples to generate a second dataset; and (g) iteratively repeating (c) through (h), where
  • the prior probability distribution may include initial observations and cost function values.
  • the properties of the plurality of new bit string samples may include cardinality constraints.
  • the properties of the plurality of new bit string samples may include frequency of appearance.
  • the method may further include, before (b), performing initial cost function evaluations on a randomly selected data element in the first dataset.
  • Operation (b) may include using matrix product states (MPS) to generate the quantum generative model.
  • the quantum generative model may be implemented as a tensor network (TN).
  • the quantum generative model may be implemented as a generative adversarial network (GAN).
  • the evaluating may include evaluating the plurality of new bit string samples based on minimizing cost function values.
  • Operations (a)-(g) may be performed in a stand-alone mode. 28.
  • the required number of cost function evaluations may be smaller than that of classical optimizers.
  • Operation (a) may include receiving the first dataset from an output of a first optimizer, and wherein the method boosts performance of the first optimizer.
  • the method may achieve lower minima than the first optimizer.
  • the first optimizer may be a classical optimizer.
  • the system may further include a Quantum Circuit Associative Adversarial Network (QC-AAN).
  • the system may further include a Quantum Circuit Born Machine (QCBM).
  • the quantum generative model may be implemented using gate-based quantum circuits.
  • the system may further include a quantum computer, which includes a plurality of qubits. Performing unsupervised training using the first dataset to generate the quantum generative model may include performing the unsupervised training on the quantum computer.
  • the quantum generative model may include a quantum-assisted generative adversarial network (qa-GAN).
  • the disclosed technology disclosed can be practiced as a system, method, device, product, computer readable media, or article of manufacture.
  • One or more features of an implementation can be combined with the base implementation. Implementations that are not mutually exclusive are taught to be combinable.
  • One or more features of an implementation can be combined with other implementations. This disclosure periodically reminds the user of these options. Omission from some implementations of recitations that repeat these options should not be taken as limiting the combinations taught in the preceding sections. These recitations are hereby incorporated forward by reference into each of the following implementations.
  • an Evolutionary Generative Algorithm is applied to solving an optimization problem, i.e., to find the inputs that minimize or maximize the value of some function.
  • the EGA method is related to, but differs from, evolutionary algorithms, such as genetic algorithms.
  • EGA uses a generative model to create a new population of samples, analogous to generating a population of children in a genetic algorithm, but more intelligently, since a generative model may learn the structure of a problem, making it more likely to generate improved samples.
  • auxiliary optimizer such as a local optimizer
  • EGA EGA-like GAA
  • a local optimizer interleaved between generation steps.
  • Evolutionary algorithms are not typically combined with an optimizer. Combining generation steps with an optimizer has been shown to provide better solutions. More generally, using an optimizer in conjunction with a generative process leads to improved solutions. For a new sample generated in a particular region of solution space, it is possible for a local optimizer to improve upon the new sample.
  • FIG. 8 is a simplified block diagram of the method steps of the disclosed EGA method and algorithm 800.
  • the method generates a population of new samples using a quantum or classical generative algorithm and may also incorporate an exploration strategy. Exploration strategies are strategies for ensuring that a cost or fitness function landscape is sampled from with sufficient diversity so that search is not too narrow, and locally optimal but globally suboptimal minima are avoided. Such exploration strategies may include optimization strategies for generic optimization approaches, or those which are tailored to genetic algorithms such as mutation rate adjustment, crossover variation, diversity maintenance, dynamic search space adjustment, self-adaptation, or other strategies.
  • the method evaluates the cost (or fitness) of the new samples according to a cost or fitness function.
  • step 830 the method selects a subset of new samples using the prior-evaluated known cost as a selection criterion.
  • the selection criterion may be, for example, selecting the n lowest-cost samples, or selecting all samples below a certain fixed cost.
  • step 840 the method runs a local optimizer using the selected subset of the new samples as starting points, to produce a set of optimized samples.
  • the local optimizer may be any kind of generic optimizer, such as a gradient descent, quasi-Newton method, particle swarm, local random search, or any other local optimizer.
  • step 850 the method adds optimized samples and may add the new samples to the dataset.
  • step 860 the method trains the generative model using the samples that have been added to the dataset.
  • step 870 the method is repeated until a termination condition is met or the predetermined number of observations is reached.
  • FIG. 9 illustrates the EGA algorithm in pseudocode according to one embodiment of the present invention.
  • lists are initialized to contain samples, costs, and probabilities, as well as a variable defining the number of samples to generate on each step of the algorithm.
  • a variable to check if the algorithm should terminate is initialized to “False.” As long as the termination condition is not met the following steps are repeated or looped:
  • Example generative models include Variational Autoencoder (VAE), Generative Adversarial Networks (GANs), or Quantum Circuit Generative Adversarial Networks (QCGANs).
  • VAE Variational Autoencoder
  • GANs Generative Adversarial Networks
  • QCGANs Quantum Circuit Generative Adversarial Networks
  • Evaluate - Newly generated samples are passed to the objective function for cost evaluation and their associated costs are returned.
  • Select - A selector function chooses a subset of samples to be optimized. The optimization steps may be computationally expensive in terms of time-cost. Therefore, the selector chooses a subset of promising starting points, typically to be used with a local optimizer.
  • An example selection function chooses a fixed number of newly generated samples with the best cost evaluation.
  • Optimize - The disclosed technology combines genetic algorithm subroutines of generation and selection with a traditional optimizer.
  • a local optimizer is used to further improve on the selected samples, which returns optimized samples and their associated costs. For a new sample generated in a particular region of solution space, it is possible for a local optimizer to improve upon the new sample.
  • sample data from both the generative model and the local optimizer are used train the generative model.
  • An example of a local optimizer is a Least Squares optimizer.
  • probabilities associated with the samples are computed, for example, via a Softmax function of their costs. This promotes the generative model to create, with higher probability, samples similar to those that have a good cost.
  • the generative model is trained using the data of samples and probabilities from a combined dataset, comprising samples generated by the exploration mechanism, the generative model, and the optimizer.
  • Example termination conditions may include terminate after a certain number of steps through the while loop; terminate after a desired cost value is achieved; terminate if the best cost value has not been improved a predetermined number of steps; or terminate if no unique samples were generated.
  • the disclosed EGA method provides a better method for generating populations in evolutionary algorithms. Other approaches, such as genetic algorithms, often rely on undirected randomness to create new samples.
  • the EGA framework uses an exploration strategy in conjunction with a generative model. The exploration strategy ensures that the solutions that are generated are not confined to a small local area of the solution space.
  • the generative model provides a more sophisticated method for generating new samples, since the generative model can learn the underlying structure of an optimization landscape to then generate high-quality samples.
  • Any reference herein to a "generative model” may, for example, refer to any trained model that can generate new data samples that are similar in statistical properties to the data the generative model was trained on.
  • Any generative model referred to herein may, for example, be a Generative Adversarial Network (GAN), a Variational Autoencoder (VAE), a Restricted Boltzmann Machine (RBM), a Deep Belief Network (DBN), a Markov Chain or Hidden Markov Model (HMM), a Pixel Recurrent Neural Network (PixelRNN), a Long Short-Term Memory Network (LSTM), or a transformer-based model (e.g., any model in the GPT (Generative Pre- trained Transformer) family of models).
  • GAN Generative Adversarial Network
  • VAE Variational Autoencoder
  • RBM Restricted Boltzmann Machine
  • DBN Deep Belief Network
  • HMM Markov Chain or Hidden Markov Model
  • PixelRNN Pixel Recurrent
  • the fundamental data storage unit in quantum computing is the quantum bit, or qubit.
  • the qubit is a quantum-computing analog of a classical digital computer system bit.
  • a classical bit is considered to occupy, at any given point in time, one of two possible states corresponding to the binary digits (bits) 0 or 1.
  • a qubit is implemented in hardware by a physical medium with quantum-mechanical characteristics.
  • Such a medium, which physically instantiates a qubit may be referred to herein as a “physical instantiation of a qubit,” a “physical embodiment of a qubit,” a “medium embodying a qubit,” or similar terms, or simply as a “qubit,” for ease of explanation. It should be understood, therefore, that references herein to “qubits” within descriptions of embodiments of the present invention refer to physical media which embody qubits.
  • Each qubit has an infinite number of different potential quantum-mechanical states.
  • the measurement produces one of two different basis states resolved from the state of the qubit.
  • a single qubit can represent a one, a zero, or any quantum superposition of those two qubit states; a pair of qubits can be in any quantum superposition of 4 orthogonal basis states; and three qubits can be in any superposition of 8 orthogonal basis states.
  • the function that defines the quantum-mechanical states of a qubit is known as its wavefunction.
  • the wavefunction also specifies the probability distribution of outcomes for a given measurement.
  • a qubit which has a quantum state of dimension two (i.e., has two orthogonal basis states), may be generalized to a d-dimensional “qudit,” where d may be any integral value, such as 2, 3, 4, or higher.
  • d may be any integral value, such as 2, 3, 4, or higher.
  • measurement of the qudit produces one of d different basis states resolved from the state of the qudit.
  • Any reference herein to a qubit should be understood to refer more generally to an d-dimensional qudit with any value of d.
  • each such qubit may be implemented in a physical medium in any of a variety of different ways.
  • physical media include superconducting material, trapped ions, photons, optical cavities, individual electrons trapped within quantum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond), molecules (e.g., alanine, vanadium complexes), or aggregations of any of the foregoing that exhibit qubit behavior, that is, comprising quantum states and transitions therebetween that can be controllably induced or detected.
  • any of a variety of properties of that medium may be chosen to implement the qubit.
  • the x component of its spin degree of freedom may be chosen as the property of such electrons to represent the states of such qubits.
  • the y component, or the z component of the spin degree of freedom may be chosen as the property of such electrons to represent the state of such qubits.
  • there may be multiple physical degrees of freedom e.g., the x, y, and z components in the electron spin example
  • the physical medium may controllably be put in a state of superposition, and measurements may then be taken in the chosen degree of freedom to obtain readouts of qubit values.
  • Certain implementations of quantum computers comprise quantum gates.
  • quantum gates In contrast to classical gates, there is an infinite number of possible single-qubit quantum gates that change the state vector of a qubit. Changing the state of a qubit state vector typically is referred to as a single-qubit rotation, and may also be referred to herein as a state change or a single-qubit quantum-gate operation.
  • a rotation, state change, or single-qubit quantum-gate operation may be represented mathematically by a unitary 2X2 matrix with complex elements.
  • a rotation corresponds to a rotation of a qubit state within its Hilbert space, which may be conceptualized as a rotation of the Bloch sphere.
  • the Bloch sphere is a geometrical representation of the space of pure states of a qubit.
  • Multi-qubit gates alter the quantum state of a set of qubits. For example, two-qubit gates rotate the state of two qubits as a rotation in the four-dimensional Hilbert space of the two qubits.
  • a Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used.
  • a quantum circuit may be specified as a sequence of quantum gates.
  • quantum gate refers to the application of a gate control signal (defined below) to one or more qubits to cause those qubits to undergo certain physical transformations and thereby to implement a logical gate operation.
  • the matrices corresponding to the component quantum gates may be multiplied together in the order specified by the gate sequence to produce a 2 n X2 n complex matrix representing the same overall state change on n qubits.
  • a quantum circuit may thus be expressed as a single resultant operator.
  • designing a quantum circuit in terms of constituent gates allows the design to conform to a standard set of gates, and thus enable greater ease of deployment.
  • a quantum circuit thus corresponds to a design for actions taken upon the physical components of a quantum computer.
  • a given variational quantum circuit may be parameterized in a suitable device-specific manner.
  • the quantum gates making up a quantum circuit may have an associated plurality of tuning parameters.
  • tuning parameters may correspond to the angles of individual optical elements.
  • the quantum circuit includes both one or more gates and one or more measurement operations.
  • Quantum computers implemented using such quantum circuits are referred to herein as implementing “measurement feedback.”
  • a quantum computer implementing measurement feedback may execute the gates in a quantum circuit and then measure only a subset (i.e., fewer than all) of the qubits in the quantum computer, and then decide which gate(s) to execute next based on the outcome(s) of the measurement(s).
  • the measurement(s) may indicate a degree of error in the gate operation(s), and the quantum computer may decide which gate(s) to execute next based on the degree of error.
  • the quantum computer may then execute the gate(s) indicated by the decision.
  • Measurement feedback may be useful for performing quantum error correction, but is not limited to use in performing quantum error correction. For every quantum circuit, there is an error-corrected implementation of the circuit with or without measurement feedback.
  • Some embodiments described herein generate, measure, or utilize quantum states that approximate a target quantum state (e g., a ground state of a Hamiltonian).
  • a target quantum state e g., a ground state of a Hamiltonian
  • quantum states there are many ways to quantify how well a first quantum state “approximates” a second quantum state.
  • any concept or definition of approximation known in the art may be used without departing from the scope hereof.
  • the first and second quantum states are represented as first and second vectors, respectively, the first quantum state approximates the second quantum state when an inner product between the first and second vectors (called the “fidelity” between the two quantum states) is greater than a predefined amount (typically labeled ⁇ ).
  • the fidelity quantifies how “close” or “similar” the first and second quantum states are to each other.
  • the fidelity represents a probability that a measurement of the first quantum state will give the same result as if the measurement were performed on the second quantum state.
  • Proximity between quantum states can also be quantified with a distance measure, such as a Euclidean norm, a Hamming distance, or another type of norm known in the art.
  • Proximity between quantum states can also be defined in computational terms. For example, the first quantum state approximates the second quantum state when a polynomial time-sampling of the first quantum state gives some desired information or property that it shares with the second quantum state.
  • quantum computers are gate model quantum computers.
  • Embodiments of the present invention are not limited to being implemented using gate model quantum computers.
  • embodiments of the present invention may be implemented, in whole or in part, using a quantum computer that is implemented using a quantum annealing architecture, which is an alternative to the gate model quantum computing architecture.
  • quantum annealing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations.
  • FIG. 2B shows a diagram illustrating operations typically performed by a computer system 250 which implements quantum annealing.
  • the system 250 includes both a quantum computer 252 and a classical computer 254. Operations shown on the left of the dashed vertical line 256 typically are performed by the quantum computer 252, while operations shown on the right of the dashed vertical line 256 typically are performed by the classical computer 254.
  • Quantum annealing starts with the classical computer 254 generating an initial Hamiltonian 260 and a final Hamiltonian 262 based on a computational problem 258 to be solved, and providing the initial Hamiltonian 260, the final Hamiltonian 262 and an annealing schedule 270 as input to the quantum computer 252.
  • the quantum computer 252 prepares a well- known initial state 266 (FIG. 2B, operation 264), such as a quantum-mechanical superposition of all possible states (candidate states) with equal weights, based on the initial Hamiltonian 260.
  • the classical computer 254 provides the initial Hamiltonian 260, a final Hamiltonian 262, and an annealing schedule 270 to the quantum computer 252.
  • the quantum computer 252 starts in the initial state 266, and evolves its state according to the annealing schedule 270 following the time- dependent Schrodinger equation, a natural quantum-mechanical evolution of physical systems (FIG. 2B, operation 268). More specifically, the state of the quantum computer 252 undergoes time evolution under a time-dependent Hamiltonian, which starts from the initial Hamiltonian 260 and terminates at the final Hamiltonian 262. If the rate of change of the system Hamiltonian is slow enough, the system stays close to the ground state of the instantaneous Hamiltonian.
  • the system may leave the ground state temporarily but produce a higher likelihood of concluding in the ground state of the final problem Hamiltonian, i.e., diabatic quantum computation.
  • the set of qubits on the quantum annealer is in a final state 272, which is expected to be close to the ground state of the classical Ising model that corresponds to the solution to the original computational problem 258.
  • the final state 272 of the quantum computer 252 is measured, thereby producing results 276 (i.e., measurements) (FIG. 2B, operation 274).
  • the measurement operation 274 may be performed, for example, in any of the ways disclosed herein, such as in any of the ways disclosed herein in connection with the measurement unit 110 in FIG. 1.
  • the classical computer 254 performs postprocessing on the measurement results 276 to produce output 280 representing a solution to the original computational problem 258 (FIG. 2B, operation 278).
  • embodiments of the present invention may be implemented, in whole or in part, using a quantum computer that is implemented using a one- way quantum computing architecture, also referred to as a measurement-based quantum computing architecture, which is another alternative to the gate model quantum computing architecture.
  • a quantum computer that is implemented using a one- way quantum computing architecture, also referred to as a measurement-based quantum computing architecture, which is another alternative to the gate model quantum computing architecture.
  • the one-way or measurement based quantum computer is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.
  • Any of the functions disclosed herein may be implemented using means for performing those functions. Such means include, but are not limited to, any of the components disclosed herein, such as the computer-related components described below.
  • FIG. 1 a diagram is shown of a system 100 implemented according to one embodiment of the present invention.
  • FIG. 2A a flowchart is shown of a method 200 performed by the system 100 of FIG. 1 according to one embodiment of the present invention.
  • the system 100 includes a quantum computer 102.
  • the quantum computer 102 includes a plurality of qubits 104, which may be implemented in any of the ways disclosed herein. There may be any number of qubits 104 in the quantum computer 102.
  • the qubits 104 may include or consist of no more than 2 qubits, no more than 4 qubits, no more than 8 qubits, no more than 16 qubits, no more than 32 qubits, no more than 64 qubits, no more than 128 qubits, no more than 256 qubits, no more than 512 qubits, no more than 1024 qubits, no more than 2048 qubits, no more than 4096 qubits, or no more than 8192 qubits.
  • the number of gates may be at least proportional to the number of qubits 104 in the quantum computer 102.
  • the gate depth may be no greater than the number of qubits 104 in the quantum computer 102, or no greater than some linear multiple of the number of qubits 104 in the quantum computer 102 (e.g., 2, 3, 4, 5, 6, or 7).
  • the qubits 104 may be interconnected in any graph pattern. For example, they be connected in a linear chain, a two-dimensional grid, an all-to-all connection, any combination thereof, or any subgraph of any of the preceding.
  • quantum computer As will become clear from the description below, although element 102 is referred to herein as a “quantum computer,” this does not imply that all components of the quantum computer 102 leverage quantum phenomena.
  • One or more components of the quantum computer 102 may, for example, be classical (i.e., non-quantum components) components which do not leverage quantum phenomena.
  • the quantum computer 102 includes a control unit 106, which may include any of a variety of circuitry and/or other machinery for performing the functions disclosed herein.
  • the control unit 106 may, for example, consist entirely of classical components.
  • the control unit 106 generates and provides as output one or more control signals 108 to the qubits 104.
  • the control signals 108 may take any of a variety of forms, such as any kind of electromagnetic signals, such as electrical signals, magnetic signals, optical signals (e.g., laser pulses), or any combination thereof.
  • control unit 106 may be a beam splitter (e.g., a heater or a mirror), the control signals 108 may be signals that control the heater or the rotation of the mirror, the measurement unit 110 may be a photodetector, and the measurement signals 112 may be photons.
  • beam splitter e.g., a heater or a mirror
  • control signals 108 may be signals that control the heater or the rotation of the mirror
  • the measurement unit 110 may be a photodetector
  • the measurement signals 112 may be photons.
  • the control unit 106 may be a bus resonator activated by a drive, the control signals 108 may be cavity modes, the measurement unit 110 may be a second resonator (e.g., a low-Q resonator), and the measurement signals 112 may be voltages measured from the second resonator using dispersive readout techniques.
  • charge type qubits e.g., transmon, X-mon, G-mon
  • flux-type qubits e.g., flux qubits, capacitively shunted flux qubits
  • circuit QED circuit quantum electrodynamic
  • the control unit 106 may be a circuit QED-assisted control unit or a direct capacitive coupling control unit or an inductive capacitive coupling control unit
  • the control signals 108 may be cavity modes
  • the measurement unit 110 may be a second resonator (e.g., a low-Q resonator)
  • the measurement signals 112 may be voltages measured from the second resonator using dispersive readout techniques.
  • the control unit 106 may be a laser
  • the control signals 108 may be laser pulses
  • the measurement unit 110 may be a laser and either a CCD or a photodetector (e.g., a photomultiplier tube)
  • the measurement signals 112 may be photons.
  • the control unit 106 may be a radio frequency (RF) antenna
  • the control signals 108 may be RF fields emitted by the RF antenna
  • the measurement unit 110 may be another RF antenna
  • the measurement signals 112 may be RF fields measured by the second RF antenna.
  • RF radio frequency
  • control unit 106 may, for example, be a laser, a microwave antenna, or a coil, the control signals 108 may be visible light, a microwave signal, or a constant electromagnetic field, the measurement unit 110 may be a photodetector, and the measurement signals 112 may be photons.
  • the control unit 106 may be nanowires, the control signals 108 may be local electrical fields or microwave pulses, the measurement unit 110 may be superconducting circuits, and the measurement signals 112 may be voltages.
  • control unit 106 may be microfabricated gates
  • control signals 108 may be RF or microwave signals
  • measurement unit 110 may be microfabricated gates
  • measurement signals 112 may be RF or microwave signals.
  • the measurement unit 110 may provide one or more feedback signals 114 to the control unit 106 based on the measurement signals 112.
  • quantum computers referred to as “one-way quantum computers” or “measurement-based quantum computers” utilize such feedback signals 114 from the measurement unit 110 to the control unit 106.
  • Such feedback signals 114 are also necessary for the operation of fault-tolerant quantum computing and error correction.
  • the control signals 108 may, for example, include one or more state preparation signals which, when received by the qubits 104, cause some or all of the qubits 104 to change their states.
  • state preparation signals constitute a quantum circuit also referred to as an “ansatz circuit.”
  • the resulting state of the qubits 104 is referred to herein as an “initial state” or an “ansatz state.”
  • the process of outputting the state preparation signal(s) to cause the qubits 104 to be in their initial state is referred to herein as “state preparation” (FIG. 2A, section 206).
  • state preparation is “initialization,” also referred to as a “reset operation,” in which the initial state is one in which some or all of the qubits 104 are in the “zero” state i.e. the default single-qubit state. More generally, state preparation may involve using the state preparation signals to cause some or all of the qubits 104 to be in any distribution of desired states. In some embodiments, the control unit 106 may first perform initialization on the qubits 104 and then perform preparation on the qubits 104, by first outputting a first set of state preparation signals to initialize the qubits 104, and by then outputting a second set of state preparation signals to put the qubits 104 partially or entirely into non-zero states.
  • control signals 108 that may be output by the control unit 106 and received by the qubits 104 are gate control signals.
  • the control unit 106 may output such gate control signals, thereby applying one or more gates to the qubits 104. Applying a gate to one or more qubits causes the set of qubits to undergo a physical state change which embodies a corresponding logical gate operation (e.g., single-qubit rotation, two-qubit entangling gate or multi-qubit operation) specified by the received gate control signal.
  • a logical gate operation e.g., single-qubit rotation, two-qubit entangling gate or multi-qubit operation
  • the qubits 104 undergo physical transformations which cause the qubits 104 to change state in such a way that the states of the qubits 104, when measured (see below), represent the results of performing logical gate operations specified by the gate control signals.
  • Quantum gate refers to the application of a gate control signal to one or more qubits to cause those qubits to undergo the physical transformations described above and thereby to implement a logical gate operation.
  • state preparation and the corresponding state preparation signals
  • application of gates and the corresponding gate control signals
  • the dividing line between state preparation (and the corresponding state preparation signals) and the application of gates (and the corresponding gate control signals) may be chosen arbitrarily.
  • some or all the components and operations that are illustrated in FIGS. 1 and 2A-2B as elements of “state preparation” may instead be characterized as elements of gate application.
  • some or all of the components and operations that are illustrated in FIGS. 1 and 2A-2B as elements of “gate application” may instead be characterized as elements of state preparation.
  • the system and method of FIGS. 1 and 2A-2B may be characterized as solely performing state preparation followed by measurement, without any gate application, where the elements that are described herein as being part of gate application are instead considered to be part of state preparation.
  • FIGS. 1 and 2A-2B may be characterized as solely performing gate application followed by measurement, without 1 any state preparation, and where the elements that are described herein as being part of state preparation are instead considered to be part of gate application.
  • the quantum computer 102 also includes a measurement unit 110, which performs one or more measurement operations on the qubits 104 to read out measurement signals 112 (also referred to herein as “measurement results”) from the qubits 104, where the measurement results 112 are signals representing the states of some or all of the qubits 104.
  • the control unit 106 and the measurement unit 110 may be entirely distinct from each other, or contain some components in common with each other, or be implemented using a single unit (i.e., a single unit may implement both the control unit 106 and the measurement unit 110).
  • a laser unit may be used both to generate the control signals 108 and to provide stimulus (e.g., one or more laser beams) to the qubits 104 to cause the measurement signals 112 to be generated.
  • the quantum computer 102 may perform various operations described above any number of times.
  • the control unit 106 may generate one or more control signals 108, thereby causing the qubits 104 to perform one or more quantum gate operations.
  • the measurement unit 110 may then perform one or more measurement operations on the qubits 104 to read out a set of one or more measurement signals 112.
  • the measurement unit 110 may repeat such measurement operations on the qubits 104 before the control unit 106 generates additional control signals 108, thereby causing the measurement unit 110 to read out additional measurement signals 112 resulting from the same gate operations that were performed before reading out the previous measurement signals 112.
  • the measurement unit 110 may repeat this process any number of times to generate any number of measurement signals 112 corresponding to the same gate operations.
  • the quantum computer 102 may then aggregate such multiple measurements of the same gate operations in any of a variety of ways.
  • the control unit 106 may generate one or more additional control signals 108, which may differ from the previous control signals 108, thereby causing the qubits 104 to perform one or more additional quantum gate operations, which may differ from the previous set of quantum gate operations.
  • the process described above may then be repeated, with the measurement unit 110 performing one or more measurement operations on the qubits 104 in their new states (resulting from the most recently- performed gate operations).
  • the system 100 may implement a plurality of quantum circuits as follows. For each quantum circuit C in the plurality of quantum circuits (FIG.
  • the system 100 performs a plurality of “shots” on the qubits 104.
  • shots The meaning of a shot will become clear from the description that follows.
  • the system 100 For each shot S in the plurality of shots (FIG. 2A, operation 204), the system 100 prepares the state of the qubits 104 (FIG. 2A, section 206). More specifically, for each quantum gate G in quantum circuit C (FIG. 2A, operation 210), the system 100 applies quantum gate G to the qubits 104 (FIG. 2A, operations 212 and 214).
  • the system 100 measures the qubit Q to produce measurement output representing a current state of qubit Q (FIG. 2A, operations 218 and 220).
  • a single “shot” involves preparing the state of the qubits 104 and applying all of the quantum gates in a circuit to the qubits 104 and then measuring the states of the qubits 104; and the system 100 may perform multiple shots for one or more circuits.
  • the HQC 300 includes a quantum computer component 102 (which may, for example, be implemented in the manner shown and described in connection with FIG. 1) and a classical computer component 306.
  • the classical computer component may be a machine implemented according to the general computing model established by John Von Neumann, in which programs are written in the form of ordered lists of instructions and stored within a classical (e.g., digital) memory 310 and executed by a classical (e.g., digital) processor 308 of the classical computer.
  • the memory 310 is classical in the sense that it stores data in a storage medium in the form of bits, which have a single definite binary state at any point in time.
  • the bits stored in the memory 310 may, for example, represent a computer program.
  • the classical computer component 304 typically includes a bus 314.
  • the processor 308 may read bits from and write bits to the memory 310 over the bus 314.
  • the processor 308 may read instructions from the computer program in the memory 310, and may optionally receive input data 316 from a source external to the computer 302, such as from a user input device such as a mouse, keyboard, or any other input device.
  • the processor 308 may use instructions that have been read from the memory 310 to perform computations on data read from the memory 310 and/or the input 316, and generate output from those instructions.
  • the processor 308 may store that output back into the memory 310 and/or provide the output externally as output data 318 via an output device, such as a monitor, speaker, or network device.
  • the quantum computer component 102 may include a plurality of qubits 104, as described above in connection with FIG. 1.
  • a single qubit may represent a one, a zero, or any quantum superposition of those two qubit states.
  • the classical computer component 304 may provide classical state preparation signals 332 to the quantum computer 102, in response to which the quantum computer 102 may prepare the states of the qubits 104 in any of the ways disclosed herein, such as in any of the ways disclosed in connection with FIGS. 1 and 2A-2B.
  • the classical processor 308 may provide classical control signals 334 to the quantum computer 102, in response to which the quantum computer 102 may apply the gate operations specified by the control signals 332 to the qubits 104, as a result of which the qubits 104 arrive at a final state.
  • the measurement unit 110 in the quantum computer 102 (which may be implemented as described above in connection with FIGS. 1 and 2A-2B) may measure the states of the qubits 104 and produce measurement output 338 representing the collapse of the states of the qubits 104 into one of their eigenstates. As a result, the measurement output 338 includes or consists of bits and therefore represents a classical state.
  • the quantum computer 102 provides the measurement output 338 to the classical processor 308.
  • the classical processor 308 may store data representing the measurement output 338 and/or data derived therefrom in the classical memory 310.
  • the steps described above may be repeated any number of times, with what is described above as the final state of the qubits 104 serving as the initial state of the next iteration.
  • the classical computer 304 and the quantum computer 102 may cooperate as co-processors to perform joint computations as a single computer system.
  • the techniques described above may be implemented, for example, in hardware, in one or more computer programs tangibly stored on one or more computer-readable media, firmware, or any combination thereof, such as solely on a quantum computer, solely on a classical computer, or on a hybrid quantum classical (HQC) computer.
  • the techniques disclosed herein may, for example, be implemented solely on a classical computer, in which the classical computer emulates the quantum computer functions disclosed herein.
  • 0 may alternatively refer to the state , and vice versa.
  • any computational basis state disclosed herein may be replaced with any suitable reference state within embodiments of the present invention.
  • the techniques described above may be implemented in one or more computer programs executing on (or executable by) a programmable computer (such as a classical computer, a quantum computer, or an HQC) including any combination of any number of the following: a processor, a storage medium readable and/or writable by the processor (including, for example, volatile and non-volatile memory and/or storage elements), an input device, and an output device.
  • Program code may be applied to input entered using the input device to perform the functions described and to generate output using the output device.
  • Embodiments of the present invention include features which are only possible and/or feasible to implement with the use of one or more computers, computer processors, and/or other elements of a computer system. Such features are either impossible or impractical to implement mentally and/or manually.
  • embodiments of the present invention use evolutionary algorithms, executing on a classical and/or quantum computer, to enhance optimization. Such a feature cannot be implemented mentally and/or manually, and is inherently rooted in computer technology.
  • any claims herein which affirmatively require a computer, a processor, a memory, or similar computer-related elements, are intended to require such elements, and should not be interpreted as if such elements are not present in or required by such claims. Such claims are not intended, and should not be interpreted, to cover methods and/or systems which lack the recited computer-related elements.
  • any method claim herein which recites that the claimed method is performed by a computer, a processor, a memory, and/or similar computer-related element is intended to, and should only be interpreted to, encompass methods which are performed by the recited computer-related element(s).
  • Such a method claim should not be interpreted, for example, to encompass a method that is performed mentally or by hand (e.g., using pencil and paper).
  • any product claim herein which recites that the claimed product includes a computer, a processor, a memory, and/or similar computer-related element is intended to, and should only be interpreted to, encompass products which include the recited computer-related element(s). Such a product claim should not be interpreted, for example, to encompass a product that does not include the recited computer-related element(s).
  • the computer program may be implemented in any programming language, such as assembly language, machine language, a high-level procedural programming language, or an object-oriented programming language.
  • the programming language may, for example, be a compiled or interpreted programming language.
  • Each such computer program may be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a computer processor, which may be either a classical processor or a quantum processor.
  • Method steps of the invention may be performed by one or more computer processors executing a program tangibly embodied on a computer-readable medium to perform functions of the invention by operating on input and generating output.
  • Suitable processors include, by way of example, both general and special purpose microprocessors.
  • the processor receives (reads) instructions and data from a memory (such as a read-only memory and/or a random access memory) and writes (stores) instructions and data to the memory.
  • Storage devices suitable for tangibly embodying computer program instructions and data include, for example, all forms of non-volatile memory, such as semiconductor memory devices, including EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD- ROMs. Any of the foregoing may be supplemented by, or incorporated in, specially-designed ASICs (application-specific integrated circuits) or FPGAs (Field-Programmable Gate Arrays).
  • a classical computer can generally also receive (read) programs and data from, and write (store) programs and data to, a non-transitory computer-readable storage medium such as an internal disk (not shown) or a removable disk.
  • Any data disclosed herein may be implemented, for example, in one or more data structures tangibly stored on a non-transitory computer-readable medium (such as a classical computer-readable medium, a quantum computer-readable medium, or an HQC computer- readable medium).
  • a non-transitory computer-readable medium such as a classical computer-readable medium, a quantum computer-readable medium, or an HQC computer- readable medium.
  • Embodiments of the invention may store such data in such data structure(s) and read such data from such data structure(s).
  • embodiments of the present invention may include methods which produce outputs that are not optimal, or which are not known to be optimal, but which nevertheless are useful. For example, embodiments of the present invention may produce an output which approximates an optimal solution, within some degree of error.
  • terms herein such as “optimize” and “optimal” should be understood to refer not only to processes which produce optimal outputs, but also processes which produce outputs that approximate an optimal solution, within some degree of error.

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Abstract

L'invention concerne un système et un procédé pour un optimisateur à amélioration quantique (QEO) utilisant des modèles génératifs quantiques pour obtenir des fonctions de coût minimum inférieures à celles des optimisateurs connus classiques ou autres. Dans un premier mode de réalisation, l'optimisateur QEO fonctionne en tant qu'amplificateur pour améliorer les performances d'optimisateurs autonomes connus dans des cas complexes où des optimisateurs connus présentent des limitations. Dans un second mode de réalisation, l'optimisateur QEO fonctionne comme un optimisateur autonome pour trouver un minimum avec le moindre nombre d'évaluations de fonction de coût. Les procédés QEO divulgués présentent de meilleures performances que celles des optimisateurs connus, y compris des optimisateurs bayésiens. Les procédés d'optimisation à amélioration quantique divulgués peuvent être basés sur des réseaux de tenseur. Les modèles génératifs peuvent également être basés sur des approches classiques, quantiques ou hybrides quantiques-classiques, comprenant des réseaux antagonistes associatifs à circuits quantiques (QC-AAN) et des machines portées par circuit quantique (QCBM). Dans un autre mode de réalisation, un algorithme génératif évolutif (EGA) utilise un modèle génératif et un optimisateur classique dans un cadre algorithmique évolutif pour générer des solutions améliorées.
PCT/US2023/036429 2022-11-01 2023-10-31 Amélioration de l'optimisation avec un algorithme génératif évolutif utilisant des modèles génératifs quantiques ou classiques Ceased WO2024232909A2 (fr)

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