A quantum machine learning algorithm based on generative models

Gao, Xiao-Shan; Zhang, Z.-Y.; Duan, Luming

doi:10.1126/sciadv.aat9004

Cited by 119 publications

(74 citation statements)

References 39 publications

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“…by combining complexity-theoretic arguments 4,7,9 , with an application in generative machine learning [14][15][16]62 , and improved training methods of generative models. Specifically, we introduced the Ising Born machine, a restricted form of a quantum circuit Born machine.…”

Section: Discussionmentioning

confidence: 99%

The Born supremacy: quantum advantage and training of an Ising Born machine

et al. 2020

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The search for an application of near-term quantum devices is widespread. Quantum machine learning is touted as a potential utilisation of such devices, particularly those out of reach of the simulation capabilities of classical computers. In this work, we study such an application in generative modelling, focussing on a class of quantum circuits known as Born machines. Specifically, we define a subset of this class based on Ising Hamiltonians and show that the circuits encountered during gradient-based training cannot be efficiently sampled from classically up to multiplicative error in the worst case. Our gradient-based training methods use cost functions known as the Sinkhorn divergence and the Stein discrepancy, which have not previously been used in the gradientbased training of quantum circuits, and we also introduce quantum kernels to generative modelling. We show that these methods outperform the previous standard method, which used maximum mean discrepancy (MMD) as a cost function, and achieve this with minimal overhead. Finally, we discuss the ability of the model to learn hard distributions and provide formal definitions for 'quantum learning supremacy'. We also exemplify the work of this paper by using generative modelling to perform quantum circuit compilation.

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Section: Discussionmentioning

confidence: 99%

The Born supremacy: quantum advantage and training of an Ising Born machine

et al. 2020

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“…While these results are specific to a particular quantum chemistry problem and the trapped-ion QC hardware, the computational methodology we develop is completely general to simulating quantum systems. We anticipate that similar advances can be applied to other optimization problems that work on variational methods, such as the quantum approximate optimization algorithm [42] and various quantum machine learning applications [43,44]. Increased attention to co-design principles like those demonstrated here will be necessary to push the boundary of possibility in near-term quantum computation.…”

Section: Discussionmentioning

confidence: 94%

Ground-state energy estimation of the water molecule on a trapped-ion quantum computer

et al. 2020

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Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

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“…Although we have chosen a nanomaterials data set to demonstrate the use of ILS, the virtues of this method are broadly applicable to a wide variety of domains, including chemistry, bioinformatics, quantum computing, social sciences, economics, energy, or health . In materials and nanoscience, applications include the classification of samples with different crystal structures, topologies, chemical, mechanical, or electronic properties.…”

Section: Discussionmentioning

confidence: 99%

Selecting Appropriate Clustering Methods for Materials Science Applications of Machine Learning

Parker

Barnard

2019

Advcd Theory and Sims

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Based on a general definition of a cluster and the quality of a clustering result, a new method for evaluating existing clustering algorithms, or undertaking clustering, capable of predicting the number and type of clusters and outliers present in a data set, regardless of the complexity of the distribution of points, is presented. This algorithm, referred to as iterative label spreading, can recognize the characteristics expected of a successful clustering result before any clustering algorithm is applied, providing a type of hyper-parameter optimization for clustering. The efficacy of the algorithm, and the assessment of clustering result, are both confirmed using large benchmark two dimensional synthetic data sets, and small multidimensional data describing a set of silver nanoparticles. It is shown that the method is ideal for studying noisy data with high dimensionality and high variance, typical of data captured in materials and nanoscience.

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A quantum machine learning algorithm based on generative models

Abstract: We propose a quantum learning algorithm for a quantum generative model and prove its advantages compared with classical models.

Cited by 119 publications

References 39 publications

The Born supremacy: quantum advantage and training of an Ising Born machine

The Born supremacy: quantum advantage and training of an Ising Born machine

Ground-state energy estimation of the water molecule on a trapped-ion quantum computer

Selecting Appropriate Clustering Methods for Materials Science Applications of Machine Learning

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