Universal discriminative quantum neural networks

Chen, Hongxiang; Wossnig, Leonard; Severini, Simone; Neven, Hartmut; Mohseni, Masoud

doi:10.1007/s42484-020-00025-7

Cited by 63 publications

(35 citation statements)

References 35 publications

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“…As a result, a new class of quantum algorithms -variational quantum algorithms (VQAs) [5,6] -have come to shape the noisy intermediate-scale quantum (NISQ) era. First rising to prominence with the introduction of the variational quantum eigensolver (VQE) [7], they have evolved to cover topics such as optimization [8], quantum chemistry [9][10][11][12][13], integer factorization [14], compilation [15], quantum control [16], matrix diagonalization [17,18], and variational quantum machine learning [19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

General parameter-shift rules for quantum gradients

Wierichs,

Izaac,

Wang

et al. 2021

Preprint

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Variational quantum algorithms are ubiquitous in applications of noisy intermediate-scale quantum computers. Due to the structure of conventional parametrized quantum gates, the evaluated functions typically are finite Fourier series of the input parameters. In this work, we use this fact to derive new, general parameter-shift rules for single-parameter gates, and provide closed-form expressions to apply them. By combining the general rule with the stochastic parameter-shift rule, we are able to extend this framework to multi-parameter quantum gates. To highlight the advantages of the general parameter-shift rules, we perform a systematic analysis of quantum resource requirements for each rule, and show that a reduction in resources is possible for higher-order derivatives. Using the example of the quantum approximate optimization algorithm, we show that the generalized parameter-shift rule can reduce the number of circuit evaluations significantly when computing derivatives with respect to parameters that feed into multiple gates. Our approach additionally allows for reconstructions of the evaluated function up to a chosen order, leading to generalizations of the Rotosolve and Quantum Analytic Descent optimization algorithms.

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Section: Introductionmentioning

confidence: 99%

General parameter-shift rules for quantum gradients

Wierichs,

Izaac,

Wang

et al. 2021

Preprint

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“…We use a synthetic dataset from recent efforts (Mohseni, Steinberg, and Bergou 2004;Chen et al 2018;Patterson et al 2021;Li, Song, and Wang 2021) focused on quantum state discrimination. In this dataset, for each pair of parameters u, v ∈ [0, 1], three input states are defined as follows:…”

Section: Datasetmentioning

confidence: 99%

“…Our effort focuses on developing QNNs for quantum data within the constraints of physically realizable quantum models (e.g., no-cloning, measurement state collapse). Among many applications, quantum state classification is of significance (Chen et al 2018) and has been studied under various specifications such as separability of quantum states (Gao et al 2018;Ma and Yung 2018), integrated quantum photonics (Kudyshev et al 2020), and dark matter detection through classification of polarization state of photons (Dixit et al 2021). In yet other applications, it has been shown that data traditionally viewed in classical settings are better modeled in a quantum framework.…”

Section: Introductionmentioning

confidence: 99%

Toward Physically Realizable Quantum Neural Networks

Heidari¹,

Grama²,

Szpankowski³

2022

Preprint

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There has been significant recent interest in quantum neural networks (QNNs), along with their applications in diverse domains. Current solutions for QNNs pose significant challenges concerning their scalability, ensuring that the postulates of quantum mechanics are satisfied, and that the networks are physically realizable. The exponential state space of QNNs poses challenges for the scalability of training procedures. The no-cloning principle prohibits making multiple copies of training samples, and the measurement postulates lead to non-deterministic loss functions. Consequently, the physical realizability and efficiency of existing approaches that rely on repeated measurement of several copies of each sample for training QNNs is unclear. This paper presents a new model for QNNs that relies on band-limited Fourier expansions of transfer functions of quantum perceptrons (QPs) to design scalable training procedures. This training procedure is augmented with a randomized quantum stochastic gradient descent technique that eliminates the need for sample replication. We show that this training procedure converges to the true minima in expectation, even in the presence of non-determinism due to quantum measurement. Our solution has a number of important benefits: (i) using QPs with concentrated Fourier power spectrum, we show that the training procedure for QNNs can be made scalable; (ii) it eliminates the need for resampling, thus staying consistent with the no-cloning rule; and (iii) enhanced data efficiency for the overall training process since each data sample is processed once per epoch. We present detailed theoretical foundation for our models and methods' scalability, accuracy, and data efficiency. We also validate the utility of our approach through a series of numerical experiments.

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“…Thus, hybrid optimization algorithms are used whenever the objective function can be evaluated more efficiently on a quantum computer than on a classical one. This is the case for applications to quantum chemistry [6][7][8], quantum control [9][10][11], quantum simulation [12,13], entanglement detection [14][15][16], state estimation [17][18][19][20][21], quantum machine learning [22][23][24][25][26], error correction [27], graph theory [28][29][30], differential equations [31][32][33], and finances [34].…”

Section: Introductionmentioning

confidence: 99%

Stochastic optimization algorithms for quantum applications

Gidi¹,

Candia²,

Muñoz-Moller³

et al. 2022

Preprint

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Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm that is executed in a classical computer, which is fed with values of the objective function that are obtained in a quantum computer. Therefore, a proper choice of optimization algorithm is essential to achieve good performance. Here, we review the use of first-order, second-order, and quantum natural gradient stochastic optimization methods, which are defined in the field of real numbers, and propose new stochastic algorithms defined in the field of complex numbers. The performance of the methods is evaluated by means of their application to variational quantum eigensolver, quantum control of quantum states, and quantum state estimation. In general, complex number optimization algorithms perform better and second-order algorithms provide a large improvement over first-order methods in the case of variational quantum eigensolver.

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Universal discriminative quantum neural networks

Cited by 63 publications

References 35 publications

General parameter-shift rules for quantum gradients

General parameter-shift rules for quantum gradients

Toward Physically Realizable Quantum Neural Networks

Stochastic optimization algorithms for quantum applications

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