Noise-Assisted Quantum Autoencoder

Cao, Chenfeng; Wang, Xin

doi:10.1103/physrevapplied.15.054012

Cited by 48 publications

(32 citation statements)

References 31 publications

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“…Here, the variational quantum algorithm (VQA) [22][23][24] is a popular paradigm for near-term quantum applications, which uses a classical optimizer to train parameterized quantum circuits to achieve certain tasks. VQA is applied to solve problems in many areas, including ground and excited states preparation [25][26][27], quantum data compression [28][29][30], combinatorial optimization [31], quantum classifier [32][33][34], and quantum metrology [35,36] In this section we present the details of cost function evaluation and optimization methods in the algorithm design. The diagram of our algorithm is shown in Fig.…”

Section: Variational Quantum Algorithmsmentioning

confidence: 99%

Variational Quantum Algorithm for Schmidt Decomposition

Chen¹,

Zhao²,

Wang³

2021

Preprint

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Entanglement plays a crucial role in quantum physics and is the key resource in quantum information processing. In entanglement theory, Schmidt decomposition is a powerful tool to analyze the fundamental properties and structure of quantum entanglement. This work introduces a hybrid quantum-classical algorithm for Schmidt decomposition of bipartite pure states on near-term quantum devices. First, we show that the Schmidt decomposition task could be accomplished by maximizing a cost function utilizing bi-local quantum neural networks. Based on this, we propose a variational quantum algorithm for Schmidt decomposition (named VQASD) of which the cost function evaluation notably requires only one estimate of expectation with no extra copies of the input state. In this sense, VQASD outperforms existent approaches in resource cost and hardware efficiency. Second, by further exploring VQASD, we introduce a variational quantum algorithm to estimate the logarithm negativity, which can be applied to efficiently quantify entanglement of bipartite pure states. Third, we experimentally implement our algorithm on Quantum Leaf using the IoP CAS superconducting quantum processor. Both experimental implementations and numerical simulations exhibit the validity and practicality of our methods for analyzing and quantifying entanglement on near-term quantum devices.

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Section: Variational Quantum Algorithmsmentioning

confidence: 99%

Variational Quantum Algorithm for Schmidt Decomposition

Chen¹,

Zhao²,

Wang³

2021

Preprint

Self Cite

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show abstract

“…These parameters will be optimized externally by a classical computer with respect to certain loss functions. Various variational algorithms using QNNs have been proposed for Hamiltonian ground and excited states preparation [25][26][27][28][29][30][31], quantum state metric estimation [32,33], Gibbs state preparation [34][35][36], quantum compiling [37][38][39][40], machine learning [16,17,[41][42][43] etc. Furthermore, unlike the strong need of error correction in fault-tolerant quantum computation, noise in shallow quantum circuits can be suppressed via error mitigation [44][45][46][47][48][49], indicating the feasibility of quantum computing with NISQ devices.…”

Section: Introductionmentioning

confidence: 99%

“…Given a matrix M ∈ C n×n , let d and v denote the errors of the inferred singular values and singular vectors in Eqs (40),(41),. respectively, then both of them are upper bounded.Loss evaluationWe consider the evaluation of o j in VQFNE, which can be rewritten aso j = u j |M |v j v j |M † |u j k1 c k2 u j |A k1 |v j v j |A † k2 |u j .…”

mentioning

confidence: 99%

Variational Quantum Singular Value Decomposition

Wang

Song

Wang

2021

Quantum

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Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.

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“…This systematic error can be considered as a local coherent noise model [26]. Several works have demonstrated noise resilience of variational algorithms [27][28][29][30][31], while [32] demonstrated performance benefits that noise can induce for training a quantum autoencoder.…”

Section: Introductionmentioning

confidence: 99%

Training Saturation in Layerwise Quantum Approximate Optimisation

Campos,

Rabinovich,

Akshay

et al. 2021

Preprint

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Quantum Approximate Optimisation (QAOA) is the most studied gate based variational quantum algorithm today. We train QAOA one layer at a time to maximize overlap with an n qubit target state. Doing so we discovered that such training always saturates-called training saturationat some depth p * , meaning that past a certain depth, overlap can not be improved by adding subsequent layers. We formulate necessary conditions for saturation. Numerically, we find layerwise QAOA reaches its maximum overlap at depth p * = n. The addition of coherent dephasing errors to training removes saturation, recovering robustness to layerwise training. This study sheds new light on the performance limitations and prospects of QAOA.

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Noise-Assisted Quantum Autoencoder

Cited by 48 publications

References 31 publications

Variational Quantum Algorithm for Schmidt Decomposition

Variational Quantum Algorithm for Schmidt Decomposition

Variational Quantum Singular Value Decomposition

Training Saturation in Layerwise Quantum Approximate Optimisation

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