Training Variational Quantum Algorithms Is NP-Hard

Bittel, Lennart; Kliesch, Martin

doi:10.1103/physrevlett.127.120502

Cited by 237 publications

(169 citation statements)

References 18 publications

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“…This information is typically in the form of a cost function dependent on the expectations of observables with respect to the state that the quantum procedure produces. In general, the training of quantum variational algorithms is NP-hard [49]. In addition, these methods are heuristic in nature.…”

Section: Variational Quantum Algorithmsmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

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Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

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Section: Variational Quantum Algorithmsmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that the cost function f (θ), in general, can be nonconvex, and it can be computationally hard in general to obtain the exact solution of the optimization problem in VQAs [57]. By contrast, this paper aims to provide a heuristic optimizer that approximately solves this optimization problem with a small number of measurement shots.…”

Section: Preliminaries a Problem Settingmentioning

confidence: 99%

Stochastic Gradient Line Bayesian Optimization: Reducing Measurement Shots in Optimizing Parameterized Quantum Circuits

Tamiya,

Yamasaki

2021

Preprint

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“…Some are general [41][42][43] while some are problem specific [44][45][46][47]. This is a vital area to address as a recent work has suggested that this sub-task is NP-hard [48]. In this work, we focus on different flavours of "black-box" optimization [41]; optimizers which are not imbued with any special information about the objective function.…”

Section: Introductionmentioning

confidence: 99%