Filtering variational quantum algorithms for combinatorial optimization

Amaro, David; Modica, Carlo; Rosenkranz, Matthias; Fiorentini, Mattia; Benedetti, Marcello; Lubasch, Michael

doi:10.48550/arxiv.2106.10055

Cited by 7 publications

(14 citation statements)

References 56 publications

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“…The initial formulation of QAOA can be seen as a truncated or Trotterized [256] version of the QA evolution to a finite number of time steps. 12 QAOA follows the adiabatic trajectory in the limit of infinite time steps, which provides evidence of good convergence properties [129]. This algorithm caters to gate-based computers.…”

Section: Quantum Approximate Optimization Algorithmmentioning

confidence: 89%

“…Alternatively, there exist evolutionary, noise-resistant techniques for optimizing the structure of the ansatz and significantly increasing the space of candidate wave functions [274]. Lastly, Amaro et al [12] introduced quantum variational filtering, which can be used to increase the probability of sampling low-eigenvalue states of an observable when the filtering operator is applied to an arbitrary quantum state. Their algorithm, Filtering VQE, was applied to combinatorial optimization problems and outperformed both standard VQE and QAOA.…”

Section: Variational Quantum Eigensolvermentioning

confidence: 99%

“…13 Hamiltonian simulation also contributes to this constraint. 14 Let Π λ denote the eigenspace projector for an eigenvalue λ of the Hermitian matrix in Equation (12), and let |b be a quantum state proportional to the right side of Equation (12). To clarify, the y-axis value of the red dot corresponding to λ, on either of the histograms in Figure 5, is Π λ |b 2 2 .…”

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

See 2 more Smart Citations

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: Quantum Approximate Optimization Algorithmmentioning

confidence: 89%

Section: Variational Quantum Eigensolvermentioning

confidence: 99%

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

See 1 more Smart Citation

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…More recently, the authors of [17] proposed a near-term ground state filtering method. Drawing inspiration from the ground state filtering of [5], instead of applying the filter operator to the initial state, they emulate the action of the filter operator by using a parameterized quantum circuit (PQC) and optimizing the parameters to minimize the Euclidean distance between the PQC-prepared state and the filter-applied state.…”

Section: Introductionmentioning

confidence: 99%

State Preparation Boosters for Early Fault-Tolerant Quantum Computation

Wang¹,

Sim²,

Johnson³

2022

Preprint

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Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization landscape, make state preparation through ansatz optimization unreliable. In this work, we introduce the method of ground state boosting, which uses a limited-depth quantum circuit to reliably increase the overlap with the ground state. This circuit, which we call a booster, can be used to augment an ansatz from VQE or be used as a stand-alone state preparation method. The booster converts circuit depth into ground state overlap in a controllable manner. We numerically demonstrate the capabilities of boosters by simulating the performance of a particular type of booster, namely the Gaussian booster, for preparing the ground state of 2 molecular system. Beyond ground state preparation as a direct objective, many quantum algorithms, such as quantum phase estimation, rely on high-quality state preparation as a subroutine. Therefore, we foresee ground state boosting and similar methods as becoming essential algorithmic components as the field transitions into using early fault-tolerant quantum computers.

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“…Remark. Although this study concentrates on QNNs and VQEs, our proposal can be effectively extended to speed up other VQAs such as quantum approximate optimization algorithms [35,36,[58][59][60].…”

mentioning

confidence: 99%

Accelerating variational quantum algorithms with multiple quantum processors

Du¹,

Yang²,

Tao³

2021

Preprint

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Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large-volume data. As such, to better exert the superiority of VQAs, it is of great significance to improve their runtime efficiency. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue. Specifically, in QUDIO, a classical central server partitions the learning problem into multiple subproblems and allocate them to multiple local nodes where each of them consists of a quantum processor and a classical optimizer. During the training procedure, all local nodes proceed parallel optimization and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in terms of the number of global iteration under the ideal scenario, while the system imperfection may incur divergent optimization. Numerical results on standard benchmarks demonstrate that QUDIO can surprisingly achieve a superlinear runtime speedup with respect to the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.

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Filtering variational quantum algorithms for combinatorial optimization

Cited by 7 publications

References 56 publications

A Survey of Quantum Computing for Finance

A Survey of Quantum Computing for Finance

State Preparation Boosters for Early Fault-Tolerant Quantum Computation

Accelerating variational quantum algorithms with multiple quantum processors

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