NISQ-HHL: Portfolio Optimization for Near-Term Quantum Hardware

Yalovetzky, Romina; Minssen, Pierre; Herman, Dylan; Pistoia, Marco

doi:10.48550/arxiv.2110.15958

Cited by 10 publications

(14 citation statements)

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“…S is the register that U is applied to, and j is a classical register; H refers to the Hadamard gate; and R k , for k = 2, 3, are the standard phase gates used by the quantum Fourier transform [256]. Adapted from [346].…”

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

“…14 These methods were executed on the Quantinuum H1 device for a few small portfolios (Table 2). A controlled-SWAP test [34] was performed between the state from HHL and the solution to the linear system obtained classically (loaded onto a quantum state) [346]. The number of H1 two-qubit ZZMax gates used is also displayed in Table 2.…”

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

“…Table 2: Comparison of the number of rotations in the eigenvalue inversion, ZZMax depth of the HHL plus the controlled-SWAP test circuits and the inner product calculated from the Qiskit statevector simulator and the Quantinuum H1 results with 3, 000 shots. Adapted from [346].…”

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

“…Two of the main components of the algorithm that contribute to this constraint are quantum phase estimation (Section 4.3) and the loading of the inverse of the eigenvalue estimations onto the amplitudes of an ancilla, called eigenvalue inversion [160]. 13 Yalovetzky et al [346] developed an algorithm called NISQ-HHL with the goal of applying it to portfolio optimization problems on NISQ devices. While it does not retain the asymptotic speedup of HHL, the authors' approach can potentially provide benefits in practice.…”

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

“…The blue bars represent the experimental results on the H1 machine-1, 000shots (left) and 2, 000 shots (right)-and we compare them with the theoretical eigenvalues (classically calculated using a numerical solver) represented with the red dots and the results from the Qiskit[9] QASM simulator represented with the orange dots. Adapted from[346].UniformlyNISQ-HHL NISQ-HHL Rotations 7 4 6 Depth 272 214 254 Simulation 0.59 0.49 0.83 H1 0.42 -0.46…”

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confidence: 99%

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A Survey of Quantum Computing for Finance

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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: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

Section: Portfolio Optimization On a Trapped-ion Devicementioning

confidence: 99%

mentioning

confidence: 99%

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Portfolio optimization plays a central role in finance to obtain optimal portfolio allocations that aim to achieve certain investment goals. Over the years, many works have investigated different variants of portfolio optimization. Portfolio optimization also provides a rich area to study the application of quantum computers to obtain advantages over classical computers. In this work, we give a sampling version of an existing classical online portfolio optimization algorithm by Helmbold et al., for which we in turn develop a quantum version. The quantum advantage is achieved by using techniques such as quantum state preparation, inner product estimation and multi-sampling. Our quantum algorithm provides a quadratic speedup in the time complexity, in terms of n, where n is the number of assets in the portfolio. The transaction cost of both of our classical and quantum algorithms is independent of n which is especially useful for practical applications with a large number of assets.

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Portfolio optimization based on quantum linear algorithm

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The rapid development of quantum computation has brought new possibilities to many fields. Especially in finance, quantum computing offers significant advantages. Recently, the portfolio optimization problem has been solved by a quantum algorithm with a mean-variance model with sparse data. However, the mean-variance model does not match the practice, and furthermore, the data is mostly dense. To fill the gap, we propose the Quantum-Enhanced Portfolio Optimization based on the mean-semi-variance model, where the mean-semi-variance model incorporates an optimized risk definition. The algorithm also effectively reduces the time complexity of solving high-dimensional linear systems and achieves sparsity independence.

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NISQ-HHL: Portfolio Optimization for Near-Term Quantum Hardware

Cited by 10 publications

References 0 publications

A Survey of Quantum Computing for Finance

A Survey of Quantum Computing for Finance

A quantum online portfolio optimization algorithm

Portfolio optimization based on quantum linear algorithm

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