# Reduction of qubits in a quantum algorithm for Monte Carlo simulation by a pseudo-random-number generator

@article{Miyamoto2019ReductionOQ, title={Reduction of qubits in a quantum algorithm for Monte Carlo simulation by a pseudo-random-number generator}, author={Koichi Miyamoto and Kenji Shiohara}, journal={Physical Review A}, year={2019}, volume={102}, pages={022424} }

It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random numbers are required to obtain one sample value of the integrand, since those problems are extremely high-dimensional integrations, for example, risk measurement of credit…

## 21 Citations

### Quantum Speedup of Monte Carlo Integration in the Direction of Dimension and its Application to Finance

- Computer Science
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It is pointed out that the number of repeated operations in the high-dimensional integration can be reduced by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers.

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This paper considers the local volatility (LV) model, in which the volatility of the underlying asset price depends on the price and time, and discusses the state preparation step of the QAE, or equivalently, the implementation of the asset price evolution.

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It is pointed out that the number of repeated operations in the high-dimensional integration can be reduced by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers.

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Quantum amplitude estimation is a key subroutine in a number of powerful quantum algorithms, including quantum-enhanced Monte Carlo simulation and quantum machine learning. Maximum-likelihood quantum…

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Pricing a multi-asset derivative is an important problem in ﬁnancial engineering, both theoretically and practically. Although it is suitable to numerically solve partial diﬀerential equations to…

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### A Survey of Quantum Computing for Finance

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A comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems more efficiently and accurately.

### Quantum algorithms for numerical differentiation of expected values with respect to parameters

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The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have…

### Noisy quantum amplitude estimation without noise estimation

- GeographyPhysical Review A
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Tomoki Tanaka, Shumpei Uno, Tamiya Onodera, Naoki Yamamoto, and Yohichi Suzuki Quantum Computing Center, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan Mitsubishi UFJ Financial…

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