Advanced Quantum Monte Carlo Simulation

[YumaNK]

Description

WHAT PROBLEM ARE YOU TRYING TO SOLVE?

We consider the problem of finding high-dimensional integrals by quantum Monte Carlo methods. When solving high-dimensional problems using classical Monte Carlo methods, the problems suffer from (1) reduced accuracy due to the poor dimensional distribution of the output sequence caused by the use of a pseudo-random number generator and (2) slow convergence of the solution (O(N^-1/2)). Since intensive investigation of quantum algorithms has progressed, it has become possible to generate pseudo-random numbers close to the true random numbers using a quantum computer (arXiv:2009.06551), which is expected to overcome the effect of the curse of dimensionality as mentioned in (1). Also, the convergence law of quantum Monte Carlo is O(N^-1), which is faster than the classical method (2), but there is a limit to the number of qubits that can be implemented. Recently, it has been proposed that high-dimensional Monte Carlo integration can be implemented even with a limited number of qubits (PRA 102, 022424 (2020)). Using this method, we will solve a high-dimensional integration problem with pseudo-random numbers generated both by a quantum computer and a classical computer, and examine whether the dimensionality problem due to (1) can be resolved while taking advantage of the properties of (2).

PROVIDE EXPECTED BUSINESS AND/OR TECHNICAL OUTCOMES

In the financial simulation, how accurate and fast investment decisions can be performed considering variety of scenarios is the key to gaining an advantage against their competitor. Recently, the quantum Monte Carlo algorithm has been attracting attention for its ability to speed up conventional multi-scenario stochastic simulations. Typical applications include Option Pricing and Risk Analysis. In this project, we aim to use quantum Monte Carlo to achieve the quadratic speedup of high-dimensional integration that occur in pricing basket options where stocks in interest are multiple and have correlations. In conventional quantum Monte Carlo methods, the number of stocks that can be simulated is assumed to be the number of qubits. Recently, a method to perform sequential high-dimensional Monte Carlo integration with few qubits using pseudo-random numbers has been proposed (PRA 102, 022424 (2020)), and the improvement of the accuracy of high-dimensional integration using advanced pseudo-random numbers has been independently reported in another paper(arXiv:2009.06551). Here, as a first attempt, we aim to use advanced quantum pseudo-random numbers and implement high-dimensional Monte Carlo integration with a few qubits. In addition, we will investigate the applicability to real-world financial problems sing real data to further improve the speed and accuracy.

Mentor/s

This project can be a specific direction of #21 issued by @amyami187

Type of participant

People with experience or passion for quantum finance.

Number of participants

1-4

Deliverable

Mid-term

・Blog Post ・Qiskit Tutorial ・Qiskit Advocate Demo ・Contribute Qiskit by adding new module

Long-term

・Financial Counterpart of explainer on quantum machine learning ・Technical Report ・Research Paper

Remark

・This proposal is initially submitted as quantum finance project in IBM Academy of Technology Ideas Board (only accessible from IBM internal network). ・Md Maruf Hossain co-leads this project.

[Cryoris]

Here's an implementation of the Foreman paper you mentioned: https://qiskit-rng.readthedocs.io/en/latest/ (I haven't tested it myself though 🙂)

[wmarufhossain]

Hello, I would like to start from the Pseudo random generator part.

[HuangJunye]

@amyami187 @YumaNK Are you going to work this direction of #21? If yes can you update the project after meeting and refining the project details and scope?

[YumaNK]

@HuangJunye

Thereafter, if there is a niche in which we can exploit - perhaps a novel application, we can work on implementing this using Qiskit and financial data.

In my understanding the direction of this issue #31 may correspond to a sort of niche in quantum finance, so that this direction inherits #21. To make #31 more compatible with #21, I just add the "explainer" into the derivable.