Encoding of Probability Distributions for Quantum Monte Carlo Using Tensor Networks

TL;DR

This paper evaluates the tensor-train cross approximation method for efficiently encoding probability distributions in quantum Monte Carlo, demonstrating improved scalability and accuracy for financial data applications.

Contribution

It introduces the TT-cross algorithm as a scalable, accurate solution for probability loading in quantum Monte Carlo using tensor networks.

Findings

TT-cross significantly improves circuit depth scalability.

The method achieves high accuracy on high-dimensional financial data.

It offers a promising approach for quantum finance applications.

Abstract

The application of Tensor Networks (TN) in quantum computing has shown promise, particularly for data loading. However, the assumption that data is readily available often renders the integration of TN techniques into Quantum Monte Carlo (QMC) inefficient, as complete probability distributions would have to be calculated classically. In this paper the tensor-train cross approximation (TT-cross) algorithm is evaluated as a means to address the probability loading problem. We demonstrate the effectiveness of this method on financial distributions, showcasing the TT-cross approach's scalability and accuracy. Our results indicate that the TT-cross method significantly improves circuit depth scalability compared to traditional methods, offering a more efficient pathway for implementing QMC on near-term quantum hardware. The approach also shows high accuracy and scalability in handling high-dimensional financial data, making it a promising solution for quantum finance applications.