Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks

TL;DR

This paper introduces a quantum algorithm that efficiently computes transition amplitudes in hybrid tensor networks by contracting non-Hermitian operators without exponential complexity, enhancing the method's applicability.

Contribution

It proposes a novel quantum algorithm combining singular value decomposition and Hadamard test to handle non-Hermitian operators in hybrid tensor networks.

Findings

Reduces exponential growth in measurement terms

Extends hybrid tensor network applicability

Demonstrates effectiveness through theoretical analysis

Abstract

The hybrid tensor network approach allows us to perform calculations on systems larger than the scale of a quantum computer. However, when calculating transition amplitudes, there is a problem that the number of terms to be measured increases exponentially with that of contracted operators. The problem is caused by the fact that the contracted operators are represented as non-Hermitian operators. In this study, we propose a method for the hybrid tensor network calculation that contracts non-Hermitian operators without the exponential increase of the number of terms. In the proposed method, calculations of transition amplitudes are performed by combining the singular value decomposition of the contracted non-Hermitian operators with the Hadamard test. The method significantly extends the applicability of the hybrid tensor network approach.