A multiprecision C++ library for matrix-product-state simulation of quantum computing: Evaluation of numerical errors

TL;DR

This paper introduces a C++ library for high-precision matrix-product-state simulations of quantum computing, enabling detailed analysis of numerical errors such as rounding and truncation.

Contribution

The library ZKCM_QC provides a practical tool for multiprecision TDMPS simulations and allows for systematic evaluation of numerical errors in quantum circuit simulations.

Findings

Numerical errors due to floating-point rounding are quantified.

Truncation errors from Schmidt coefficient cutoff are analyzed.

The library facilitates accurate quantum simulation error assessment.

Abstract

The time-dependent matrix-product-state (TDMPS) simulation method has been used for numerically simulating quantum computing for a decade. We introduce our C++ library ZKCM_QC developed for multiprecision TDMPS simulations of quantum circuits. Besides its practical usability, the library is useful for evaluation of the method itself. With the library, we can capture two types of numerical errors in the TDMPS simulations: one due to rounding errors caused by the shortage in mantissa portions of floating-point numbers; the other due to truncations of nonnegligible Schmidt coefficients and their corresponding Schmidt vectors. We numerically analyze these errors in TDMPS simulations of quantum computing.