Zeta-regularized vacuum expectation values from quantum computing simulations

TL;DR

This paper explores using quantum computing to numerically evaluate zeta-regularized vacuum expectation values in quantum field theories, linking path integrals and Fourier integral operator zeta-functions for regularization.

Contribution

It introduces a novel approach to compute zeta-regularized vacuum expectation values using quantum algorithms, bridging quantum field theory and quantum computing.

Findings

Demonstrates quantum algorithms can evaluate zeta-regularized quantities

Provides a simple example of zeta-regularization in quantum field theory

Establishes a connection between path integrals and Fourier zeta-functions

Abstract

The zeta-regularization allows to establish a connection between Feynman's path integral and Fourier integral operator zeta-functions. This fact can be utilized to perform the regularization of the vacuum expectation values in quantum field theories. In this proceeding, we will describe the concept of the zeta-regularization, give a simple example and demonstrate that quantum computing can be employed to numerically evaluate zeta-regulated vacuum expectation values on a quantum computer.