Efficient quantum algorithms for testing symmetries of open quantum systems

TL;DR

This paper introduces efficient quantum algorithms for testing symmetries in open quantum systems using Hilbert-Schmidt distance, simplifying previous fidelity-based methods and applicable to various quantum scenarios.

Contribution

It presents a novel, computationally efficient quantum algorithm for symmetry testing in open quantum systems based on Hilbert-Schmidt distance, applicable to states, channels, and Lindbladians.

Findings

Algorithms successfully tested on amplitude damping channel and spin chain.

Method effectively detects symmetries within and outside finite symmetry groups.

Approach reduces computational complexity compared to fidelity-based methods.

Abstract

Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us to simplify calculations and characterize potentially complicated dynamics of the system with relative ease. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. In our present work, we develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers. Our approach estimates asymmetry measures based on the Hilbert--Schmidt distance, which is significantly easier, in a computational sense, than using fidelity as a metric. The method is derived to measure symmetries of states, channels, Lindbladians, and measurements. We apply this method to a number of scenarios involving open quantum systems, including the amplitude damping channel and a spin chain, and we test for symmetries within and outside the finite symmetry group of the Hamiltonian and Lindblad operators.