Measuring distance between quantum states on a quantum computer

TL;DR

This paper introduces protocols for measuring distances between quantum states and their evolution speeds on quantum computers, enabling better characterization of quantum systems and their dynamics.

Contribution

The paper presents new protocols for quantifying distances between pure and mixed quantum states and measuring their evolution speeds on quantum computers.

Findings

Protocols successfully implemented on ibmq-santiago quantum computer.

Accurate measurement of quantum state distances demonstrated.

Speed of quantum system evolution quantified using developed methods.

Abstract

We propose protocols for determining the distances in Hilbert space between pure and mixed quantum states prepared on a quantum computer. In the case of pure quantum states, the protocol is based on measuring the square of modulus of scalar product between certain states. Determination of the distance between mixed quantum states is reduced to measuring the squares of modules of scalar products between all pure states included in the mixed states. In addition, we develop a protocol that allows one to determine the speed of evolution of the spin system simulated by a quantum computer. These protocols we apply to measure distances and speeds of evolution of different quantum systems implemented on the ibmq-santiago quantum computer.