Scalable Algorithms for Power Function Calculations of quantum states in NISQ Era

TL;DR

This paper introduces scalable, efficient algorithms for calculating power functions of quantum states in the NISQ era, using Hadamard testing and Gate Set Tomography, with applications to entropy computation.

Contribution

It presents two novel algorithms for quantum state power calculations, optimizing gate usage and analyzing their errors, advancing quantum computational techniques.

Findings

Gate Set Tomography algorithm reduces two-qubit gate usage

Both algorithms accurately compute quantum state powers

Applied to Von Neumann entropy of random states

Abstract

This article focuses on the development of scalable and quantum bit-efficient algorithms for computing power functions of random quantum states. Two algorithms, based on Hadamard testing and Gate Set Tomography, are proposed. We provide a comparative analysis of their computational outcomes, accompanied by a meticulous evaluation of inherent errors in the gate set tomography approach. The second algorithm exhibits a significant reduction in the utilization of two-qubit gates compared to the first. As an illustration, we apply both methods to compute the Von Neumann entropy of randomly generated quantum states.