Quantum computation of nuclear observables involving linear combination of unitary operators

TL;DR

This paper introduces a quantum computing approach using linear combinations of unitaries and the Hadamard test to efficiently compute nuclear observables, demonstrated on the deuteron electric quadrupole moment.

Contribution

It presents a novel method combining LCU and Hadamard test techniques for calculating nuclear observables on quantum computers, applicable to various operators.

Findings

Successful computation of deuteron quadrupole moment

Comparison of Jordan-Wigner and Gray code encodings

Versatile approach for general observable calculations

Abstract

We present the quantum computation of nuclear observables where the operators of interest are first decomposed in terms of the linear combination of unitaries. Then we utilise the Hadamard test and the linear combination of unitaries (LCU) based methods to compute the expectation values. We apply these methods to calculate the electric quadrupole moment of deuteron. The results are compared for the Jordan-Wigner transformation and Gray code encoding. We discuss the versatility of our approach that can be utilized in general to calculate several observables on a quantum computer.