Demonstrating quantum computing with the quark model

TL;DR

This paper demonstrates how quantum computing can be applied to quantum mechanics problems, specifically calculating energies and transition amplitudes in a quark model using variational methods and error mitigation techniques.

Contribution

It introduces a step-by-step quantum computing approach to solve nonrelativistic quark models, including variational imaginary time evolution and transition amplitude calculations.

Findings

Successful calculation of ground and excited states of charmonium

Implementation of error mitigation techniques

Use of Hadamard test for transition amplitudes

Abstract

The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational quantum imaginary time evolution implemented using automatic differentiation to determine ground and excited states of charmonium. The calculation of transition amplitudes is illustrated utilizing the Hadamard test. Examples of readout and gate error mitigation are included.