Casimir energy with chiral fermions on a quantum computer

TL;DR

This paper explores how to compute Casimir energy for chiral fermions using quantum computers, demonstrating the setup, accuracy, and scalability of such calculations with potential applications in physics and cosmology.

Contribution

It introduces a method to calculate Casimir energy for chiral fermions on quantum computers using VQE and compares lattice and continuum results, highlighting scalability and accuracy.

Findings

The calculation accuracy improves with more qubits.

The number of Pauli terms scales with qubits.

Lattice and continuum results are consistent for free fields.

Abstract

In this paper we discuss the computation of Casimir energy on a quantum computer. The Casimir energy is an ideal quantity to calculate on a quantum computer as near term hybrid classical quantum algorithms exist to calculate the ground state energy and the Casimir energy gives physical implications for this quantity in a variety of settings. Depending on boundary conditions and whether the field is bosonic or fermionic we illustrate how the Casimir energy calculation can be set up on a quantum computer and calculated using the Variational Quantum Eigensolver algorithm with IBM QISKit. We compare the results based on a lattice regularization with a finite number of qubits with the continuum calculation for free boson fields, free fermion fields and chiral fermion fields. We use a regularization method introduced by Bergman and Thorn to compute the Casimir energy of a chiral fermion. We show how the accuracy of the calculation varies with the number of qubits. We show how the number of Pauli terms which are used to represent the Hamiltonian on a quantum computer scales with the number of qubits. We discuss the application of the Casimir calculations on quantum computers to cosmology, nanomaterials, string models, Kaluza Klein models and dark energy.