Casimir energy with chiral fermions on a quantum computer
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.
Juliette K. Stecenko Yuan Feng Michael McGuigan