Systematic input scheme of many-boson Hamiltonians with applications to the two-dimensional $\phi ^4$ theory

TL;DR

This paper introduces a systematic quantum input scheme for many-boson Hamiltonians, enabling efficient quantum simulations of field theories like the two-dimensional ^4 theory using quantum computers.

Contribution

It presents a novel input scheme employing quantum registers and squeezed boson operators, facilitating the encoding and simulation of many-boson Hamiltonians on quantum hardware.

Findings

Hybrid quantum-classical calculations match exact results.

The scheme effectively encodes the two-dimensional ^4 Hamiltonian.

Demonstrates feasibility of quantum simulations for field theories.

Abstract

We develop a novel, systematic input scheme for many-boson Hamiltonians in order to solve field theory problems within the light-front Hamiltonian formalism via quantum computing. We present our discussion of this input scheme based on the light-front Hamiltonian of the two-dimensional $\phi ^4$ theory. In our input scheme, we employ a set of quantum registers, where each register encodes the occupation of a distinct boson mode as binaries. We squeeze the boson operators of each mode and present the Hamiltonian in terms of unique combinations of the squeezed boson operators. We design the circuit modules for these unique combinations. Based on these circuit modules, we block encode the many-boson Hamiltonian utilizing the idea of quantum walk. For demonstration purposes, we present the spectral calculations of the Hamiltonian utilizing the hybrid quantum-classical symmetry-adapted quantum Krylov subspace diagonalization algorithm based on our input scheme, where the quantum computations are performed with the IBM Qiskit quantum simulator. The results of the hybrid calculations agree with exact results.