Superconformal Quantum Mechanics on a Quantum Computer

TL;DR

This paper explores the simulation of superconformal quantum mechanics on quantum computers, employing variational algorithms and path integral methods to compare results with exact solutions and discuss implications for quantum gravity.

Contribution

It introduces quantum algorithms for simulating superconformal quantum mechanics and compares their accuracy with exact solutions, advancing quantum simulation techniques for complex quantum systems.

Findings

VQE accurately approximates ground states of SCQM with and without noise.

Trotter-Suzuki method reproduces Feynman path integrals for SCQM.

Quantum simulations provide insights relevant to quantum gravity via AdS/CFT.

Abstract

We investigate superconformal quantum mechanics (SCQM) on a quantum computer. We study the ground state of the mass deformed SCQM on a quantum computed using the Variational Quantum Eigensolver (VQE) using a one boson and one boson - one fermion Hilbert space with and without noise and compare the accuracy of the results. We study the Feynman path integral for SCQM using the Evolution of Hamiltonian (EOH) algorithm on the quantum computer using the Trotter-Suzuki approximation and compare with the exact result. We consider an N boson and N fermion version of SCQM given be the Supersymmetric Calogero-Moser-Sutherland (SCMS) model. We compare the ground state of SCMS theory obtained using the VQE computation with the exact solution. Finally we discuss the implications of the the numerical simulation of SCQM on a quantum computer for the simulation of quantum gravity in light of the Anti-de Sitter/Superconformal field theory (AdS/CFT) correspondence.