Toward simulating Superstring/M-theory on a quantum computer

TL;DR

This paper proposes a quantum computing framework to simulate supersymmetric matrix models related to superstring/M-theory, enabling exploration of complex quantum gravitational phenomena beyond traditional analytical methods.

Contribution

It introduces a four-step quantum simulation protocol for supersymmetric matrix models, including regularization, adiabatic state preparation, real-time dynamics simulation, and measurement techniques.

Findings

Regularization of the BMN matrix model via Fock space truncation.

Implementation of adiabatic state preparation using Wan-Kim algorithm.

Construction of quantum algorithms for real-time dynamics and measurements.

Abstract

We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. Our prescription consists of four steps: regularization of the Hilbert space, adiabatic state preparation, simulation of real-time dynamics, and measurements. Regularization is performed for the BMN matrix model with the introduction of energy cut-off via the truncation in the Fock space. We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state. Then, we provide an explicit construction for simulating real-time dynamics utilizing techniques of block-encoding, qubitization, and quantum signal processing. Lastly, we present a set of measurements and experiments that can be carried out on a quantum computer to further our understanding of superstring/M-theory beyond analytic results.