Toward simulating superstring/M-theory on a quantum computer

• Published in: The journal of high energy physics Vol. 2021; no. 7; pp. 1 - 56
• Main Authors: Gharibyan, Hrant, Hanada, Masanori, Honda, Masazumi, Liu, Junyu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021; Springer Nature B.V; SpringerOpen
• Subjects: Adiabatic flow; Algorithms; Black Holes in String Theory; Classical and Quantum Gravitation; Eigenvectors; Elementary Particles; Gravitation theory; High energy physics; Hilbert space; M theory; M(atrix) Theories; Physics; Physics and Astronomy; Quantum computers; Quantum computing; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Real time; Regular Article - Theoretical Physics; Regularization; Relativity Theory; Signal processing; Simulation; String Theory; Supersymmetry; Time measurement; Black Holes in String Theory; M(atrix) Theories; M-Theory
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP07(2021)140

A bstract 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.