Toward simulating Superstring/M-theory on a quantum computer

• Published in: arXiv.org
• Main Authors: Gharibyan, Hrant, Hanada, Masanori, Honda, Masazumi, Liu, Junyu
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 21.07.2021
• Subjects: Adiabatic flow; Algorithms; Eigenvectors; Gravitation theory; Hilbert space; M theory; Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Theory; Physics - Quantum Physics; Quantum computers; Quantum computing; Quantum theory; Real time; Regularization; Signal processing; Simulation; Supersymmetry; Time measurement
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2011.06573

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.