Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo

TL;DR

This paper compares quantum computing, deep learning, and Lattice Monte Carlo methods for simulating matrix quantum mechanics, focusing on their effectiveness in calculating the low-energy spectrum relevant to quantum gravity and black holes.

Contribution

It systematically evaluates and compares quantum computing, deep learning, and traditional lattice methods for matrix quantum mechanics simulations.

Findings

Quantum computing shows promise in simulating low-energy spectra.

Deep learning approaches can approximate matrix quantum mechanics dynamics.

Lattice Monte Carlo remains a benchmark for accuracy.

Abstract

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the development of better quantum algorithms (quantum error correction codes) and for the realization of a quantum theory of gravity. Quantum computing and deep learning offer us potentially useful approaches to study the dynamics of matrix quantum mechanics. In this paper we perform a systematic survey for quantum computing and deep learning approaches to matrix quantum mechanics, comparing them to Lattice Monte Carlo simulations. In particular, we test the performance of each method by calculating the low-energy spectrum.