A Matrix Big Bang on a Quantum Computer

TL;DR

This paper explores quantum simulations of non-critical M-theory matrix models, demonstrating reduced qubit requirements and applying quantum algorithms to compute ground states, singularities, and BRST invariants.

Contribution

It introduces quantum algorithms for simulating non-critical M-theory matrix models, highlighting their simplicity and efficiency over critical theories.

Findings

Fewer qubits and Pauli terms needed for non-critical M-theory

Quantum algorithms successfully compute ground state energies

Simulation of Matrix Big Bang singularities on quantum computers

Abstract

M-theory is a mysterious theory that seeks to unite different string theories in one lower dimension. The most studied example is eleven dimensional but other dimensions have been considered. The non-critical M-theories seek to unite different non-critical string theories. From the point of view of computing, non-critical M-theories should be simpler to simulate as they have fewer fields than eleven dimensional M-theory. The simplicity of non-critical M-theory carries over to quantum computing and we show that the quantum simulation requires fewer qubits and Pauli terms than critical M-theory. As an example quantum calculation we study the quantum computation of the ground state energy of Matrix models of non-critical M-theory in 3d in the finite difference and oscillator basis and compare the accuracy, number of qubits and number of Pauli terms of the different basis using the Variational Quantum Eigensolver (VQE) algorithm. We study non-critical M- Theory solutions with space-time singularities referred to as a "Matrix Big Bang" on the Quantum Computer using the Evolution of Hamiltonian (EOH) quantum algorithm using the Trotter approximation and compare the accuracy and results the can be obtained using quantum computation. Finally we consider the BRST quantization of the 3d M-theory Matrix model using quantum computation and compute BRST invariant states by studying the BRST Laplacian using the VQE algorithm.