Quantum algorithms for transport coefficients in gauge theories

Abstract

In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables requiring dramatically smaller volumes: transport coefficients. These form nonperturbative inputs into theoretical models of heavy ions; thus, their calculation reduces theoretical uncertainties without the need for a full-scale simulation of the collision. We derive the necessary lattice operators in the Hamiltonian formulation and describe how to obtain them on quantum computers. Additionally, we discuss ways to efficiently prepare the relevant thermal state of a gauge theory.

15 pages, 4 figures

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• Primitive Quantum Gates for Dihedral Gauge Theories
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Improved Hamiltonians for Quantum Simulations
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
• Quantum Computing for Heavy Quarkonium Spectroscopy
• Boltzmann Distributions on a Quantum Computer via Active Cooling
• Large scale multi-node simulations of ${\mathbb{Z}}_2$ gauge theory quantum circuits using Google Cloud Platform