Simulating quantum field theory with a quantum computer

Abstract

Forthcoming exascale digital computers will further advance our knowledge of quantum chromodynamics, but formidable challenges will remain. In particular, Euclidean Monte Carlo methods are not well suited for studying real-time evolution in hadronic collisions, or the properties of hadronic matter at nonzero temperature and chemical potential. Digital computers may never be able to achieve accurate simulations of such phenomena in QCD and other strongly-coupled field theories; quantum computers will do so eventually, though I'm not sure when. Progress toward quantum simulation of quantum field theory will require the collaborative efforts of quantumists and field theorists, and though the physics payoff may still be far away, it's worthwhile to get started now. Today's research can hasten the arrival of a new era in which quantum simulation fuels rapid progress in fundamental physics.

Nearly Optimal Lattice Simulation by Product Formulas

“…As an immediate application, our result gives a rigorous proof of the Jordan-Lee-Preskill claim about the complexity of simulating quantum field theory [6]. Recent works have analyzed the gate complexity of other quantum field theory simulations [39], including digital simulation of gauge theories [40]. The lattice Hamiltonians there have similar locality, so our analysis still applies.…”

Quantum Information Hidden in Quantum Fields

“…The latter is of great importance as a possible theoretical support for practical applications in scattering processes of elementary particles at high energies. Until now, quantum algorithms to simulate QFT [13,14] have mainly used lattices.…”

“…The absolute value of the variation of n g with respect to n is: (13) and the quantum fluctuations of the metric n g are:…”

“…However, quantum simulation might become possible once quantum fields are reduced to a quantum network of qubits. A seemingly argument was proposed by Preskill [13] and by Jordan et al [14], who recognized that in order to build up an efficient quantum algorithm to quantum simulate the 4  theory, the field should be "represented with finitely many qubits by discretization of space via a lattice, and discretization of the field value at each lattice site".…”

“…The QFT must first be adjusted before being simulated, and the regulator is typically a lattice, which, however, breaks Lorentz's invariance. For the topic of quantum simulation of QFT, see, for example [13,14]. Points 2, 3, and 4 will be discussed in more detail below.…”