Abstract

We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge theories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.

Highlights

  • Physical processes using quantum circuits with reasonable costs in time

  • We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer

  • We will study how the orbifold construction can be used for digital quantum simulation and analyze its advantages and disadvantages compared to an approach based on the Kogut and Susskind1 (KS) formulation

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Summary

Orbifold construction of lattice gauge theory

We introduce the orbifold construction of pure Yang-Mills theory on a lattice. The orbifold construction uses non-compact variables rather than compact variables (unitary link variables); in section 2.2, the relation to the formulation with unitary link variables is made clear. The adjective ‘orbifold’ comes from the original construction [12], which obtained the lattice action from a matrix model via the orbifold projection. For concreteness we consider the (3 + 1)-dimensional theory. The same construction works for (2 + 1)- and (1 + 1)-dimensional theories as well, as we will briefly see in the end of section 2.1

Orbifold lattice
Connection to the unitary-link formalism
Symmetry at discretized level
Realization on a quantum computer
Fock space truncation
Gauge-singlet constraint
Ground state preparation
Optimal choice of regularization parameter μ and ω
Example of efficient time-evolution algorithm
Measuring glueballs
Other observables
Jordan-Lee-Preskill bound on Hilbert space
From orbifolds to Kogut-Susskind
Conclusion and outlook
Hamiltonian formulation and quantum simulation
Adding topological terms
A Orbifold projection from matrix model
B Review of the Kogut-Susskind formulation
H E a3 2 n
C Regularization in the coordinate basis
Full Text
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