Qubit Regularization of Quantum Field Theories

TL;DR

This paper introduces qubit regularization as a finite-dimensional approach to simulating quantum field theories on quantum computers, demonstrating potential for asymptotic freedom within finite local Hilbert spaces using a new basis.

Contribution

It proposes the MDTN basis for constructing qubit-regularized lattice gauge theories and explores the emergence of asymptotic freedom in finite-dimensional settings.

Findings

Asymptotic freedom can emerge in finite-dimensional Hilbert spaces in (1+1) dimensions.

The MDTN basis facilitates the construction of new qubit-regularized lattice gauge theories.

Finite-dimensional regularization may be sufficient for certain quantum field theories.

Abstract

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.