Estimating truncation effects of quantum bosonic systems using sampling algorithms

Abstract

To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.

22 pages, 4 figures

References in corpus (6)

• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• Gluon Digitization via Character Expansion for Quantum Computers
• Qubitization strategies for bosonic field theories
• Simulating scalar field theories on quantum computers with limited resources
• Continuous-variable neural-network quantum states and the quantum rotor model
• Neural-Network Quantum States for Periodic Systems in Continuous Space

Cited by in corpus (4)

• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Toward QCD on Quantum Computer: Orbifold Lattice Approach
• Fixing detailed balance in ancilla-based dissipative state engineering
• Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors