A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model

TL;DR

This paper presents a detailed, step-by-step method for simulating the 2D Fermi-Hubbard model on quantum computers using local operations, addressing the challenges of mapping fermionic systems to qubit-based hardware.

Contribution

It introduces a practical recipe for simulating strongly-correlated fermionic matter, focusing on the Derby-Klassen mapping and including all steps from state preparation to measurement.

Findings

Explicit resource estimates for quantum quench simulations

Demonstration of local operation-based simulation approach

Discussion of future challenges in fermionic quantum simulation

Abstract

The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of quantum computing technologies are built around qubits and discrete gate-based operations, the translation of the physical problem into this framework is a crucial step. This translation will often be device specific, and a suboptimal implementation will be punished by the exponential compounding of errors on real devices. The importance of an efficient mapping is already revealed for models of spinful fermions in two or three dimensions, which naturally arise when the relevant physics relates to electrons. Using the most direct and well-known mapping, the Jordan-Wigner transformation, leads to a non-local representation of local degrees of freedom, and necessities efficient decompositions of non-local unitary gates into a sequence of hardware accessible local gates. In this paper, we provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. To provide the ingredients for such a recipe, we briefly review the plethora of different approaches that have emerged recently but focus on the Derby-Klassen compact fermion mapping in order to make our discussion concrete. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device, preparing initial states such as ground states, simulation of unitary time evolution, and measurement of observables and spectral functions. We explicitly compute the resource requirements for simulating a global quantum quench and conclude by discussing the challenges and future directions for simulating strongly-correlated fermionic matter on quantum computers.