Experimental Demonstration of Break-Even for the Compact Fermionic Encoding

TL;DR

This paper demonstrates that a new local encoding and compilation scheme enable the simulation of larger fermionic models on quantum computers, overcoming previous limitations caused by noise and non-local mappings.

Contribution

The authors introduce 'corner hopping', a compilation method, and two error mitigation techniques, enabling larger fermionic simulations on quantum hardware.

Findings

Achieved the largest digital quantum simulation of a fermionic model to date.

Reduced fermionic hopping simulation cost by 42%.

Successfully prepared the ground state of a 6x6 Fermi-Hubbard model on 48 qubits.

Abstract

The utility of solving the Fermi-Hubbard model has been estimated in the billions of dollars. Digital quantum computers can in principle address this task, but have so far been limited to quasi one-dimensional models. This is because of exponential overheads caused by the interplay of noise and the non-locality of the mapping between fermions and qubits. Here, we show experimentally that a recently developed local encoding can overcome this problem. We develop a new compilation scheme, called "corner hopping", that reduces the cost of simulating fermionic hopping by 42% which allows us to conduct the largest digital quantum simulations of a fermionic model to date, using a trapped ion quantum computer to prepare adiabatically the ground state of a 6 x 6 spinless Fermi-Hubbard model encoded in 48 physical qubits. We also develop two new error mitigation schemes for systems with conserved quantities, one based on local postselection and one on extrapolation of local observables. Our results suggest that Fermi-Hubbard models beyond classical simulability can be addressed by digital quantum computers without large increases in gate fidelity.