Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits

TL;DR

This paper proposes using a double chain of qubits with specific couplings to emulate the one-dimensional Fermi-Hubbard model, enabling quantum simulation of fermionic systems with potential physical implementations like transmon qubits.

Contribution

It introduces a method to map a double chain of qubits onto the Fermi-Hubbard model and discusses practical implementation protocols for quantum simulation.

Findings

Mapping of qubit chains onto the Fermi-Hubbard model demonstrated

Proposed measurement protocols to verify simulation accuracy

Analysis of transmon-based implementation feasibility

Abstract

The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with XX and ZZ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the ZZ interaction arises due to an inductive coupling and the XX interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators.