Hardware-efficient fermionic simulation with a cavity-QED system

TL;DR

This paper proposes a hardware-efficient method using cavity-QED systems to perform digital quantum simulations of fermionic models, significantly reducing circuit depth for nonlocal transformations like Jordan-Wigner.

Contribution

It introduces a cavity-QED based approach that efficiently implements nonlocal fermionic transformations, reducing circuit depth compared to traditional local connectivity schemes.

Findings

Reduces circuit depth by a factor of N^2 for Jordan-Wigner transformations.

Efficient implementation of nonlocal fermionic mappings using cavity modes.

Applicable to Fermi-Hubbard models on N×N lattices.

Abstract

In digital quantum simulation of fermionic models with qubits, non-local maps for encoding are often encountered. Such maps require linear or logarithmic overhead in circuit depth which could render the simulation useless, for a given decoherence time. Here we show how one can use a cavity-QED system to perform digital quantum simulation of fermionic models. In particular, we show that highly nonlocal Jordan-Wigner or Bravyi-Kitaev transformations can be efficiently implemented through a hardware approach. The key idea is using ancilla cavity modes, which are dispersively coupled to a qubit string, to collectively manipulate and measure qubit states. Our scheme reduces the circuit depth in each Trotter step of the Jordan-Wigner encoding by a factor of $N^2$, comparing to the scheme for a device with only local connectivity, where $N$ is the number of orbitals for a generic two-body Hamiltonian. Additional analysis for the Fermi-Hubbard model on an $N\times N$ square lattice results in a similar reduction. We also discuss a detailed implementation of our scheme with superconducting qubits and cavities.