Hardware-efficient fermionic simulation with a cavity–QED system

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 N2, 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？×？N square lattice results in a similar reduction. We also discuss a detailed implementation of our scheme with superconducting qubits and cavities