Hardware-efficient fermionic simulation with a cavity–QED system

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 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. Coupling ancilla modes to a string of qubits in a cavity QED system allows the efficient quantum simulation of fermionic problems. This constitutes a challenge for most existing boson-based platforms for quantum simulation, as simulating a fermionic system require non-local transformations that impose a computational overhead. A team lead by Mohammad Hafezi at the University of Maryland, Los Alamos National Laboratory and Dartmouth College has shown that the collective manipulation and read out of an ensemble of superconducting qubits granted by introducing a dispersive coupling to microwave cavity photons grants access to the generation of non-local operations directly. This digital circuit QED architecture reduces the number of operations necessary to simulate fermionic systems by an amount that scales quadratically in the size of the system, making it more hardware-efficient than existing alternatives.