In digital quantum simulation of fermionic models with qubits, one requires the use of non-local maps for encoding. 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 (JW) or Bravyi-Kitaev (BK) 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 JW (BK) encoding, by a factor of\ N2\ (NlogN), where\ N\ is the number of orbitals for a generic two-body Hamiltonian. Additional analysis for the Fermi-Hubbard model on an\ N{\texttimes}N\ square lattice results in a similar reduction. We also discuss a detailed implementation of our scheme with superconducting qubits and cavities.

}, doi = {10.1038/s41534-018-0065-3}, url = {https://www.nature.com/articles/s41534-018-0065-3}, author = {Guanyu Zhu and Yigit Subasi and James D. Whitfield and Mohammad Hafezi} }