Hardware-efficient fermionic simulation with a cavity\u2013QED system

Guanyu Zhu,Mohammad Hafezi,James D Whitfield,Yiğit Subaşı

doi:10.1038/s41534-018-0065-3

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.

Highlights

Quantum computers are widely touted as a new frontier for simulating quantum systems.[1,2] The simulation of quantum chemistry,[3,4,5,6,7] strongly correlated fermionic systems,[8,9,10,11,12] and lattice gauge theories,[13,14] are among the crucial applications.[15]
We focus on fluxonium qubits here, one can generate quantum non-demolition (QND) interaction in more general cases for other qubits such as transmons
In this article, we have shown that, in the context of cavity/circuitQED architecture, the use of the common cavity modes greatly simplifies the non-local string-like encoding needed for fermionic simulation, such as Jordan–Wigner and Bravyi–Kitaev transforms

Summary

INTRODUCTION

Quantum computers are widely touted as a new frontier for simulating quantum systems.[1,2] The simulation of quantum chemistry,[3,4,5,6,7] strongly correlated fermionic systems,[8,9,10,11,12] and lattice gauge theories,[13,14] are among the crucial applications.[15]. We present an experimental implementation of our scheme in a circuit-QED platform,[26,27,28,29,30,31,32,33,34,35,36,37,38] where experimental progress on fermionic and quantum chemistry simulation has been recently achieved.[4,7] In particular, we use dispersive coupling of microwave cavity photons to superconducting qubits[30,38] to generate non-local string operations non-perturbatively This digital approach offers better scaling in the collective gate time than a previous analog scheme where multi-spin interactions are generated perturbatively,[39] resulting in an exponential decrease with the number of Pauli operators to be implemented.

RESULTS

CONCLUSION AND DISCUSSION

METHODS