Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields
Eleanor Crane from MIT ( @MITMechE ) presents at the QuDits for Quantum Technology workshop, hosted by the Quantum Interactions Theory Group at the Institute for Quantum Computing, University of Waterloo. Learn more: https://quantum-interactions.com/
Finding a scalable and universal framework for quantum simulation of strongly correlated fermions and bosons is an important goal for fields ranging from materials science to high-energy physics. While digital qubit-only quantum computers in principle offer such universality, the overhead encountered in mapping bosons to qubits, particularly in spatial dimension D is greater than 1, renders this endeavour extremely challenging to implement in practice. Here, we develop an approach to simulate bosonic matter, fermionic matter, and Abelian gauge fields in D is equal to 2 on near-term hybrid oscillator-qubit quantum processors. This approach avoids the boson-to-qubit overhead altogether, which makes the process viable on NISQ era hybrid devices for modestly large boson number cutoffs. We present novel compilation strategies, enabling exact bosonic density-density or parity-dependent interaction terms, and non-local qubit coupling terms including a novel compilation of the U(1) magnetic field term that would be challenging to implement in qubit-only NISQ hardware. We show how our compilation strategies can be used to study both dynamics and ground states by introducing a hybrid oscillator-qubit variational quantum eigensolver. To illustrate the promise of our compilation methods we numerically simulate experiments for the Z2 and the U(1) quantum link model including the dominant sources of hardware error for superconducting qubits coupled to high-Q cavities. We show that near-term devices can observe signatures of phase transitions in these models by developing measurement techniques for non-local observables such as string-order correlators and the superfluid stiffness. Finally, we compare the gate complexity of all-qubit and hybrid oscillator-qubit hardware for Trotter-based simulations of lattice gauge theories, finding a prefactor advantage of our approach of up to three orders of magnitude. Our work opens a path toward using oscillator-qubit hardware such as can be found in superconducting, trapped ion, and neutral atom platforms. Altogether, this work illustrates the potential of, and provides an explicit manual for, using hybrid oscillator-qubit hardware for simulating models containing strongly correlated fermions and bosons and gauge fields.
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