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Research paper: Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware



The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with severely restricted resources, this overhead may be unjustifiable. In this work, we develop quantum algorithms for Hamiltonian simulation "one level below" the circuit model, exploiting the underlying control over qubit interactions available in principle in most quantum hardware implementations. This sub-circuit model approach significantly reduces both the run-time of the algorithm, and the propagation of errors during the algorithm -- particularly important when resources are too limited to perform active error correction.
To quantify the benefits of this approach, we apply it to a canonical example: time-dynamics simulation of the 2D spin Fermi-Hubbard model. We derive analytic circuit identities for efficiently synthesising multi-qubit evolutions from two-qubit interactions. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime, a novel low-weight fermion encoding, and a careful analysis of error propagation in the sub-circuit model algorithm, we improve upon the previous best methods for Hamiltonian simulation by multiple orders of magnitude. For example, for a 5 x 5 Fermi-Hubbard lattice -- already challending on classical supercomputers -- we reduce the circuit-depth-equivalent from 800,160 to 2960. This brings Hamiltonian simulation, previously beyond reach of current hardware for non-trivial examples, significantly closer to being feasible in the NISQ era.


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