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Hamiltonian Simulation Algorithms for Near-term Quantum Hardware by Laura Clinton; Johannes Bausch; Toby Cubitt is a Biochemistry, Genetics and Molecular Biology article available to read on EtoBox.

What is Hamiltonian Simulation Algorithms for Near-term Quantum Hardware about?

## Abstract 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 this work, we develop quantum algorithms for Hamiltonian simulation "one level below” the circuit model, exploiting the underlying control over qubit interactions available in most quantum hardware and deriving analytic circuit identities for synthesising multi-qubit evolutions from two-qubit interactions. We then analyse the impact of these techniques under the standard error model where errors occur per gate, and an error model with a constant error rate per unit time. To quantify the benefits of this approach, we apply it to time-dynamics simulation of the 2D spin Fermi-Hubbard model. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime and an analysis of error propagation, we find that e.g. for a 5 × 5 Fermi-Hubbard lattice we reduce the circuit depth from 1, 243, 586 using the best previous fermion encoding and error bounds in the literature, to 3, 209 in the per-gate error model, or the circuit-depth-equivalent to 259 in the per-time error model. This brings Ha

Who reads Hamiltonian Simulation Algorithms for Near-term Quantum Hardware?

Author

Laura Clinton; Johannes Bausch; Toby Cubitt

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Biochemistry, Genetics and Molecular Biology (Life Sciences)