Systematic time-coarse graining for driven quantum systems

• URL: http://arxiv.org/abs/2407.06068v1
• Date: Mon, 8 Jul 2024 16:11:52 GMT
• Title: Systematic time-coarse graining for driven quantum systems
• Authors: Leon Bello, Wentao Fan, Aditya Gandotra, Hakan E. Türeci,
• Abstract summary: We present a time-coarse graining (STCG) framework that provides a Quantum Master Equation (QME) for the time-coarse grained density matrix of a driven quantum system. We present three case studies examining the numerical stability, convergence and the interpretive utility of the coarse-grained QME at high orders.
• Score: 7.217684156614636
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fidelity requirements on quantum devices necessitate faster and stronger drives, pushing into regimes where the rotating-wave approximation (RWA) is no longer adequate. In those regimes, high-frequency processes generated by counter-rotating terms can significantly modify the long-term dynamics of a quantum system. Exploring these regimes is difficult even numerically, since system dynamics exhibiting disparate time-scales are often stiff and unstable. In this work, we present a systematic time-coarse graining (STCG) framework that addresses these issues by directly providing a Quantum Master Equation (QME) for the time-coarse grained density matrix of a driven quantum system. STCG allows the perturbative calculation of effective unitary and non-unitary generators describing the relevant slow dynamics at any given order of truncation beyond the RWA, and is accompanied by a complete software framework written in Julia, \textbf{QuantumGraining.jl}, for efficient implementation. We present three case studies examining the numerical stability, convergence and the interpretive utility of the coarse-grained QME at high orders. These examples illustrate two key results: observables measured by finite bandwidth apparatus can differ significantly from exact dynamics due to the effect of the counter-rotating terms, and that this can be captured by solving the STCG QME with basic low-order ODE solvers.

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