{"ID":2899834,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.01215","arxiv_id":"2507.01215","title":"A Fundamental Bound for Robust Quantum Gate Control","abstract":"We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence the average) gate fidelity obeys the lower bound $F \\ge \\Flb\\bigl(\\tf \\Omeff\\bigr)$, where $\\tf$ is the gate duration and $\\Omeff$ is a single frequency-like measure that aggregates \\emph{all} bounded uncertainty sources, e.g., coherent control imperfections, unknown couplings, and residual environment interactions, without assuming an initially factorizable system-bath state or a completely positive map. The bound is obtained by combining an interaction-picture averaging method with a Bellman-Gronwall inequality and holds for any finite-norm Hamiltonian decomposition. Hence it applies equally to qubits, multi-level qudits, and ancilla-assisted operations. Because $\\Flb$ depends only on the dimensionless product $\\tf\\Omeff$, it yields a device-independent metric that certifies whether a given hardware platform can, in principle, reach a specified fault-tolerance threshold, and also sets a quantitative target for robust-control synthesis and system identification.","short_abstract":"We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence the average) gate fidelity obeys the lower bound $F \\ge \\Flb\\bigl(\\tf \\Omeff\\bigr...","url_abs":"https://arxiv.org/abs/2507.01215","url_pdf":"https://arxiv.org/pdf/2507.01215v2","authors":"[\"Robert L. Kosut\",\"Daniel A. Lidar\",\"Herschel Rabitz\"]","published":"2025-07-01T22:26:04Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"math.OC\"]","methods":"[\"Large Language Model\"]","has_code":false}