A Fundamental Bound for Robust Quantum Gate Control

• URL: http://arxiv.org/abs/2507.01215v2
• Date: Thu, 10 Jul 2025 18:14:32 GMT
• Title: A Fundamental Bound for Robust Quantum Gate Control
• Authors: Robert L. Kosut, Daniel A. Lidar, Herschel Rabitz,
• Abstract summary: We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties.<n>We prove that the worst-case (and hence the average) gate fidelity obeys the lower bound $F ge Flbbigl(tf Omeffbigr)$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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