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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.01215 |
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| _version_ | 1866918088757215232 |
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| author | Kosut, Robert L. Lidar, Daniel A. Rabitz, Herschel |
| author_facet | Kosut, Robert L. Lidar, Daniel A. Rabitz, Herschel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fundamental Bound for Robust Quantum Gate Control Kosut, Robert L. Lidar, Daniel A. Rabitz, Herschel Quantum Physics Optimization and Control 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. |
| title | A Fundamental Bound for Robust Quantum Gate Control |
| topic | Quantum Physics Optimization and Control |
| url | https://arxiv.org/abs/2507.01215 |