Fundamental Costs of Noise-Robust Quantum Control: Speed Limits and Complexity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914081714208768 |
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| author | Zeng, Junkai Deng, Xiu-Hao |
| author_facet | Zeng, Junkai Deng, Xiu-Hao |
| contents | Noise is ubiquitous in quantum systems and is a major obstacle for the advancement of quantum information science. Noise-robust quantum control achieves high-fidelity operations by engineering the evolution path so that first-order noise contributions cancel at the final time. Such dynamical error correction typically incurs a time overhead beyond standard quantum speed limits. We derive general lower bounds on control complexity that quantify this overhead for quasi-static coherent noise under bounded control amplitude. For a single noise source, we prove a universal time lower bound for first-order robustness and give a constructive scheme that implements any target gate robustly in time 4T plus a constant time. For robustness against an entire noise space, we show dimension lower bounds on the number M of segments in any mixed-unitary schedule from two mechanism: (i) a coherent dimension bound when the error subspace contains an irreducible block isomorphic to su(q), and (ii) a projection dimension bound when the noise space contains the trace-zero span of orthogonal projectors. Under bounded speed, these bounds on number of segments imply time lower bounds. With only local controls robust against noise space defined on a graph, we obtain a graph-orthogonality time bound scales linear with graph chromatic number. We illustrate the bounds through examples. Collectively, these results establish quantitative limitations on the feasibility of first-order noise-resilient operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Costs of Noise-Robust Quantum Control: Speed Limits and Complexity Zeng, Junkai Deng, Xiu-Hao Quantum Physics Noise is ubiquitous in quantum systems and is a major obstacle for the advancement of quantum information science. Noise-robust quantum control achieves high-fidelity operations by engineering the evolution path so that first-order noise contributions cancel at the final time. Such dynamical error correction typically incurs a time overhead beyond standard quantum speed limits. We derive general lower bounds on control complexity that quantify this overhead for quasi-static coherent noise under bounded control amplitude. For a single noise source, we prove a universal time lower bound for first-order robustness and give a constructive scheme that implements any target gate robustly in time 4T plus a constant time. For robustness against an entire noise space, we show dimension lower bounds on the number M of segments in any mixed-unitary schedule from two mechanism: (i) a coherent dimension bound when the error subspace contains an irreducible block isomorphic to su(q), and (ii) a projection dimension bound when the noise space contains the trace-zero span of orthogonal projectors. Under bounded speed, these bounds on number of segments imply time lower bounds. With only local controls robust against noise space defined on a graph, we obtain a graph-orthogonality time bound scales linear with graph chromatic number. We illustrate the bounds through examples. Collectively, these results establish quantitative limitations on the feasibility of first-order noise-resilient operations. |
| title | Fundamental Costs of Noise-Robust Quantum Control: Speed Limits and Complexity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.07183 |