Fundamental Costs of Noise-Robust Quantum Control: Speed Limits and Complexity

• URL: http://arxiv.org/abs/2510.07183v1
• Date: Wed, 08 Oct 2025 16:21:33 GMT
• Title: Fundamental Costs of Noise-Robust Quantum Control: Speed Limits and Complexity
• Abstract summary: Noise is ubiquitous in quantum systems and is a major obstacle for the advancement of quantum information science.<n>Noise-robust quantum control achieves high-fidelity operations by engineering the evolution path so that first-order noise contributions cancel at the final time.<n>We derive general lower bounds on control complexity that quantify this overhead for quasi-static coherent noise under bounded control amplitude.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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