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arXiv · 2604.01048

Distilling Unitary Operations: A No-Go Theorem and Minimal Realization

Jiayi Zhao·Yu-Ao Chen·Guocheng Zhen·Chengkai Zhu·Ranyiliu Chen·Xin Wang
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Abstract

Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic execution of quantum algorithms requires a higher-order approach to mitigate errors on the operations themselves. In this work, we investigate universal unitary purification: the task of utilizing a quantum higher-order operation to partially restore the ideal action of an unknown unitary corrupted by a known noise model. Focusing on canonical depolarizing noise, we first reveal a fundamental operational obstruction. We prove that within the indefinite causal order framework, no nontrivial 2-slot higher-order operation can universally purify the set of single-qubit unitaries. Overcoming this strict limitation, we establish that a 3-slot parallel architecture provides the minimal realization for non-trivial purification. We analytically derive the optimal average fidelity within the parallel 3-slot class, demonstrating that it strictly surpasses trivial strategies by systematically utilizing ancillary qubits as a quantum memory to absorb errors. Furthermore, we provide a concrete quantum circuit construction attaining this parallel optimum. Our results establish the strict theoretical boundaries of distilling clean operations from noisy gates, offering immediate architectural insights for robust gate design.

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Jiayi Zhao, Yu-Ao Chen, Guocheng Zhen, Chengkai Zhu, Ranyiliu Chen, Xin Wang. 2026-04-01. Distilling Unitary Operations: A No-Go Theorem and Minimal Realization. https://arxiv.org/abs/2604.01048

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