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Physical Review A

Mitigating noise effects in phase estimation via a quantum cyclic n -switch

Zhen-Dong Wei, Wei‐Bin Yan, Zhong‐Xiao Man, Yun‐Jie Xia, Ying-Jie Zhang, Qing-yu Cai

Published Jun 23, 2026• 0 citations
Publisher
DOI
10.1103/gt5c-vgcm

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Virtual distillation has been proposed as an error mitigation protocol for estimating the expectation values of observables in quantum algorithms. It proceeds by creating a cyclic permutation of M noisy copies of a quantum state using a sequence of controlled-swap gates. If the noise does not shift the dominant eigenvector of the density operator away from the ideal state, then the error in expectation-value estimation can be exponentially reduced with M . In practice, subsequent error mitigation techniques are required to suppress the effect of noise in the cyclic permutation circuit itself, leading to increased experimental complexity. Here, we perform a careful analysis of the effect of uncorrelated, identical noise in the cyclic permutation circuit and find that the estimation of expectation value of observables are robust against dephasing noise. We support the analytical result with numerical simulations and find that 67% of errors are reduced for M=2 , with physical dephasing error probabilities as high as 10% . Our results imply that a broad class of quantum algorithms can be implemented with higher accuracy in the near-term with qubit platforms where non-dephasing errors are suppressed, such as superconducting bosonic qubits and Rydberg atoms.
The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of distributed quantum metrology. Therefore, it is significant to effectively overcome the entanglement-distribution loss and channel noise of dissipative environments and improve the measurement-sensitivity. Here, we introduce noiseless linear amplifier (NLA) based on photon catalysis into distributed phase estimation to mitigate the loss and noise. Through utilizing a series of reduction and equivalence relations to simplify the problem of distributed phase estimation to a single-parameter estimation situation, our results show that Photon catalysis (PC)-NLAs can effectively mitigate the loss and noise of dissipative environments, and greatly improve the measurement-sensitivity. More interestingly, we find that adding thermal photons of environment has positive contributions on the measurement-sensitivity under certain circumstances. Our scheme should prove valuable for the global wide-area quantum sensor network.
Noise is the main source that hinders us from fully exploiting quantum advantages in various quantum informational tasks. However, characterizing and calibrating the effect of noise is not always feasible in practice. Especially for quantum parameter estimation, an estimator constructed without precise knowledge of noise entails an inevitable bias. Recently, virtual purification-based error mitigation (VPEM) has been proposed to apply for quantum metrology to reduce such a bias occurring from unknown noise. While it was demonstrated to work for particular cases, whether VPEM always reduces a bias for general estimation schemes is unclear. For more general applications of VPEM to quantum metrology, we study factors determining whether VPEM can reduce the bias. We find that the closeness between the dominant eigenvector of a noisy state and the ideal quantum probe (without noise) with respect to an observable determines the reducible amount of bias by VPEM. Next, we show that one should carefully choose the reference point of the target parameter, which gives a smaller bias than others because the bias depends on the reference point. Otherwise, even if the dominant eigenvector and the ideal quantum probe are close, the bias of the mitigated case could be larger than the nonmitigated one. Finally, we analyze the error mitigation for a phase estimation scheme under various noises. Based on our analysis, we predict whether VPEM can effectively reduce a bias and numerically verify our results.