2026-10-12 · arXiv Quantum Physics
arXiv:2508.01884v3 Announce Type: replace
Abstract: We analytically investigate the robustness of the Bernstein-Vazirani and Deutsch-Jozsa algorithms against single-qubit Pauli noise, of which bit-flip, phase-flip, and depolarizing noise are special cases, using the density-matrix formalism. For a general Pauli channel acting on each qubit after every gate, we derive exact closed-form expressions for the success probability of a single run as a function of the error probabilities and the number of qubits $n$, and validate them against Qiskit simulations. The noise enters only through the probability $\varepsilon$ with which each output bit is flipped. Under bit-flip noise with error probability $p 1/2$ the most probable outcome of the Bernstein-Vazirani algorithm is the complement of the correct one, which classical post-processing corrects, whereas depolarizing and phase-flip noise never bias the output toward a wrong outcome. For the Deutsch-Jozsa algorithm, the success probability is the average over constant and balanced oracles, and the results are given for the single-variable balanced oracle, which is shown to be the least robust of all balanced oracles for $\varepsilon
原文链接：https://arxiv.org/abs/2508.01884
查看更多资讯请见 AI 行业资讯。