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<p>We establish a sufficient condition under which autonomous quantum error correction (AutoQEC) can effectively restore Heisenberg scaling (HS) in quantum metrology. Specifically, we show that if all Lindblad operators associated with the noise commute with the signal Hamiltonian and a particular constrained linear equation admits a solution, then an ancilla-free AutoQEC scheme with finite <i>R</i> (where <i>R</i> represents the ratio between the engineered dissipation rate for AutoQEC and the noise rate) can approximately preserve HS with a desired small additive error <i>ϵ</i> &gt; 0 over any time interval 0 ≤ <i>t</i> ≤ <i>T</i>. We emphasize that the error scales as <i>ϵ</i> = <i>O</i>(<i>κ</i><i>T</i>/<i>R</i><sup><i>c</i></sup>) where <i>c</i> is a positive integer and <i>κ</i> is the noise rate, indicating that the required <i>R</i> decreases significantly with increasing <i>c</i> to achieve a desired error. Furthermore, we discuss that if the sufficient condition is not satisfied, logical errors may be induced that cannot be efficiently corrected by the canonical AutoQEC framework. Finally, we numerically verify our analytical results by employing concrete examples of phase estimation under dephasing noise.</p>

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Restoring Heisenberg scaling in time via autonomous quantum error correction

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月15日

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  • Hyukgun Kwon,
  • Uwe R. Fischer,
  • Seung-Woo Lee,
  • Liang Jiang

摘要

We establish a sufficient condition under which autonomous quantum error correction (AutoQEC) can effectively restore Heisenberg scaling (HS) in quantum metrology. Specifically, we show that if all Lindblad operators associated with the noise commute with the signal Hamiltonian and a particular constrained linear equation admits a solution, then an ancilla-free AutoQEC scheme with finite R (where R represents the ratio between the engineered dissipation rate for AutoQEC and the noise rate) can approximately preserve HS with a desired small additive error ϵ > 0 over any time interval 0 ≤ t ≤ T. We emphasize that the error scales as ϵ = O(κT/Rc) where c is a positive integer and κ is the noise rate, indicating that the required R decreases significantly with increasing c to achieve a desired error. Furthermore, we discuss that if the sufficient condition is not satisfied, logical errors may be induced that cannot be efficiently corrected by the canonical AutoQEC framework. Finally, we numerically verify our analytical results by employing concrete examples of phase estimation under dephasing noise.