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Noise-Resilient Heisenberg-limited Quantum Sensing via Indefinite-Causal-Order Error Correction

Hang Xu, Xiaoyang Deng, Ze Zheng, Tailong Xiao, Guihua Zeng

TL;DR

An ICO-based QEC protocol is introduced, providing the first application of indefinite causal order (ICO) to QEC and revealing ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing.

Abstract

Quantum resources can, in principle, enable Heisenberg-limited (HL) sensing, yet no-go theorems imply that HL scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use in quantum sensing is constrained by stringent requirements, including prior noise characterization, restrictive signal-noise compatibility conditions, and measurement-based syndrome extraction with global control. Here we introduce an ICO-based QEC protocol, providing the first application of indefinite causal order (ICO) to QEC. By coherently placing auxiliary controls and noisy evolution in an indefinite causal order, the resulting noncommutative interference enables an auxiliary system to herald and correct errors in real time, thereby circumventing the limitations of conventional QEC and restoring HL scaling. We rigorously establish the protocol for single- and multi-noise scenarios and demonstrate its performance in single-qubit, many-body, and continuous-variable platforms. We further identify regimes in which error correction can be implemented entirely by unitary control, without measurements. Our results reveal ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing.

Noise-Resilient Heisenberg-limited Quantum Sensing via Indefinite-Causal-Order Error Correction

TL;DR

An ICO-based QEC protocol is introduced, providing the first application of indefinite causal order (ICO) to QEC and revealing ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing.

Abstract

Quantum resources can, in principle, enable Heisenberg-limited (HL) sensing, yet no-go theorems imply that HL scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use in quantum sensing is constrained by stringent requirements, including prior noise characterization, restrictive signal-noise compatibility conditions, and measurement-based syndrome extraction with global control. Here we introduce an ICO-based QEC protocol, providing the first application of indefinite causal order (ICO) to QEC. By coherently placing auxiliary controls and noisy evolution in an indefinite causal order, the resulting noncommutative interference enables an auxiliary system to herald and correct errors in real time, thereby circumventing the limitations of conventional QEC and restoring HL scaling. We rigorously establish the protocol for single- and multi-noise scenarios and demonstrate its performance in single-qubit, many-body, and continuous-variable platforms. We further identify regimes in which error correction can be implemented entirely by unitary control, without measurements. Our results reveal ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing.
Paper Structure (4 theorems, 14 equations, 4 figures)

This paper contains 4 theorems, 14 equations, 4 figures.

Key Result

Theorem 1

Consider a set of noises $L \coloneqq \{L_i\}_{i=1}^m$ of the probe. For a minimal group-generating set $G \coloneqq \{ L'_i \}_{i=1}^{m_a}$ of $L$, if there exists a set of gates $D \coloneqq \{ D_i\}_{i=1}^{m_a}$ satisfying then the IQEC protocol only requires $m_a$ auxiliary qubits to correct the noise set.

Figures (4)

  • Figure 1: Schematic of the IQEC protocol. The evolution order ${\cal{C}}_{ij}$ of the probe is controlled by the computational basis of the auxiliary qubits.
  • Figure 2: (a) Results of the single qubit for different protocols under single noise. The $\sigma_x$ or $\sigma_z$ in the legend denotes the noise operator. (b) Results of the single qubit for IQEC protocol under unknown noises.
  • Figure 3: Results of the two-qubit for different protocols with different noises.
  • Figure 4: (a) Results of the continuous variable system, where $\Delta t=0.25$. (b) Results of the syndrome-based and syndrome-free schemes for IQEC.

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Corollary 1
  • Theorem 3