Ilmu Komputer & AI editorial
Open AccessOA2026
Phase-Cycled Randomized Benchmarking of Quantum Processors: Recovering Hidden Classical Noise Correlations
An eight-setting phase-cycle measurement exposes classical temporal correlations that standard Clifford-twirling randomized benchmarking conceals, validated on an IBM processor.
Mirza Samad Ahmed Baig; Syeda Anshrah Gillani; Abdul Akbar Khan; Muhammad Omer Khan· 2026· DOI 10.48550/arXiv.2609.06448
The core problem
Randomized benchmarking (RB) is a cornerstone protocol for characterizing quantum processors, yet its Clifford-twirling structure imposes a fundamental identifiability limitation: the averaged response is even in the noise phase, so classical temporal correlations can remain hidden. The authors (Baig, Gillani, Khan, and Khan) address this gap by asking whether a controlled measurement can recover correlations that RB averages away. They focus on a stationary symmetric telegraph fluctuator, a canonical model of classical two-state noise, and show that continuous evolution and independent stationary resets at slot boundaries produce identical mean responses for arbitrary fixed idle modulations. This equivalence motivates a new observable—the connected sine-phase covariance—that vanishes for independent slot noise and fixed detuning without invoking a weak-phase or Gaussian approximation. The work thus supplies an explicit connection between a benchmarking identifiability limitation and a controlled correlation measurement, while making no claim of native or quantum-memory detection.
Innovation
Two acquisitions on an IBM processor compare engineered shared-sign phases with independently reset phases that have identical marginals. The primary contrasts are 0.254 and 0.211, with empirical 95% intervals [0.177, 0.331] and [0.136, 0.285], respectively. All negative-control intervals include zero, confirming that the measurement does not produce spurious correlations. The simulation trials and closed telegraph response validate the construction and quantify the empirical coverage of the paired bootstrap estimator. The conservative confidence set provides finite-sample guarantees. Notably, at equal shot and sensing-window budgets, an ideal Ramsey/echo estimator is more precise in every tested class, indicating that the phase-cycle measurement trades precision for the ability to detect correlations that Ramsey/echo cannot. The results establish that the eight-setting phase-cycle measurement can recover hidden classical noise correlations that standard RB misses.
Randomized benchmarking (RB) is a cornerstone protocol for characterizing quantum processors, yet its Clifford-twirling structure imposes a fundamental identifiability limitation: the averaged response is even in the noise phase, so classical temporal correlations can remain hidden. The authors (Baig, Gillani, Khan, and Khan) address this gap by asking whether a controlled measurement can recover correlations that RB averages away. They focus on a stationary symmetric telegraph fluctuator, a canonical model of classical two-state noise, and show that continuous evolution and independent stationary resets at slot boundaries produce identical mean responses for arbitrary fixed idle modulations. This equivalence motivates a new observable—the connected sine-phase covariance—that vanishes for independent slot noise and fixed detuning without invoking a weak-phase or Gaussian approximation. The work thus supplies an explicit connection between a benchmarking identifiability limitation and a controlled correlation measurement, while making no claim of native or quantum-memory detection.
The authors construct an eight-setting phase-cycle measurement of the connected sine-phase covariance under ideal Clifford twirling and classical idle dephasing. The protocol cycles the phase of idle modulation across eight settings to isolate the covariance component that is odd in the noise phase, which standard RB suppresses. The observable is defined so that it vanishes for independent slot noise and for fixed detuning, without requiring a weak-phase or Gaussian approximation. To validate the construction, the authors derive a closed-form telegraph response, perform independent circuit calculations, and run 800 simulation trials. They also quantify the empirical coverage of a paired bootstrap estimator and provide a separate conservative confidence set that states its finite-sample assumptions. The methodology is designed to be robust: the phase-cycle measurement is compared against an ideal Ramsey/echo estimator at equal shot and sensing-window budgets, and the latter is found to be more precise in every tested class.
Why it matters
The key insight is that Clifford-twirled RB responses are even in the noise phase, so classical temporal correlations are invisible to standard RB. The phase-cycle measurement breaks this symmetry by cycling the phase of idle modulation, making the connected sine-phase covariance accessible. The equivalence between continuous evolution and independent stationary resets at slot boundaries for a stationary symmetric telegraph fluctuator is a strong theoretical result: it means that the mean response is insensitive to whether the noise evolves continuously or is reset, for arbitrary fixed idle modulations. This equivalence underpins the identifiability limitation and motivates the new observable. The observable vanishes for independent slot noise and fixed detuning without weak-phase or Gaussian approximations, making it broadly applicable. The IBM processor results show statistically significant positive contrasts, while negative controls include zero, supporting the validity of the method. However, the ideal Ramsey/echo estimator is more precise at equal budgets, suggesting that the phase-cycle approach is best suited for detecting correlations rather than precise parameter estimation. The authors explicitly state that no native or quantum-memory detection is claimed, keeping the scope to classical noise correlations. The work connects a benchmarking identifiability limitation to a controlled correlation measurement, offering a new tool for quantum processor characterization.
Who should read this
CS practitioners and researchers
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