Authors: Mirza Samad Ahmed Baig, Syeda Anshrah Gillani, Abdul Akbar Khan, Muhammad Omer Khan
Organizations: Fandaqah, Al Khobar, Saudi Arabia · Heidelberg University, Heidelberg, Germany · Argaam, Riyadh, Saudi Arabia · Fortanixor, United Arab Emirates
Randomized benchmarking can hide classical temporal correlations because its Clifford-twirled response is even in the noise phase. For a stationary symmetric telegraph fluctuator, we show that continuous evolution and independent stationary resets at slot boundaries yield identical mean responses for arbitrary fixed idle modulations. We construct an eight-setting phase-cycle measurement of the connected sine-phase covariance under ideal Clifford twirling and classical idle dephasing. This observable vanishes for independent slot noise and fixed detuning without a weak-phase or Gaussian approximation. A closed telegraph response, independent circuit calculations and 800 simulation trials validate the construction and quantify the empirical coverage of a paired bootstrap estimator. A separate conservative confidence set states its finite-sample assumptions. Two acquisitions on an IBM processor compare engineered shared-sign and independently reset phases with identical marginals. Their 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. At equal shot and sensingwindow budgets, an ideal Ramsey/echo estimator is more precise in every tested class. The result supplies an explicit connection between a benchmarking identifiability limitation and a controlled correlation measurement. No native or quantum-memory detection is claimed.
Figures & tables
Model
Detection
Bootstrap
Finite bound
coverage
coverage
Continuous RTN
100.0
92.5
100.0
Independent reset
4.5
95.5
100.0
Fixed detuning
6.5
93.5
100.0
Independent Gaussian
5.5
94.5
100.0
Table 1: Held-out simulation calibration. Entries are percentages over 200 trials per class. Detection means the nominal two-sided bootstrap interval excludes zero. The conservative bound uses Eq. ( 11 ).
Figure 1: Simulation and exact theory. (a) Continuous telegraph noise and independent slot resets have identical mean gap scans. (b) The phase-cycle covariance distinguishes them; the separation dependence is the ideal uncoupled-interval prediction of Eq. ( 8 ). (c) Median and central 95% sampling ranges over independent simulated experiments, with crosses marking population values. These are sampling-distribution ranges, not confidence intervals from one experiment.
Model
RB
Ramsey/echo
Ratio
Continuous RTN
0.0777
0.0269
2.89
Independent reset
0.0798
0.0432
1.85
Fixed detuning
0.0793
0.0188
4.22
Independent Gaussian
0.0824
0.0318
2.59
Table 2: Root mean squared error for the same sine covariance in ideal simulation. Neither method has native drift or imperfect gates in this comparison.
Arm
Estimate
95% interval
Acquisition 1
Shared sign
0.2580
[0.1935,0.3182]
Independent reset
0.0040
[−0.0704,0.0779]
Fixed detuning
0.0456
[−0.0304,0.1195]
No injection
0.0416
[−0.0410,0.1265]
Acquisition 2
Table 3: Measured injected phase-cycle contrasts and empirical 95% intervals. The ideal population contrast is 0.2287 for shared signs and zero for the other arms.
Figure 2: Hardware response to engineered phase correlations. Points and error bars are connected estimates and paired block bootstrap intervals for each acquisition; crosses are ideal population predictions.
Figure 3: Audit of the stored native EPC summaries. (a) Offset-aware phenomenological fit. (b) Best residual after profiling nonnegative nuisance parameters, versus the Gaussian-ball cutoff. The tested model curves fail this adequacy diagnostic, so no exclusion region is shaded or claimed.
How complex can the responses of a quantum device become as it runs longer with a fixed internal memory? We quantify this complexity through sequential response capacity: how many adaptive testing stages, each using a fresh run, can continue to separate possible processes by a prescribed gap in response probabilities. For fixed system and memory sizes, we establish a tight law relating this capacity to run length and probability resolution. At fixed resolution, the capacity grows on the order of KlogK, where K is the number of time steps in each run. Our construction attains this growth using time-dependent phase rotations on a single visible qubit with no additional internal memory; its tests give response probabilities exactly zero or one. Under the same tests, classical stochastic processes that measure in a fixed basis at every step have only linear capacity at fixed sizes and resolution. For phase sequences selected by a stored classical label, we then quantify how known independent Pauli noise changes this logarithmic enhancement. With ideal controls and weak residual phase noise after correction, we prove matching capacity bounds at a fixed small probability gap. These bounds identify the inverse residual phase-flip probability as the coherence timescale that limits the extra logarithmic growth.
Yibin Wang
Graduate School of Mathematics, Nagoya University, Nagoya, 464-8601, Aichi, Japan.
Ancilla reuse in repeated syndrome extraction couples reset quality to logical-cycle latency. We evaluate blind reset -- unitary-only recycling via scaled sequence replay -- on IQM Garnet, Rigetti Ankaa-3, and IonQ under matched seeds, sequence lengths, and shot budgets. Using ancilla cleanliness F_clean=P(|0>), per-cycle latency, and a distance-3 repetition-code logical-error proxy, platform-calibrated simulation identifies candidate regions where blind reset cuts cycle latency by up to 38x under NVQLink-class feedback overhead while maintaining F_clean >= 0.86 for L <= 6. Hardware experiments on IQM Garnet confirm blind-reset cleanliness >= 0.84 at L=8 (1024 shots, seed 42); platform-calibrated simulation for Rigetti Ankaa-3 predicts comparable performance. Architecture-dependent crossover lengths are L* ~ 12 (IQM), ~ 11 (Rigetti), ~ 1 (IonQ), and ~ 78 with GPU-linked external feedback. Two added analyses tighten deployment boundaries: a T1/T2 sensitivity map identifies coherence-ratio regimes, and error-bound validation confirms measured cleanliness remains consistent with the predicted diagnostic envelope. A deployment decision matrix translates these results into backend-specific policy selection.
Sangkeum Lee
Department of Computer Engineering, Hanbat National University, Daejeon 34158, Republic of Korea
Can a small quantum computer forecast a changing signal better than an ordinary classical method? Many studies say yes, but the classical methods they compare against are often left in a basic, untuned state while the quantum model is carefully optimised. We ask what happens when the classical competitor is given exactly the same care: the same size and the same amount of tuning effort. We study two popular reasons a quantum reservoir is thought to help, using exact simulations of small quantum systems (up to eleven qubits) on prediction tasks. In both cases the quantum advantage disappears once the comparison is fair. In the first, extra quantum measurements add nothing that a simple classical formula of the same size does not already provide. In the second, a feedback loop genuinely helps the quantum model, turning a useless setup into a working predictor, yet a well-tuned classical network still predicts slightly more accurately, and the gap is statistically reliable. Our point is not that quantum reservoirs can never win, but that two of their commonly cited advantages do not hold up against fair classical competitors at this scale. We provide these matched comparisons as a simple, reusable checklist for honest benchmarking. All results are fully reproducible from fixed random seeds.