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Closed-Loop Phase-Coherence Compensation for Superconducting Qubits Integrated Computational and Hardware Validation of the Aurora Method

Futoshi Hamanoue

TL;DR

The combined results support pre-calibrated Aurora-DD as a practical, stable, and hardware-compatible phase-coherence compensator for NISQ devices in single-qubit settings.

Abstract

We present an emulator-based and hardware feasibility study of Aurora-DD, a phase-coherence compensation method that integrates a sign-based feedback update of a global phase offset (Delta phi) with a fixed-depth XY8 dynamical decoupling (DD) scaffold. The feedback optimization is performed offline on a calibrated emulator and the resulting Delta phi* is deployed as pre-calibrated phase compensation on hardware. This represents an "offline closed-loop, online open-loop" feasibility demonstration. Using an Aer-based emulator calibrated with ibm_fez device parameters, Aurora-DD achieves substantial reductions in mean-squared error of the measured expectation value <Z>, yielding 68-97% improvement across phase settings phi = 0.05, 0.10, 0.15, 0.20 over n=30 randomized trials. These large-n emulator results provide statistically stable evidence that the combined effect of XY8 and Delta phi* suppresses both dephasing and systematic phase bias. On real superconducting hardware (ibm_fez), we perform a small-sample (n=3) multi-phase validation campaign. Aurora-DD yields point estimates corresponding to approximately 99.2-99.6% reduction in absolute error relative to a no-DD baseline across all tested phase points. These hardware numbers are reported transparently as feasibility evidence under tight queue and credit constraints. In contrast, the auxiliary Aurora+ZNE branch exhibits instability: shallow two-point ZNE occasionally amplifies calibration inconsistencies and produces large error outliers. We therefore relegate ZNE analysis to the Appendix and position Aurora-DD (without ZNE) as the primary contribution. Overall, the combined results support pre-calibrated Aurora-DD as a practical, stable, and hardware-compatible phase-coherence compensator for NISQ devices in single-qubit settings.

Closed-Loop Phase-Coherence Compensation for Superconducting Qubits Integrated Computational and Hardware Validation of the Aurora Method

TL;DR

The combined results support pre-calibrated Aurora-DD as a practical, stable, and hardware-compatible phase-coherence compensator for NISQ devices in single-qubit settings.

Abstract

We present an emulator-based and hardware feasibility study of Aurora-DD, a phase-coherence compensation method that integrates a sign-based feedback update of a global phase offset (Delta phi) with a fixed-depth XY8 dynamical decoupling (DD) scaffold. The feedback optimization is performed offline on a calibrated emulator and the resulting Delta phi* is deployed as pre-calibrated phase compensation on hardware. This represents an "offline closed-loop, online open-loop" feasibility demonstration. Using an Aer-based emulator calibrated with ibm_fez device parameters, Aurora-DD achieves substantial reductions in mean-squared error of the measured expectation value <Z>, yielding 68-97% improvement across phase settings phi = 0.05, 0.10, 0.15, 0.20 over n=30 randomized trials. These large-n emulator results provide statistically stable evidence that the combined effect of XY8 and Delta phi* suppresses both dephasing and systematic phase bias. On real superconducting hardware (ibm_fez), we perform a small-sample (n=3) multi-phase validation campaign. Aurora-DD yields point estimates corresponding to approximately 99.2-99.6% reduction in absolute error relative to a no-DD baseline across all tested phase points. These hardware numbers are reported transparently as feasibility evidence under tight queue and credit constraints. In contrast, the auxiliary Aurora+ZNE branch exhibits instability: shallow two-point ZNE occasionally amplifies calibration inconsistencies and produces large error outliers. We therefore relegate ZNE analysis to the Appendix and position Aurora-DD (without ZNE) as the primary contribution. Overall, the combined results support pre-calibrated Aurora-DD as a practical, stable, and hardware-compatible phase-coherence compensator for NISQ devices in single-qubit settings.

Paper Structure

This paper contains 44 sections, 18 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework of Aurora
  3. Bloch-Equation Model of NISQ Noise
  4. Phase-Error Proxy δZ
  5. Objective Function: Phase-Error MSE
  6. Closed-Loop Update Rule: Sign-Based Gradient Descent
  7. Summary of Theoretical Properties
  8. Methods
  9. Aurora-DD Overview
  10. Choice of $n=30$ emulator repetitions.
  11. Calibration of the Aer Noise Model and $\Delta\phi^\ast$
  12. Rationale for using a single global $\Delta\phi^\ast$.
  13. Hardware Configuration
  14. Circuit Construction
  15. Trial Structure and Conditions
  16. ...and 29 more sections

Figures (4)

  • Figure 1: Baseline vs Aurora-DD (hardware, feasibility study). Aurora-DD yields approximately two orders of magnitude reduction in absolute error across all $\phi$ in this small-$n$ campaign. Error bars indicate standard deviation across trials.
  • Figure 2: Ideal vs Baseline vs Aurora-DD (hardware). Aurora-DD restores the expected cosine relationship $\langle Z\rangle \approx \cos\phi$, while the baseline measurements are heavily distorted by dephasing in the chosen stress-test regime.
  • Figure 3: Instability of ZNE under DD. ZNE amplifies calibration inconsistencies when combined with deep DD blocks, producing large extrapolation errors. This motivates limiting ZNE to Appendix analysis only.
  • Figure 4: Effect of ZNE on Aurora-DD under realistic hardware noise (ibm_fez, $n=3$). Zero-Noise Extrapolation (ZNE) exhibits strong instability on ibm_fez: errors increase by one to two orders of magnitude and variance becomes large, indicating that ZNE overfits to stochastic noise fluctuations. Aurora-DD (no ZNE) remains stable and consistently low-error across all $\phi$ values. This figure demonstrates why ZNE is excluded from the main hardware analysis.