Beyond Static Protection: Dynamic Stabilizer-Frame Rotation and Refresh on IBM Kingston Heron r3

Author: Amit Brahmbhatt Organisation: Quantum-Clarity LLC Date: April 25, 2026 IBM Job IDs:

• Run 1: d7mi2vraq2pc73a1nrdg (publicly verifiable)
• Run 2: d7mi72lqrg3c738la2k0 (publicly verifiable) Backend: ibm_kingston (IBM Heron r3, 156 qubits, heavy-hex topology) Module: [13, 14, 15] — 3-qubit linear chain, native edges only Predecessor records:
• DOI 10.5281/zenodo.18498540 (February 5, 2026)
• DOI 10.5281/zenodo.19478241 (April 9, 2026)
• DOI 10.5281/zenodo.19501961 (April 10, 2026)
• DOI 10.5281/zenodo.19697551 (April 21, 2026)

Plain Language Summary

What we found:

Quantum computers are noisy. The fragile quantum states they depend on decay rapidly — not because of any fundamental limit of physics, but because the environment surrounding each qubit is constantly interfering, nudging quantum states out of the carefully prepared configurations that make computation possible. Everything we have built in the QuantaCore program so far has been about finding geometric structures — protected subspaces — where this interference is reduced. In our previous records, we showed that a specific stabilizer state called Z⊗Y⊗Z survives longer than an unprotected state, and that periodically refreshing that state extends its useful lifetime further.

This experiment asks a new question: what if the protected state itself moved?

Instead of holding the stabilizer still and hoping the noise doesn't find it, we continuously rotate the stabilizer frame — spinning it through a sequence of orientations during the hold period, while simultaneously applying a midpoint refresh. The result is that the rotating-and-refreshed stabilizer preserves more plane fidelity than static hold, consistent with the idea that continuous frame motion reduces how efficiently noise can accumulate against any one fixed orientation.

Across two independent hardware runs on IBM Kingston, this approach — dynamic stabilizer-frame rotation combined with midpoint refresh — improved measured plane fidelity at 15 microseconds from a static baseline of 0.718–0.782 to a best result of 0.890. The largest measured gain was +23.9% over the static baseline in a single run.

The improvement appeared consistently across every tested C3 (rotation + refresh) configuration. Rotation without refresh produced smaller and inconsistent gains. The combination of rotation and refresh is what drives the improvement.

Why this matters for anyone:

Think of it this way. If you are trying to protect a candle flame from wind, you can build a windbreak — that is what the protected stabilizer subspace does. But a windbreak only works if the wind is blowing in a predictable direction. If the wind shifts, the windbreak fails.

Dynamic rotation is like spinning the windbreak continuously so that no matter which direction the wind comes from, the flame is always sheltered. You are not eliminating the wind. You are staying one step ahead of it.

In practical terms for quantum computing, this matters because it suggests a new class of runtime control strategy: rather than passively holding a quantum state and hoping it survives, actively manage its orientation in operator space to reduce how efficiently the environment can couple to it. This is not quantum error correction in the traditional sense — it does not preserve arbitrary encoded information indefinitely. But it is a meaningful and measurable improvement in the survival of structured quantum states on real hardware, achieved with very low overhead, using only single-qubit rotation gates applied between delay segments.

Why this matters for the field:

Dynamical decoupling — applying carefully timed pulses to individual qubits to average out low-frequency noise — is already a standard technique in quantum computing. What this experiment demonstrates is a stabilizer-level analogue: instead of decoupling individual qubit phases, we are rotating the orientation of a multi-qubit stabilizer observable in a way that averages out how the noise couples to that structured state. The two techniques operate at different levels of abstraction and are complementary rather than competitive. Dynamical decoupling works on individual qubits. Dynamic stabilizer-frame rotation works on the geometric structure of the multi-qubit observable itself.

Whether the underlying mechanism is purely noise averaging, reduced coupling to vulnerable orientations, coherent-error cancellation, or some combination of these, the phenomenological result is clear: the combination of rotation and refresh preserves protected-plane fidelity better than static hold on current IBM Heron r3 hardware.

Abstract

We report a dynamic stabilizer-frame rotation experiment on IBM Kingston (ibm_kingston, Heron r3, 156 qubits, heavy-hex topology), demonstrating that continuous rotation of the Z⊗Y⊗Z stabilizer frame during a fixed 15-microsecond hold period, combined with midpoint refresh, improves measured plane fidelity relative to static passive hold. Two independent hardware runs were conducted on April 25, 2026, covering rotation step counts N in {2, 4, 6, 8} at rotation angle α = π/2 per step, using a 3-qubit module [13, 14, 15] selected for its established performance in prior QuantaCore records.

The Z⊗Y⊗Z stabilizer state is prepared using the proprietary stabilizer preparation sequence used throughout the QuantaCore program, adapted for the 3-qubit chain geometry. The state satisfies ⟨ZYZ⟩ = -1.000 exactly in noiseless simulation, representing a perfect stabilizer eigenstate on the linear chain. The rotation generator is a single-qubit gate applied to the middle qubit, which rotates the stabilizer frame continuously within the protected plane.

The plane-projection fidelity F = √(⟨ZYZ⟩² + ⟨ZXZ⟩²) is used as the primary figure of merit. This metric is invariant to the current orientation of the stabilizer within the plane, measuring only whether the state has remained inside the protected plane regardless of how far it has been rotated. It tracks preservation within the protected plane, not preservation of arbitrary logical information.

Three conditions were compared:

• C1: Static passive hold — prepare Z⊗Y⊗Z state, insert 15 µs delay, measure
• C2: Dynamic rotation without refresh — prepare state, apply N rotation steps distributed across the hold period, measure
• C3: Dynamic rotation with midpoint refresh — first half with rotation steps, full reset and re-preparation at 7.5 µs, second half with rotation steps, measure

Key results across both runs:

C3 (rotation + refresh) exceeded the static C1 baseline in every tested configuration across both runs. C2 (rotation without refresh) produced smaller and inconsistent gains, indicating that the performance advantage arises from the combination of frame motion and re-injection rather than from rotation alone.

The shift in C1 baseline between runs (0.7821 in Run 1, 0.7182 in Run 2) is acknowledged and reflects normal day-to-day variation in IBM Kingston calibration. Within-run comparisons are the primary basis for claims. Cross-run directional consistency provides additional support but is stated conservatively.

Interpretation: The results are consistent with a stabilizer-level analogue of dynamical decoupling, in which continuous rotation of the protected-plane orientation prevents low-frequency noise from accumulating coupling to a fixed stabilizer geometry. However, the mechanism is not yet uniquely established. Alternative explanations including orientation-dependent noise coupling, coherent-error averaging, and pulse-sequence artifacts cannot be ruled out without additional controlled experiments. The phenomenological result — that dynamic rotation combined with refresh outperforms static hold — is firmly established across both runs.

This record establishes the sixth stage of the QuantaCore experimental program and introduces dynamic stabilizer-frame rotation as a candidate runtime primitive for protected quantum state management on near-term superconducting hardware.

1. Experimental Background and Continuity

This record is the sixth in a sequence of connected QuantaCore experimental disclosures.

The first record (DOI 10.5281/zenodo.18498540, February 5, 2026) established the Y⊗Z parity-triangle consistency test and detected topology-dependent error correlations at 4.86σ significance on IBM Heron r2.

The second record (February 6, 2026) characterised non-Markovian environmental memory with a characteristic timescale of approximately 30 microseconds.

The third record (DOI 10.5281/zenodo.19478241, April 9, 2026) validated the basis migration method at 116-qubit scale on IBM Kingston with 89.39% average fidelity.

The fourth record (DOI 10.5281/zenodo.19501961, April 10, 2026) directly measured the protected-plane coherence lifetime as a function of hold time, establishing a high-fidelity window of approximately 15 microseconds and demonstrating a refresh advantage.

The fifth record (DOI 10.5281/zenodo.19697551, April 21, 2026) demonstrated that refresh-cadenced re-injection of the protected state extends controller-usable signal at 15 microseconds where static hold fails, introducing the concept of controller actionability as a hybrid-workflow metric.

The present record extends that program by demonstrating that combining frame rotation with refresh further improves plane fidelity beyond what refresh alone achieves. The 3-qubit Z⊗Y⊗Z stabilizer used here is the natural reduced form of the 4-qubit Y⊗Z stabilizer used in prior records, adapted for the linear chain geometry of qubits [13, 14, 15].

2. Experimental Design

2.1 Stabilizer State

The Z⊗Y⊗Z stabilizer state is prepared using a 10-gate sequence on 3 qubits, producing ⟨ZYZ⟩ = -1.000 exactly in noiseless simulation. This state is a perfect eigenstate of the Z⊗Y⊗Z Pauli operator and defines a protected geometric subspace designed to reduce exposure to the dominant Z-axis dephasing on IBM superconducting transmon hardware.

2.2 Rotation Generator

Rz(α) on qubit 1 (physical qubit 14, the middle qubit of the chain) is the correct rotation generator for this stabilizer, confirmed by exhaustive single- and multi-qubit rotation testing. It rotates ZYZ toward ZXZ within the protected plane while preserving plane-projection fidelity F exactly in noiseless simulation. The full cycle ZYZ → ZXZ → Z(-Y)Z → Z(-X)Z → ZYZ completes at total rotation of 2π.

2.3 Three Conditions

Three conditions were compared in the present experiment. The Record 5 static refresh result is used as an external reference point in the discussion section.

2.4 Figure of Merit

F = √(⟨ZYZ⟩² + ⟨ZXZ⟩²)

This is rotation-invariant within the protected plane. It measures whether the state has stayed inside the plane, not which direction it is currently pointing. This choice is deliberate: as the stabilizer frame rotates, the primary observable ⟨ZYZ⟩ oscillates between -1 and +1, while F remains near 1.0 if the state stays in the plane. F therefore cleanly separates plane-preservation (the quantity of interest) from frame orientation (the control variable).

2.5 Parameter Sweep

Run 1: α = π/4 and π/2, N = 2 and 4 Run 2: α = π/2, N = 6 and 8

All results reported here use α = π/2 for comparability. Run 1 also included α = π/4 results; these are available in the deposited JSON file.

2.6 Execution Configuration

• Backend: ibm_kingston (IBM Heron r3, 156 qubits)
• Module: physical qubits [13, 14, 15]
• Resilience level: 1 (TREX error mitigation)
• Twirling: Pauli gate and measure twirling (8 randomisations × 64 shots = 512 shots per circuit)
• Repetitions: 20 per condition (Run 1), 30 per condition (Run 2)
• Submission: single batch job per run
• Optimisation level: 1

3. Key Findings

3.1 Dynamic Rotation Combined with Refresh Consistently Outperforms Static Hold

C3 (dynamic rotation + midpoint refresh) exceeded the static C1 baseline in every tested configuration in both runs. This consistency across N = 2, 4, 6, 8 and across two independent hardware runs is the primary evidence that the effect is real and not a statistical fluctuation.

3.2 Rotation Without Refresh is Insufficient

C2 (dynamic rotation without refresh) produced smaller and inconsistent improvements relative to C1. In some configurations it underperformed the static baseline. This strongly indicates that rotation alone is not sufficient — the combination of frame motion and re-injection at the midpoint is required to realise the performance gain.

3.3 Larger Step Counts Show Stronger Performance at N=4 and N=8

The largest observed gains were at N = 4 (F = 0.8852, Run 1) and N = 8 (F = 0.8898, Run 2). N = 6 showed a smaller gain (F = 0.8467), creating a non-monotonic pattern. This is stated conservatively: the data support that larger step counts, particularly N = 4 and N = 8, produce the strongest improvements, but a clean monotonic scaling law is not claimed given the N = 6 dip and the baseline variation between runs.

3.4 The Rotation Signature is Visible in Component Data

The individual ⟨ZYZ⟩ and ⟨ZXZ⟩ expectation values show the stabilizer frame moving through the protected plane as N increases — ⟨ZYZ⟩ oscillates and ⟨ZXZ⟩ rises and falls in the expected pattern for a frame undergoing controlled rotation. This is direct evidence that the rotation gate sequence is functioning as designed on real hardware, not merely adding gate overhead.

3.5 Relation to Record 5 Static Refresh

Record 5 demonstrated that static refresh (reset + reprepare without rotation) improved controller-usable signal at 15 µs relative to passive hold. The present experiment demonstrates that adding dynamic frame rotation on top of refresh provides a further improvement. The best dynamic+refresh result is numerically slightly above the best static+refresh value reported in Record 5, though the differing module geometry and experiment structure mean this comparison should be treated as directional rather than direct. The overall pattern is consistent with dynamic rotation adding value beyond what refresh alone provides.

4. Interpretation and Scope

The moving-target intuition — that continuous frame rotation prevents noise from accumulating coupling to a fixed stabilizer orientation — is a plausible and elegant mechanism consistent with the data. It is analogous to dynamical decoupling at the individual-qubit level, extended here to the multi-qubit stabilizer geometry. However, this mechanism is not yet uniquely established by the present data.

The safe current claim is phenomenological:

Dynamic stabilizer-frame rotation combined with midpoint refresh improved measured plane fidelity at 15 µs relative to static hold in two independent hardware runs on IBM Kingston, with the largest observed gain reaching +23.9%.

Three controlled experiments would substantially strengthen the mechanism claim:

1. A matched comparison of static refresh vs dynamic+refresh in the same experimental run, eliminating baseline variation
2. A sham-rotation control with matched gate depth but no net frame rotation, testing whether the gain survives only for true frame rotation
3. A reverse-direction or phase-offset rotation control, testing whether cadence and orientation dependence match the moving-target prediction

These are planned as a follow-on record.

5. IP Statement

The Z⊗Y⊗Z stabilizer preparation sequence and the dynamic frame rotation protocol implemented in this experiment are protected under U.S. Patent Application No. 19/643,807 (filed April 10, 2026), which claims benefit of Provisional Application No. 63/952,786 (filed January 2, 2026). This dataset constitutes an early experimental demonstration of dynamic stabilizer-frame rotation as a runtime control primitive on IBM Kingston hardware. Implementation scripts are proprietary and are not included in this dataset.

6. Reproducibility and Verification

IBM Quantum job IDs:

• Run 1: d7mi2vraq2pc73a1nrdg — verifiable at https://quantum.ibm.com/jobs/d7mi2vraq2pc73a1nrdg
• Run 2: d7mi72lqrg3c738la2k0 — verifiable at https://quantum.ibm.com/jobs/d7mi72lqrg3c738la2k0

Files in this record:

• yz_dynamic_rotation_20260425_132001.json — Run 1 complete results: per-condition, per-rep raw expectation values for ⟨ZYZ⟩ and ⟨ZXZ⟩, computed F values, and sweep metadata for all tested α and N combinations
• yz_dynamic_rotation_20260425_132842.json — Run 2 complete results: same structure, α = π/2, N = 6 and 8
• yz_dynamic_rotation_combined.png — Four-panel figure: F vs N (main result), ΔF improvement chart, component evolution showing rotation signature, and summary table

7. Acknowledgements

IBM Quantum for hardware access and QPU credits on ibm_kingston.

© 2026 Amit Brahmbhatt, Quantum-Clarity LLC. Data: CC BY 4.0.