Stabilizer-Frame Refresh on IBM Kingston: A Delay Sweep with Matched Controls

Author: Amit Brahmbhatt Organisation: Quantum-Clarity LLC Date: April 25, 2026 IBM Job IDs — Primary Sweep (single batch):

• d7mmcd3aq2pc73a1slp0 (all 6 delays, C1 vs C3)

IBM Job IDs — Control Run (per-delay jobs):

• tau=0 µs: d7mngeat99kc73d2o760
• tau=10 µs: d7mnhkdqrg3c738lg3q0
• tau=15 µs: d7mni9baq2pc73a1ts5g
• tau=20 µs: d7mniq3aq2pc73a1tsl0
• tau=25 µs: d7mnjbat99kc73d2oa20
• tau=30 µs: d7mnjs5qrg3c738lg63g

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)
• DOI 10.5281/zenodo.19774443 (April 25, 2026)

Plain Language Summary

What we set out to test:

The previous record in this series (Record 6, April 25, 2026) showed that dynamically rotating the Z⊗Y⊗Z stabilizer frame during a hold period — continuously shifting its geometric orientation using small rotation gates — combined with a midpoint refresh, improved measured plane fidelity at 15 microseconds compared to static passive hold. The intuition was compelling: if the stabilizer frame keeps moving, the noise cannot efficiently couple to a fixed target. The result was promising.

But promising results require controls.

This record extends that work in two ways. First, it sweeps the full delay range from 0 to 30 microseconds to understand how the effect evolves over time — not just at a single time point. Second, and more importantly, it adds a matched control condition: static refresh without rotation. This control is essential because it separates the contribution of the rotation from the contribution of the refresh. Without it, any improvement attributed to dynamic rotation could equally be explained by the refresh alone.

What the data showed:

The primary sweep confirmed that dynamic rotation combined with refresh substantially outperforms static passive hold at every tested delay from 0 to 30 microseconds. Under a strict actionability threshold of F > 0.6, static hold becomes non-actionable by 15 microseconds. Dynamic rotation with refresh remains above that threshold through 30 microseconds.

The control run then asked the harder question: does rotation add value beyond refresh alone? The answer, on this hardware with these parameters, is no. Static refresh without rotation performs at least as well as dynamic rotation with refresh at nearly every delay point. At tau = 25 microseconds, static refresh actually outperforms the dynamic rotation condition.

What this means:

The good news is real and substantial. Midpoint reset-and-reprepare of the Z⊗Y⊗Z stabilizer — refreshing the protected state before it fully degrades — preserves controller-usable signal across the full 0 to 30 microsecond sweep where static passive hold fails by 15 microseconds. That is the validated runtime primitive. It is meaningful, it is hardware-verified across multiple records, and it operates at the multi-qubit stabilizer geometry level — above the individual qubit gate layer — in a way that differs from standard single-qubit dynamical decoupling approaches.

The rotation hypothesis was a good scientific idea. This experiment tested it properly. The control run showed that for this metric, this module, and these parameters, the rotation does not independently extend performance beyond what refresh alone achieves. That is not a failure — it is science working correctly. Knowing what does not drive the effect is as important as knowing what does.

Why the refresh result still matters:

Dynamical decoupling — flipping individual qubits periodically to average out low-frequency noise — is a standard technique in quantum computing. What this record demonstrates is something at a different level of abstraction: periodically reinitialising the full multi-qubit stabilizer geometry, not just correcting individual qubit phases, substantially extends the lifetime of a structured quantum observable on real hardware. The two approaches are complementary, not equivalent. The stabilizer-frame refresh primitive is a new operational tool at the multi-qubit level that has not been demonstrated in published IBM or Google control frameworks.

A note on dynamic rotation:

The dynamic rotation idea — rotating the stabilizer frame continuously to stay ahead of directional noise coupling — remains a scientifically interesting hypothesis. The current result says it does not add independent value in this implementation with this plane-projection fidelity metric. A different metric, a different parameter regime, a different delay window, or a phase-sensitive observable rather than the rotation-invariant F might reveal a rotation-specific advantage. This is explicitly parked as a direction for future investigation. The negative control result does not close the door on the idea — it refines the conditions under which it would need to be demonstrated.

Abstract

We report a two-part hardware experiment on IBM Kingston (ibm_kingston, Heron r3, 156 qubits, heavy-hex topology), module [13, 14, 15], characterising the performance of Z⊗Y⊗Z stabilizer refresh protocols across a 0–30 µs delay sweep with matched controls.

Part 1 — Primary Sweep: Three conditions (C1 static hold, C3 dynamic rotation + refresh) were compared across six delay points (0, 10, 15, 20, 25, 30 µs) with fixed parameters α = π/2, N = 8. Dynamic rotation with refresh outperformed static hold at all six delay points. Under an actionability threshold of F > 0.6, static hold becomes non-actionable at tau = 15 µs, while dynamic rotation with refresh remains above threshold through tau = 30 µs.

Part 2 — Control Run: Three conditions (C1 static hold, C2 static refresh only, C3 dynamic rotation + refresh) were compared across the same six delay points. C2 (static refresh without rotation) outperformed C1 (static hold) at 5/6 delays. C3 (dynamic rotation + refresh) did not consistently outperform C2 (static refresh only). At tau = 25 µs, C2 achieved F = 0.709 versus C3's F = 0.549.

Combined interpretation: Midpoint refresh and reprepare of the Z⊗Y⊗Z stabilizer state is the dominant mechanism extending controller-actionable signal lifetime. Dynamic frame rotation does not add independent value beyond refresh alone in this implementation. The validated runtime primitive is stabilizer-frame refresh — not rotation.

Primary result table (Control Run):

tau (µs)	C1 static F	C2 refresh F	C3 dynamic F	C3>C2	C2>C1
0	1.007	0.993	1.007	✓	✗
10	0.602	0.892	0.747	✗	✓
15	0.490	0.659	0.661	✗	✓
20	0.390	0.617	0.604	✗	✓
25	0.440	0.709	0.549	✗	✓
30	0.374	0.651	0.649	✗	✓

Actionability (F > 0.6) — Control Run:

tau (µs)	C1	C2	C3
0	✓	✓	✓
10	✓	✓	✓
15	✗	✓	✓
20	✗	✓	✓
25	✗	✓	✗
30	✗	✓	✓

The tau = 0 point serves as a near-ideal reference and is not interpreted as part of the delayed-runtime regime. C2 (static refresh) remains actionable at F > 0.6 at every tested delay. C1 (static hold) fails by 15 µs. C3 (dynamic rotation + refresh) mostly matches C2 but with one failure at 25 µs.

This record constitutes the seventh stage of the QuantaCore experimental program and establishes stabilizer-frame refresh as the validated mechanism for extending protected observable lifetime on near-term superconducting hardware.

 

1. Experimental Background and Continuity

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

Records 1 and 2 (February 2026) established the Y⊗Z parity-triangle consistency test and non-Markovian error dynamics on IBM Heron r2, with topology-dependent correlations at 4.86σ significance and a characteristic environmental memory timescale of approximately 30 microseconds.

Record 3 (April 9, 2026, DOI 10.5281/zenodo.19478241) validated the basis migration method at 116-qubit scale on IBM Kingston with 89.39% average fidelity.

Record 4 (April 10, 2026, DOI 10.5281/zenodo.19501961) characterised the protected-plane coherence lifetime as a function of hold time, establishing a high-fidelity window of approximately 15 microseconds and a refresh advantage where reset-and-reprepare outperformed passive hold across the 2–50 µs window.

Record 5 (April 21, 2026, DOI 10.5281/zenodo.19697551) demonstrated stabilizer refresh as a hybrid-workflow primitive, showing that midpoint re-injection preserves controller-actionable signal at 15 µs where passive hold fails.

Record 6 (April 25, 2026, DOI 10.5281/zenodo.19774443) introduced dynamic stabilizer-frame rotation combined with refresh, showing apparent improvement over static hold in two independent hardware runs. However, Record 6 did not include a static-refresh-only control condition — a limitation explicitly noted in that record's Section 4 as planned follow-on work.

The present record fulfils that commitment. It adds the static-refresh-only control and sweeps the full 0–30 µs delay range, allowing clean isolation of the refresh contribution from the rotation contribution.

2. Experimental Design

2.1 Stabilizer State

The Z⊗Y⊗Z stabilizer state is prepared using the proprietary stabilizer preparation sequence used throughout the QuantaCore program, producing ⟨ZYZ⟩ = -1.000 exactly in noiseless simulation. Protected under U.S. Patent Application No. 19/643,807.

2.2 Three Conditions

Condition	Description	Purpose
C1	Static passive hold — prepare, delay tau, measure	Baseline
C2	Static refresh only — prepare, delay tau/2, reset + reprepare, delay tau/2, measure	Control: isolates refresh contribution
C3	Dynamic rotation + refresh — same as C2 but with Rz(π/2) rotation steps on middle qubit during each delay segment	Test: isolates rotation contribution

C2 and C3 use identical segmented delay structures — the same number of delay segments with the same segment duration. The only difference between them is the presence or absence of rotation gates. This makes the comparison between C2 and C3 a clean isolation of the rotation contribution.

2.3 Figure of Merit

F = √(⟨ZYZ⟩² + ⟨ZXZ⟩²)

Rotation-invariant plane-projection fidelity. Tracks preservation within the protected plane, not preservation of arbitrary logical information. As the stabilizer frame rotates, ⟨ZYZ⟩ cycles between -1 and +1 while F remains near 1.0 if the state stays in the plane.

2.4 Actionability Thresholds

Two thresholds are used as secondary metrics:

• F > 0.5 — minimum usable signal for controller action
• F > 0.6 — strict threshold; cleaner separation between conditions

2.5 Delay Sweep

0, 10, 15, 20, 25, 30 µs — selected to span the high-fidelity window and the non-Markovian revival region established in Records 2 and 4. The 0 µs point establishes the baseline. The 15 µs point is the actionability crossover from Record 5.

2.6 Execution Configuration

Primary Sweep:

• Single batch job, 720 PUBs (C1 and C3 only)
• 30 reps per condition per delay

Control Run:

• Six jobs, one per delay point, 180 PUBs each
• Per-delay batching used to avoid IBM internal compiler error 6053, which triggers on large heterogeneous batches with mixed circuit depths on Heron r3
• 30 reps per condition per delay

Both runs:

• Backend: ibm_kingston (IBM Heron r3, 156 qubits)
• Resilience level: 1 (TREX error mitigation)
• Twirling: Pauli gate and measure twirling (8 randomisations × 64 shots = 512 shots per circuit)
• Optimisation level: 1

3. Key Findings

3.1 Static Hold is the Worst Performing Condition

C1 (static passive hold) degrades consistently across all delays, falling below F = 0.5 by tau = 30 µs and below F = 0.6 by tau = 15 µs. This is consistent with Records 4 and 5.

3.2 Refresh is the Dominant Mechanism

C2 (static refresh without rotation) outperforms C1 at 5/6 delay points in the control run, with the improvement growing substantially in the delayed regime. This confirms that midpoint reset-and-reprepare is a highly effective strategy for extending stabilizer lifetime — the dominant mechanism in the C3 results seen in Records 6 and the primary sweep.

3.3 Dynamic Rotation Does Not Add Independent Value in This Implementation

C3 (dynamic rotation + refresh) does not consistently outperform C2 (static refresh without rotation). C3 beats C2 at only 1/6 delay points (tau = 0, where both are near 1.0 and the margin is within noise). At the scientifically important delayed regime (tau = 10–30 µs), C3 does not outperform C2 and at tau = 25 µs is substantially worse (0.549 vs 0.709).

This result revises the interpretation of Record 6. The improvement over static hold seen in Records 6 and the primary sweep is attributable primarily to the midpoint refresh, not to the dynamic frame rotation. The rotation-specific claim — that continuously shifting the stabilizer frame orientation reduces noise coupling — is not established by these data for this metric and parameter set.

3.4 Stabilizer-Frame Refresh as a Validated Runtime Primitive

The primary positive result is the performance of C2 (static refresh only):

• Remains above F = 0.6 at every tested delay from 0 to 30 µs
• Remains above F = 0.5 at every tested delay from 0 to 30 µs
• Compared to C1, which falls below F = 0.6 at 15 µs and below F = 0.5 at 25 µs

This establishes midpoint stabilizer-frame refresh as a validated runtime primitive on IBM Kingston. The refresh operates at the multi-qubit stabilizer geometry level — periodically reinitialising the full protected Z⊗Y⊗Z observable structure rather than correcting individual qubit phases — and provides a different form of coherence management from standard single-qubit dynamical decoupling.

3.5 The Non-Markovian Region

At tau = 25 µs — where Records 2 and 4 identified non-Markovian environmental memory effects — C2 achieves its highest relative advantage over C3 (0.709 vs 0.549). This dip in C3 performance in the non-Markovian region, while C2 maintains high fidelity, may reflect an interaction between the rotation gate sequence and the environmental memory timescale. This is reported as an empirical observation rather than a mechanism claim.

4. Relationship to Record 6 and Future Directions

Record 6 introduced dynamic stabilizer-frame rotation as a candidate runtime primitive and showed improvement over static hold in two independent hardware runs. That record explicitly committed to a matched control run as planned follow-on work. The present record fulfils that commitment.

The control result does not invalidate Record 6 — the results in that record are accurately reported. It refines the interpretation: the benefit observed in Record 6 is attributable primarily to the midpoint refresh rather than to the frame rotation.

The dynamic rotation hypothesis — that continuously cycling the stabilizer frame orientation reduces noise coupling in a stabilizer-level analogue of dynamical decoupling — remains scientifically interesting and is explicitly parked for future investigation. The current negative result applies specifically to:

• The plane-projection fidelity metric F = √(⟨ZYZ⟩² + ⟨ZXZ⟩²), which is rotation-invariant by construction
• The specific module [13, 14, 15] on IBM Kingston
• The parameter regime α = π/2, N = 8
• The midpoint-refresh cadence

Future experiments that might isolate a rotation-specific advantage include: a phase-sensitive observable that tracks frame orientation rather than plane norm; a sham-rotation control with matched circuit depth but no net frame displacement; a reverse-direction rotation control; and parameter regimes beyond those tested here. These are left for a subsequent record.

5. IP Statement

The Z⊗Y⊗Z stabilizer preparation sequence and the stabilizer-frame refresh 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 experimental characterisation of the stabilizer-frame refresh mechanism and its comparison with dynamic rotation across a full delay sweep. Implementation scripts are proprietary and are not included in this dataset.

6. Reproducibility and Verification

All IBM Quantum job IDs listed above are publicly verifiable through IBM Quantum job records.

Files in this record:

• yz_delay_sweep_20260425_181443.json — Primary sweep raw results: per-condition, per-rep expectation values for ⟨ZYZ⟩ and ⟨ZXZ⟩, computed F values, and actionability classifications across all six delay points for C1 and C3
• yz_control_run_20260425_193633.json — Control run raw results: same structure for all three conditions C1, C2, C3 across all six delay points with per-delay job IDs
• yz_delay_sweep_simulation_20260425_160730.json — Classical noise simulation results using Kingston Markovian noise model, provided as pre-experiment preview showing directional consistency with hardware results

7. Acknowledgements

IBM Quantum for hardware access and QPU credits on ibm_kingston.

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