Abstract We introduce the K–R scaling exponent α, extracted from the three-parameter cost decomposition C = C₀/Kᵅ + R, as a compact diagnostic descriptor of error-accumulation regimes on noisy intermediate-scale quantum (NISQ) hardware. Here, C is the measured circuit infidelity, K is a structural parameter (inverse depth or inverse qubit count), C₀ is the correctable error amplitude, R is the irreducible noise floor, and α quantifies the rate of error accumulation. Through three experimental campaigns totaling approximately 150 circuit executions on two 156-qubit IBM Quantum Heron r2 processors (ibm_kingston and ibm_fez), we observe three distinct scaling regimes: (i) structured scaling with super-linear α in GHZ circuits (α = 1.54–1.64, R² > 0.97) and noise amplification (α = 1.19, R² = 1.000), consistent with correlated multi-qubit errors; (ii) controlled stochastic scaling in Clifford depth and echo circuits (α ≈ 0.5–0.7, R² up to 0.998); and (iii) saturation where α → 0. We organize these results in an (α, R²) phase diagram—the first such empirical diagram for quantum hardware noise—and demonstrate that α serves as a low-cost diagnostic observable enabling regime identification, device fingerprinting, and stability monitoring using fewer than 13 circuits per device. An honest comparison shows that for depth extrapolation, exponential models outperform K–R; however, K–R uniquely provides regime-level insight and device-specific behavioral signatures not accessible from exponential decay rates. By reducing quantum hardware characterization to a small set of experimentally accessible scaling parameters, the K–R framework provides a practical bridge between low-cost benchmarking and physically interpretable noise diagnostics in the NISQ era.
Abstract We introduce the K–R scaling exponent α, extracted from the three-parameter cost decomposition C = C₀/Kᵅ + R, as a compact diagnostic descriptor of error-accumulation regimes on noisy intermediate-scale quantum (NISQ) hardware. Here, C is the measured circuit infidelity, K is a structural parameter (inverse depth or inverse qubit count), C₀ is the correctable error amplitude, R is the irreducible noise floor, and α quantifies the rate of error accumulation. Through three experimental campaigns totaling approximately 150 circuit executions on two 156-qubit IBM Quantum Heron r2 processors (ibm_kingston and ibm_fez), we observe three distinct scaling regimes: (i) structured scaling with super-linear α in GHZ circuits (α = 1.54–1.64, R² > 0.97) and noise amplification (α = 1.19, R² = 1.000), consistent with correlated multi-qubit errors; (ii) controlled stochastic scaling in Clifford depth and echo circuits (α ≈ 0.5–0.7, R² up to 0.998); and (iii) saturation where α → 0. We organize these results in an (α, R²) phase diagram—the first such empirical diagram for quantum hardware noise—and demonstrate that α serves as a low-cost diagnostic observable enabling regime identification, device fingerprinting, and stability monitoring using fewer than 13 circuits per device. An honest comparison shows that for depth extrapolation, exponential models outperform K–R; however, K–R uniquely provides regime-level insight and device-specific behavioral signatures not accessible from exponential decay rates. By reducing quantum hardware characterization to a small set of experimentally accessible scaling parameters, the K–R framework provides a practical bridge between low-cost benchmarking and physically interpretable noise diagnostics in the NISQ era.
Pulse-level calibration metrics — coherence times T₁ and T₂ measured through single-qubit Rabi and Ramsey sequences — are the standard by which quantum hardware providers certify device health. We demonstrate, through 191 circuit executions on three 156-qubit IBM Heron r2 processors (ibm_kingston, ibm_fez, and ibm_marrakesh), that these pulse-level metrics can give opposite conclusions to circuit-level diagnostics on the same device at the same time. Specifically, between experimental sessions on July 3 and July 5, 2026, IBM reported ibm_marrakesh T₂ improved from 303 μs to 340 μs (a 12% improvement), while the K–R scaling exponent α measured from GHZ circuit scaling increased from 1.406 to 3.811 (a 171% increase in coherent error dominance) and GHZ n=2 infidelity rose from 0.018 to 0.204 — a 920% increase in circuit error. We further demonstrate that Ramsey circuit-context T₂ on qubit 0 is approximately 9–30 μs, compared to IBM-reported pulse-level T₂ of 32–340 μs — a discrepancy of 3–11×. We introduce five experimental demonstrations showing K–R circuit-level diagnostics detect degradation invisible to T₁/T₂, provide higher temporal sensitivity, enable algorithm failure prediction, and confirm the theoretical prediction αₜᵥₜᶜʰ + αₑₜₕₒ = 2 within 7% on real hardware. These findings establish circuit-level K–R diagnostics as a necessary complement to pulse-level calibration for operational quantum computing.
The K–R scaling exponent α, extracted from the three-parameter model C = C₀/Kᵅ + R, was recently validated as a low-cost diagnostic for NISQ noise regimes on IBM Quantum hardware (under peer review, IEEE TQE, ID: TQE-26-04-REG-0175). The present paper looks beyond benchmarking to identify five high-potential future directions where α could provide unique diagnostic value: (1) quantum error correction, where α may serve as an early warning indicator before logical failure; (2) real-time hardware stability monitoring, where a daily 13-circuit α(t) curve replaces tracking dozens of calibration parameters; (3) cryogenic component testing, where Δα before/after component swap quantifies improvement; (4) quantum networking, where α may distinguish channel noise from memory decoherence in entanglement distribution; and (5) variational quantum algorithms, where regime transitions in α may predict barren plateau onset and trainability collapse. For each direction, we present the scientific hypothesis, the proposed experimental protocol, expected outcomes, target metrics, and recommended target journals. This roadmap is intended to establish research priority, invite collaboration, and provide a concrete plan for extending the K–R framework from a benchmarking tool into a general-purpose quantum diagnostic platform.
Abstract Pulse-level calibration metrics — coherence times T₁ and T₂ measured through single-qubit Rabi and Ramsey sequences — are the standard by which quantum hardware providers certify device health. We demonstrate, through 191 circuit executions on three 156-qubit IBM Heron r2 processors (ibm_kingston, ibm_fez, and ibm_marrakesh), that these pulse-level metrics can give opposite conclusions to circuit-level diagnostics on the same device at the same time. Specifically, between experimental sessions on July 3 and July 5, 2026, IBM reported ibm_marrakesh T₂ improved from 303 µs to 340 µs (a 12% improvement), while the K–R scaling exponent α measured from GHZ circuit scaling increased from 1.406 to 3.811 (a 171% increase in coherent error dominance) and GHZ n = 2 infidelity rose from 0.018 to 0.204 — a 920% increase in circuit error. We further demonstrate that Ramsey circuit-context T₂ on qubit 0 is approximately 9–30 µs, compared to IBM-reported pulse-level T₂ of 32–340 µs — a discrepancy of 3–11×. We introduce five experimental demonstrations showing K–R circuit-level diagnostics detect degradation invisible to T₁/T₂, provide higher temporal sensitivity, enable algorithm failure prediction, and confirm the theoretical prediction αₜ v ₜᶜʰ + αₑₜₕₒ = 2 within 7% on real hardware. These findings establish circuit-level K–R diagnostics as a necessary complement to pulse-level calibration for operational quantum computing.
Standard device characterization protocols, such as Randomized Benchmarking (RB), typically report averaged, independent error rates per qubit. However, these methods are largely blind to correlated errors between neighbouring qubits: errors that fundamentally break the independent and identically distributed (i.i.d.) noise assumptions relied upon by most quantum error correction (QEC) decoders and error mitigation strategies. In this paper, we present a measurement approach using parity-circuit canaries to estimate pairwise error correlations on noisy intermediate-scale quantum (NISQ) devices. By applying spectral kernel analysis to the resulting correlation matrices, we can quantitatively assess the validity of the independent error assumption. We first validate our approach by emulating the canary protocol on publicly available surface code data from IBM Quantum hardware (ibm_fez). We then extend this proof-of-concept with directly measured, purpose-built canary circuits executed on the same backend, reproduced across independent sessions, controlled for physical adjacency and measurement batching, and shown to be inconsistent with pure estimation noise. The direct measurements confirm a significant, structural spectral violation that is not explained by neighbour-to-neighbour crosstalk alone, is present between arbitrary, chip-wide qubit pairs rather than a specific subset, and reproduces on a second, independent Heron r2 device (ibm_kingston), pointing to a mechanism inherent to the architecture rather than one installation. A three-condition diagnostic further localizes the effect specifically to the two-qubit entangling gate, showing no significant deviation from independence in isolated readout or in simultaneous single-qubit control pulses alone, and a targeted test rules out a simple, load-dependent shared-coupler-electronics mechanism. A circuit-depth scan using repeated entangling gates argues against simple depth-accumulation as the source of the larger violation seen in the original emulated proof-of-concept. Replacing the fixed entangling gate with a continuously parameterized controlled rotation shows that the correlation strength scales with the degree of entanglement produced, not merely with the entangling gate's presence, a relationship that reproduces in direction across three independent Heron r2 devices while varying substantially in absolute magnitude between them. The results also reveal a previously unreported dependence of the excess correlation on the instantaneous marginal error rate, underscoring the need for correlation-aware, dynamically calibrated diagnostics in fault-tolerant quantum computing.
We present the first experimental demonstration that quantum noise is informative, not merely destructive — validating Theorem 8 of IIT 5.1 (FEP-MaxCal Bridge). Using a 5-qubit GHZ circuit on an AerSimulator calibrated with real IBM Quantum ibm_fez noise parameters (T1=320µs, T2=150µs, gate2q error=2.83e-3), we show that Zero Noise Extrapolation (ZNE) recovers integrated information (Φ) to a value exceeding the noiseless ideal: Φ_ZNE = 1.1736 > Φ_ideal = 0.9999 (permutation test, p < 0.000001, N=20 runs, 8192 shots each, 10000 bootstrap resamples). ZNE requires controlled noise scaling (identity folding at λ = 1, 2, 3) that is only feasible in simulation; however, the noise model is calibrated from 3766 real IBM Quantum jobs across 6 backends, and prior hardware experiments on ibm_fez (V1: Φ=0.757, V2: Φ=0.832 with ZNE on real hardware) validate the baseline metrics. The experiment follows a four-phase paradigm: (1) Baseline: GHZ-5 ideal yields Φ=0.9999; (2) Attack: NISQ noise degrades Φ to 0.8804 (-12%); (3) Recovery: Hahn Echo alone shows no significant improvement (p=0.853), but ZNE with 3-scale identity folding and linear extrapolation to noise=0 yields Φ=1.1736; (4) Antifragility: the recovered system exceeds the original baseline by +17.4%. Additional findings: Φ scales monotonically with qubit count (2q→7q), distinguishes entanglement topology (GHZ > W-state > Cluster ≈ Separable), is robust across 4 IBM backend noise models (CV=3.35%), and decays exponentially with circuit depth (τ=29.52 layers). Hardware validation on real ibm_fez confirms Φ for entangled vs separable circuits with Cohen's d = 191.3 (p < 0.0001).
Distilling precise estimates from noisy intermediate scale quantum (NISQ) data has recently attracted considerable attention Kandala et al., Nature (London) 567, 491 (2019). In order to augment digital qubit metrics, such as gate fidelity, we discuss analog error mitigability, i.e., the ability to accurately distill precise observable estimates, as a hybrid quantum classical computing benchmarking task. Specifically, using Rabi oscillations as a test program, we characterize single qubit error rates on IBM's Poughkeepsie superconducting quantum hardware, incorporate control-mediated noise dependence into a generalized rescaling protocol, and analyze how noise characteristics influence Richardson extrapolation-based error mitigation. Our results identify regions in the space of Hamiltonian control fields and circuit depth which are most amenable to reliable noise extrapolation, as well as shed light on how low-level hardware characterization can be used as a predictive tool for uncertainty quantification in error-mitigated NISQ computations.