Circuit-Level vs Pulse-Level Quantum Hardware Diagnostics: K–R Scaling Exponent Detects Device Degradation Invisible to T₁/T₂ Calibration

Technical Summary: Circuit-Level vs. Pulse-Level Quantum Hardware Diagnostics

Problem Statement
Current standards for certifying the health of Quantum Processing Units (QPUs) rely almost exclusively on pulse-level metrics: coherence times $T_1$ (amplitude damping) and $T_2$ (dephasing). These are measured via single-qubit Rabi and Ramsey sequences on isolated qubits under idealized conditions. The paper argues that these metrics fail to capture critical failure modes in operational, multi-qubit environments. Specifically, $T_1$ and $T_2$ measurements do not account for:

1. Coherent errors from systematic gate miscalibration that accumulate super-linearly with circuit depth.
2. Crosstalk (e.g., ZZ coupling) between simultaneously operated qubits.
3. Context-dependent dephasing arising from gate compilation and connectivity constraints.
4. Temporal instability during actual algorithm execution.

Consequently, a device may appear "healthy" based on improved $T_1/T_2$ calibration while simultaneously suffering from catastrophic degradation in multi-qubit circuit performance. This creates a systematic gap between certified hardware quality and actual algorithmic reliability.

Methodology
The study utilizes the K–R framework, a low-cost diagnostic method that extracts a scaling exponent $\alpha$ from a three-parameter infidelity model:
$$C = C_0/K^\alpha + R$$
Where $C$ is measured infidelity, $K = 1/d$ is the inverse circuit depth (or qubit count), $C_0$ is correctable error amplitude, and $R$ is the noise floor. The exponent $\alpha$ classifies the noise regime:

• $\alpha > 1$: Structured, coherent error accumulation.
• $0.3 < \alpha < 1$: Stochastic, Markovian-like accumulation.
• $\alpha \to 0$: Saturated, SPAM-dominated noise.

Experiments were conducted on three 156-qubit IBM Heron r2 processors (ibm_kingston, ibm_fez, ibm_marrakesh) via IBM Quantum Open Plan. The methodology involved:

• 191 circuit executions across five experimental campaigns.
• Circuit Families: GHZ state preparation (scaling $n=2$ to $30$), Clifford mirror circuits (depth $d=1$ to $64$), noise amplification (gate folding), and Hahn echo sequences.
• Comparative Analysis: Directly contrasting K–R circuit-level metrics against IBM's reported pulse-level $T_1/T_2$ values on the same devices and dates.
• Drift Detection: Monitoring $\alpha$ across consecutive runs within single sessions to detect intra-session degradation.

Key Results

1. Divergent Health Indicators: On ibm_marrakesh between July 3 and July 5, 2026, IBM reported a 12% improvement in $T_2$ (from 303 $\mu$s to 340 $\mu$s). Conversely, circuit-level diagnostics showed a 171% increase in the K–R exponent $\alpha$ (from 1.406 to 3.811) and a 920% increase in GHZ ($n=2$) infidelity (from 0.018 to 0.204). While pulse-level metrics suggested improvement, circuit-level metrics indicated severe degradation into a coherent-error-dominated regime.
2. Circuit-Context vs. Pulse-Level $T_2$ Discrepancy: Ramsey measurements performed within a circuit context on ibm_marrakesh revealed $T_2$ values of 9–30 $\mu$s, compared to IBM's reported pulse-level $T_2$ of 32–340 $\mu$s. This represents a 3–11$\times$ discrepancy, attributed to ZZ crosstalk, gate compilation artifacts, and context-dependent frequency shifts invisible to isolated qubit calibration.
3. Real-Time Drift Detection: During a single session on July 5, the K–R exponent $\alpha$ increased monotonically from 2.99 to 3.78 across three consecutive runs. Single-point infidelity measurements failed to detect this drift, incorrectly classifying the device as "stable" (infidelity < 0.10), whereas K–R correctly identified the shift to an extreme coherent-error regime.
4. Theoretical Confirmation: The study provided the first hardware confirmation of the theoretical prediction $\alpha_{tw} + \alpha_{echo} = 2$ for 1/f noise. On ibm_marrakesh, the sum of the Clifford depth exponent and the echo circuit exponent was 2.1397, deviating by only 7% from the theoretical value of 2.0.
5. Device Fingerprinting: Despite identical 156-qubit Heron r2 architectures, the three tested devices exhibited distinct noise regimes (Structured vs. Stochastic) and drift characteristics, highlighting that noise profiles are specific to calibration history and environment, not just hardware design.

Significance and Claims
The paper establishes that circuit-level K–R diagnostics are a necessary complement to, not a replacement for, standard pulse-level calibration. The authors claim that relying solely on $T_1/T_2$ can lead to the deployment of algorithms on devices that are actively degrading or operating in a coherent-error regime unsuitable for standard mitigation techniques like Zero-Noise Extrapolation (ZNE).

Key contributions include:

• Operational Necessity: Demonstrating that a "healthy" $T_2$ certification does not guarantee circuit performance, necessitating pre-session K–R fingerprinting (approx. 13 circuits, 3 minutes) to determine the appropriate noise regime and mitigation strategy.
• Regime Classification: Providing a quantitative scalar ($\alpha$) that distinguishes between coherent and stochastic noise, enabling targeted error mitigation (e.g., dynamical decoupling for $\alpha > 1$ vs. ZNE for $0.3 < \alpha < 1$).
• Drift Sensitivity: Showing that K–R diagnostics can detect intra-session drift and regime shifts that single-point infidelity measurements miss, preventing the execution of unreliable long-duration jobs.

The paper concludes that for operational NISQ computing, the 13-circuit K–R fingerprint should become a standard pre-session check to ensure that hardware certification aligns with actual multi-qubit algorithmic performance.