A Fine-Grained and Efficient Reliability Analysis Framework for Noisy Quantum Circuits

TL;DR

This work introduces a Noise Proxy Circuit (NPC) and Proxy Fidelity to enable accurate, state-independent reliability evaluation of noisy quantum circuits without quantum execution or state tomography. By tracking noise channels (depolarizing, thermal relaxation, SPAM) through NPC and aggregating per-qubit reliabilities, the framework delivers fidelity-level estimates with linear-time scalability. Empirical results across BV, GHZ, and random circuits show Proxy Fidelity closely tracks true fidelity (AAD 0.031–0.069) while offering superior interpretability and robust ranking consistency over traditional metrics. The approach provides a practical, scalable foundation for reliability-aware quantum circuit design and optimization on NISQ devices.

Abstract

Evaluating the reliability of noisy quantum circuits is essential for implementing quantum algorithms on noisy quantum devices. However, current quantum hardware exhibits diverse noise mechanisms whose compounded effects make accurate and efficient reliability evaluation challenging. While state fidelity is the most faithful indicator of circuit reliability, it is experimentally and computationally prohibitive to obtain. Alternative metrics, although easier to compute, often fail to accurately reflect circuit reliability, lack universality across circuit types, or offer limited interpretability. To address these challenges, we propose a fine-grained, scalable, and interpretable framework for efficient and accurate reliability evaluation of noisy quantum circuits. Our approach performs a state-independent analysis to model how circuit reliability progressively degrades during execution. We introduce the Noise Proxy Circuit (NPC), which removes all logical operations while preserving the complete sequence of noise channels, thereby providing an abstraction of cumulative noise effects. Based on the NPC, we define Proxy Fidelity, a reliability metric that quantifies both qubit-level and circuit-level reliability. We further develop an analytical algorithm to estimate Proxy Fidelity under depolarizing, thermal relaxation, and readout error channels. The proposed framework achieves fidelity-level reliability estimation while remaining execution-free, scalable, and interpretable. Experimental results show that our method accurately estimates circuit fidelity, with an average absolute difference (AAD) ranging from 0.031 to 0.069 across diverse circuits and devices.

Figures (9)

• Figure 1: Overview of the proposed reliability evaluation framework. Given a noisy quantum circuit, a corresponding NPC is constructed by removing all logical gates while preserving the complete sequence of noise channels, including depolarizing, thermal relaxation, and SPAM errors. Using quantum hardware calibration data, the framework estimates each qubit’s reliability decay through successive noise channels in a state-independent and execution-free manner, and derives a set of qubit proxy fidelities $\{f_1, f_2, \ldots, f_n\}$. These qubit-level reliabilities are then aggregated into the circuit proxy fidelity $f = \prod_{i=1}^{n} f_i$.
• Figure 2: Schematic illustration of the qubit Noise Proxy Circuit. The qubit evolves from the initial state $\rho$ to $\rho'$ through depolarizing $\mathcal{D}(p)$, thermal relaxation $\mathcal{T}(t)$, and SPAM noise $\mathcal{R}(e)$ channels. The final proxy fidelity is computed according to Eq. \ref{['eq:qubit_fid']}.
• Figure 3: Relationship between qubit proxy fidelity and entanglement degree (negativity) under different noise channels. For both depolarizing (a) and thermal relaxation (b) noise, the entanglement degree decreases as noise strength increases, and the estimated qubit proxy fidelity decreases accordingly. The strong proportional relationship between the two confirms that the proxy fidelity effectively reflects noise-induced degradation of quantum correlations. The numerical procedure is provided in Appendix \ref{['app:fig_5']}.
• Figure 4: Illustration of circuit-level proxy fidelity evaluation. (a) Tracking reliability along logical qubit trajectories during circuit execution. (b) Qubit proxy fidelity decay across operations, compared with actual fidelity. (c) Decomposition of two-qubit noise channels into parallel single-qubit channels. (d) Modeling SWAP-induced noise via two channel sequences.
• Figure 5: Qubit-level fidelity estimation results. (a) Overall estimation accuracy across 3,276 readout qubits collected from 320 noisy circuit executions. The estimated proxy fidelities closely match the ground-truth fidelities, achieving an AAD of 0.036 and a coefficient of determination ($R^2$) of 0.94. (b) Fidelity degradation with circuit depth in two-qubit ID circuits. As the number of gate layers increases, both actual and estimated fidelities decrease consistently, demonstrating that the proposed method accurately captures cumulative noise effects. (c) Heterogeneous qubit reliability within a 5-qubit BV circuit. The estimated fidelities closely track per-qubit variations caused by different noise channels, confirming the method’s ability to capture structure-dependent noise accumulation.