Qufid Advances Quantum Program Fidelity Estimation with Adaptive Measurement Budgets

Fidelity estimation presents a significant challenge in validating quantum programs on today’s noisy intermediate-scale quantum (NISQ) devices. Tingting Li, Ziming Zhao from Zhejiang University, and Jianwei Yin from Zhejiang University, alongside their colleagues, address this problem with a novel adaptive framework called QuFid. Their research introduces a method to dynamically determine the necessary measurement budget by analysing circuit structure and real-time statistical feedback, offering a substantial improvement over existing fixed or learning-based approaches. By modelling programs as directed acyclic graphs and incorporating backend-specific noise characteristics, QuFid provides a lightweight yet principled way to quantify circuit complexity and reduce measurement costs while maintaining accuracy , a crucial step towards reliable quantum computation.

Adaptive Noise-Aware Framework for Quantum Measurement Planning

Quantum computing exploits quantum-mechanical phenomena such as superposition and entanglement to enable advances in optimization (Urbanek, Nachman, and de Jong 2020; Ayanzadeh et al0.2023), simulation (Zhu et al0.2024; Xiang, Chen et al0.2017), and cryptography (Shor 1999; Xu et al0.2024a). These noise sources degrade computational accuracy and make reliable state evaluation inherently challenging, hindering practical deployment and necessitating careful device characterization prior to execution. Benchmarking techniques such as randomized benchmarking (RB) (Magesan, Gambetta, and Emerson 2012) and cross-entropy benchmarking (XEB) (Boixo et al0.2018) assess device performance through repeated circuit executions and statistical analysis (Sun et al0.2014).

In practice, however, the number of repetitions (shots) is typically chosen heuristically: insufficient shots lead to inaccurate fidelity estimates, while excessive shots waste scarce quantum resources. Recent efforts have explored fidelity prediction and reliability estimation using pre-characterized noise models or learning-based approaches (Tan et al0.2023; Wang et al0.2022b). While effective in controlled settings, these methods rely on prior knowledge of device-specific noise characteristics, which are often time-varying and difficult to obtain in real-world environments (Li et al0.2025c). As a result, there remains a pressing need for adaptive fidelity estimation strategies that can dynamically determine measurement budgets while accounting for both circuit structure and hardware-induced effects.

Through their investigation, researchers identify three fundamental challenges in determining the number of repetitions required for quantum benchmarking.(i) Noise heterogeneity. Quantum noise, including both Markovian and non-Markovian components (Breuer and Petruccione 2002), varies across devices and over time (Kandala et al0.2019), making static or universal repetition rules unreliable. (ii) Circuit-hardware discrepancy. During transpilation, qubit mapping, circuit rewriting, and optimization (McKay et al0.2018) reshape the circuit’s dependency structure and noise exposure (Li et al0.2025a).Existing approaches lack a unified way to quantify the resulting structural deformation and its impact on measurement reliability. (iii) Precision-latency trade-off.

Fidelity evaluation must balance statistical accuracy (e. g., for validation and verification) against rapid turnaround (e. g. ,0.2021). Fidelity estimation is modeled as a structure-aware analysis problem that connects circuit dependencies, noise propagation, and statistical convergence. This formulation induces a noise-propagation operator whose structural properties reflect the circuit’s intrinsic complexity after transpilation. Algorithm 1 details the adaptive fidelity measurement pipeline.

Circuit Structure and Noise Propagation Analysis are critical

The study meticulously constructs a DAG representation of quantum programs, where each node represents a gate and directed edges encode non-commutative control-flow dependencies induced by shared qubits. This allows explicit capture of execution-order constraints and inter-gate interactions, providing a unified abstraction for both logical circuit structure and error propagation. Experiments converted the Bernstein-Vazirani circuit into a DAG and then a MultiDi-Graph, with nodes storing gate parameters and edges encoding relationships, demonstrating the technique’s versatility. Transpilation’s impact is quantified using graph-level structural deformation metrics, ∆struct(G0, Gt) = {∆deg, ∆path, ∆conn}, measuring shifts in node degree, expansion of critical paths, and connectivity inflation, offering a backend-aware, noise-model-agnostic assessment.

A weighted adjacency matrix, A, incorporates structural deformation, with weights reflecting dependency strength modulated by factors like dependency expansion and connectivity inflation. The noise-propagation operator, P = D−1A, normalises outgoing dependencies, forming a row-stochastic transition matrix where Pij represents the probability of noise originating at gate vi influencing gate vj. Repeated application of P models a Markovian diffusion process, abstracting cumulative noise propagation across execution steps, a departure from simpler random walk approaches. Algorithm 1 summarises the adaptive measurement pipeline, beginning with DAG conversion and construction of structural deformation metrics. The adaptive batch size is calculated as P = C(G) · log(D), where C(G) is the spectral complexity and D is the depth of the transpiled circuit.,.

QuFid reduces measurement costs for quantum fidelity

Measurements confirm that this approach effectively links circuit structure, hardware-induced deformation, and measurement uncertainty within a unified framework. Results demonstrate that QuFid’s adaptive batch size, calculated as C(G) · log(D), where C(G) represents spectral complexity and D is the depth of the transpiled circuit, dynamically adjusts to the specific characteristics of each quantum computation. The algorithm iteratively executes measurements, accumulating data into a set T, and calculates the mean fidelity F and standard deviation σ. A confidence interval CI, defined as zα · σ / √|T|, is then used to determine convergence; the process halts when CI falls below a target error bound δ, ensuring statistically reliable results.

Tests prove that this confidence-driven early stopping mechanism minimises unnecessary resource consumption. Furthermore, the study details the construction of the quantum circuit graph, representing the program as a DAG where nodes correspond to quantum gates and edges encode control-flow dependencies. This DAG representation explicitly captures execution-order constraints and inter-gate interactions, providing a unified abstraction for both logical circuit structure and error propagation. The research team successfully converted a Bernstein-Vazirani circuit into a MultiDiGraph, demonstrating the framework’s ability to handle complex quantum algorithms and their associated dependencies. This work paves the way for more efficient and reliable quantum computations in the NISQ era.

QuFid adapts fidelity estimation via noise mapping

The authors acknowledge limitations in fully capturing long-range temporal correlations and suggest that incorporating localised deformation metrics could further enhance adaptivity. Future work may extend QuFid’s compatibility to other quantum frameworks, such as MindSpore Quantum, and explore multi-objective optimisation encompassing fidelity, latency, and energy consumption. This work represents a step towards more resource-efficient and interpretable methodologies for testing quantum programs. By integrating structural circuit analysis with runtime statistical guarantees, QuFid offers a balance between accuracy and efficiency, potentially easing the path towards practical quantum computation. The framework’s ability to dynamically adjust measurement budgets based on observed noise propagation is a key advancement in mitigating the challenges posed by current NISQ hardware.