AutoQuREO: A Framework for Automated Quantum Resource Estimation and Optimization

AutoQuREO is an automated framework for full-stack quantum resource estimation and optimization, introduced in this paper. The framework is designed to address key limitations in existing quantum resource estimation (QRE) approaches, which are described as largely compilation-heavy or domain-knowledge-guided symbolic annotations, and tightly coupled to long-term fault-tolerant assumptions, limiting their topical applicability.

The paper identifies four core novelties of AutoQuREO:

1. Full-stack flexibility (N1): AutoQuREO imposes no fixed notion of layers, architectures, or fault-tolerance assumptions. Instead, users define arbitrary stacks composed of modular layers.

2. Library for rapid prototyping (N2): The framework provides a library of composable code implementations (called modules) and models that allow users to instantiate end-to-end QRE pipelines with minimal boilerplate code.

3. Surrogate synthesis of resource models (N3): To overcome the scalability limits of compilation-based estimation and the domain-expertise requirement of symbolic annotation, AutoQuREO introduces surrogate synthesis for resource models.

4. Automated optimization (N4): Resource estimation is embedded within an optimization loop that supports multi-objective user-guided Pareto front analysis and downstream deployment.

The framework represents a quantum computing stack as an ordered collection of layers, each encapsulating a functional stage of running an end-to-end quantum solution. Each layer can have multiple implementations as either modules (compilable code that produces quantum circuits) or models (surrogate resource estimators). The framework uses an adapter design pattern for plug-and-play compatibility, with adapters characterized by metadata including cost (classical computational time) and confidence (closeness of resource estimate to actual resources).

A key technical contribution is the neuro-symbolic (NeSy) surrogate modeling approach, which combines neuro-evolution using augmented topologies (NEAT) with symbolic regression via PySR. The paper states: NEAT captures intricate empirical patterns, while PySR extracts structured representations that are formalizable and compositional. This enables scalable estimation that progressively replaces costly compilation-based ground-truth while remaining analytically explainable.

The framework also implements lifelong learning, where resource estimation data generated for each evaluated configuration are persistently retained and reused to improve surrogate models across the stack. This allows AutoQuREO to progressively replace expensive compilation-based estimation with efficient approximations.

The paper demonstrates AutoQuREO through three representative case studies:

Scenario I examines Trotterized Hamiltonian simulation of the transverse-field Ising model with error mitigation via zero-noise extrapolation (ZNE). The study finds that even at very low depolarizing error rates (e.g., 1×10−5), trivially increasing the Trotter order or the number of Trotter steps does not guarantee improved accuracy and that for every depolarizing error rate, there exists an optimal Trotter configuration that balances the algorithmic error and physical error. The results also show that ZNE's effectiveness depends strongly on the accumulated circuit error.

Scenario II covers three interconnected studies: (1) universal error correction using the Steane code with Reed-Muller T-teleportation, characterizing logical error rates (LER) and physical error rates (PER) across all-to-all and square connectivity topologies; (2) gate decomposition accuracy using GridSynth, where the paper derives an optimal decomposition accuracy model (ϵopt ≈ 2.28√p + 162.43p via PySR, compared to the analytical ϵopt ≈ 2.85√p); and (3) ground-state energy estimation of the Hydrazine molecule using iterative quantum phase estimation (iQPE), demonstrating that the optimal GridSynth accuracy achieves a consistent runtime reduction of approximately 85.7% for ep values ranging from 2 to 14 when extended to surface code implementations.

Scenario III studies QAOA applied to MaxCut with various mixer ansätze (Vanilla-X, Vanilla-Y, Multiangle-X, Grover, DCA-X), comparing superconducting and trapped-ion backends with different error mitigation strategies. Key findings include that multiangle-X ansätze consistently outperforms all other ansätze choices and that the impact of error mitigation on the outcome is dependent on other factors. The η2 effect size analysis shows that the largest impact is due to the QAOA type reflected in its η2 value of 0.9073.

The paper positions AutoQuREO as a general-purpose platform for advancing quantum technology readiness and a system-level digital twin for quantum computing stacks, designed to support improvement across NISQ, EFTQC, and FTQC regimes. Future work includes integration with emerging intermediate representations, GPU-accelerated QRE, active learning, and large language models for autoformalization.

Improvements to AI Systems Based on AutoQuREO

1. Neuro-Symbolic Surrogate Modeling for AI-Driven Resource Prediction

• Improvement: Integrate a dual-path architecture combining NEAT (neuro-evolution) with symbolic regression (e.g., PySR) into AI systems that estimate computational costs, latency, or energy consumption.

• Capability: The AI can learn complex empirical patterns from expensive simulations or real-world measurements, then distill them into formal, explainable equations (e.g., ϵ opt ≈ 2.28√p + 162.43p). This enables fast, accurate predictions without re-running costly ground-truth compilations, and allows users to inspect and validate the underlying logic.

2. Lifelong Learning with Persistent Data Reuse for Adaptive Optimization

• Improvement: Implement a memory-augmented learning loop where every evaluated configuration (input, output, cost, confidence) is stored and reused to continuously retrain surrogate models.

• Capability: The AI system improves its own predictive accuracy over time as it encounters more data, progressively replacing expensive evaluations with cheap approximations. This is ideal for iterative design tasks (e.g., circuit synthesis, hardware configuration) where the search space is vast and repeated evaluations are prohibitive.

3. Multi-Objective Pareto-Front Optimization with User-Guided Trade-offs

• Improvement: Embed resource estimation within a multi-objective optimizer that supports user-defined constraints (e.g., error rate vs. runtime vs. qubit count) and automatically generates Pareto-optimal solutions.

• Capability: The AI can explore trade-offs across conflicting goals, such as minimizing both algorithmic error and physical error in quantum circuits. It can present a set of non-dominated configurations, letting users select based on their priorities—useful for hardware-software co-design, cloud resource allocation, or autonomous system tuning.

4. Modular, Adapter-Based Stack Abstraction for Cross-Domain AI

• Improvement: Adopt a plug-and-play layer architecture where each functional stage (e.g., compilation, error mitigation, execution) has interchangeable modules or surrogate models, connected via adapters with metadata (cost, confidence).

• Capability: The AI can dynamically assemble arbitrary pipelines from reusable components, test different combinations (e.g., error correction code vs. connectivity topology) without rewriting code. This enables rapid prototyping and benchmarking across diverse hardware backends (superconducting, trapped-ion) and fault-tolerance regimes (NISQ, FTQC).

5. Data-Driven Optimal Configuration Discovery

• Improvement: Use the framework’s optimization loop to automatically identify optimal parameters (e.g., Trotter steps, GridSynth accuracy) for a given error rate, rather than relying on heuristics or manual tuning.

• Capability: The AI can discover non-trivial relationships—e.g., that increasing Trotter order does not always improve accuracy under noise—and recommend configuration sets that balance algorithmic and physical errors. This is directly applicable to autonomous experiment design, hyperparameter tuning in ML, or control of noisy physical systems.

6. Effect-Size Analysis for Feature Importance in AI Decision-Making

• Improvement: Incorporate statistical effect-size metrics (e.g., η2) into the AI’s evaluation loop to rank the influence of different factors (e.g., ansatz type, error mitigation strategy, backend).

• Capability: The AI can explain which design choices dominate outcomes (e.g., QAOA type with η2 = 0.9073) and ignore negligible factors, enabling more efficient search and clearer interpretability for human stakeholders. This is valuable for feature selection in predictive models and for prioritizing engineering efforts.

7. Cross-Regime Generalization via Stack-Agnostic Digital Twins

• Improvement: Train the AI on a unified stack representation that spans NISQ, early fault-tolerant (EFTQC), and fully fault-tolerant (FTQC) regimes, using the same modular layers and surrogates.

• Capability: The AI can transfer knowledge across technology readiness levels—e.g., using insights from noisy intermediate-scale experiments to predict performance of future fault-tolerant systems—reducing the need for separate models per hardware generation. This enables long-term strategic planning and investment decisions in quantum computing or other emerging technologies.

8. Automated Formalization and Symbolic Extraction for AI Explainability

• Improvement: Leverage the symbolic regression component to convert black-box AI predictions into closed-form expressions that can be formally verified and composed into larger models.

• Capability: The AI can provide auditable, human-readable justifications for its recommendations (e.g., optimal accuracy scales as 2.28√p), making it suitable for safety-critical applications where transparency is required, such as medical device calibration or autonomous vehicle resource management.