Hybrid Quantum Program Evaluation Framework

• HQPEF is a modular, metrics-driven framework that enables the evaluation and optimization of quantum-classical hybrid workflows.
• It integrates language abstractions, multi-layer compilation passes, and cross-platform benchmarking to support scalable, reproducible hybrid computations.
• The framework employs detailed performance metrics and real-time audits, facilitating robust error mitigation and workflow optimization in HPC environments.

A Hybrid Quantum Program Evaluation Framework (HQPEF) is a modular, metrics-driven system designed to enable, optimize, and validate the execution of quantum-classical hybrid workflows in scientific and high-performance computing environments. Contemporary HQPEF implementations integrate language and hardware abstraction, extensible compiler stacks, workflow-aware metrics, and cross-platform benchmarking, facilitating robust programming, optimization, and evaluation of hybrid quantum algorithms across diverse architectures. At their core, HQPEFs instantiate layered abstractions—kernel authoring, compilation to intermediate representations, device-aware transformation passes, integrated execution management, and real-time performance audits—to support reproducible and scalable hybrid computations (McCaskey et al., 2018, Remme et al., 19 May 2025, Osei et al., 23 Nov 2025).

1. Architectural Foundations and Core Abstractions

HQPEF architectures systematically extend classical accelerator frameworks (e.g., CUDA, OpenCL) to hybrid quantum settings by introducing abstractions and workflows specific to quantum program integration and evaluation. The canonical HQPEF design consists of:

• Frontends and Language Plugins: HQPEF frontends support domain-specific languages (DSLs) and quantum-language plugins (e.g., Scaffold, Quil, chemistry DSLs), each conforming to a standardized Compiler interface that emits quantum kernels recognizable by the framework.
• Intermediate Representation (IR): The IR comprises in-memory trees of Instruction objects—encompassing quantum gates, measurements, barriers—and supports multiple views: on-disk serialization (binary/human-readable), and control-flow or circuit-style directed acyclic graphs (DAGs).
• Compiler Passes: HQPEF compilers are structured into interoperable passes:
  1. Preprocessors: Device-aware and error-mitigation transformations.
  2. Optimizers: Algebraic simplification and gate cancellation routines.
  3. Transformations: Qubit mapping, SWAP insertion, and routing.
  4. Mapping Passes: Target-specific lowering to quantum machine instructions (QMI).

• Backend Abstractions ("Accelerators"): Execution is offloaded to abstract accelerator objects encompassing cloud-based QPUs, local drivers, or software simulators.

• Postprocessing: Programmable functors implement error-mitigation or additional classical corrections after QPU measurement.

This layered structure enables the host program to author, compile, and execute quantum kernels, manage device-level execution and error mitigation, retrieve results, and integrate the quantum step into classical optimization loops (McCaskey et al., 2018).

2. Formal Program Model and Metric Taxonomy

HQPEF frameworks formalize kernel interfaces, program representations, compiler pass semantics, and quantitative metrics:

• Kernel Signatures: Formally, a quantum kernel is

$\mathtt{__quantum\_kernel} : (\mathcal{B}, \mathbf{P}) \rightarrow \mathcal{B}$

where $\mathcal{B}$ is an AcceleratorBuffer (measurement container), and $\mathbf{P} \in \mathbb{R}^n$ denotes parameter vectors (e.g., gate angles).

• IR and Passes: The IR is a finite list $[I_1, \dots, I_m]$ of instructions, with passes acting as transformations $T: \mathrm{IR} \rightarrow \mathrm{IR}$, subject to semantic preservation (modulo device error rates and constraints), often guided by cost models (e.g., SWAP count minimization).
• Performance Metrics: HQPEF quantifies hybrid programs via:
  • Circuit depth: Longest path in IR DAG.
  • Gate and two-qubit gate counts: Enumerated per IR.
  • Qubit fidelity: Sourced from hardware calibration metadata.
  • End-to-end latency: Wall-time including backend queuing.
• HQPEF-Py (Osei et al., 23 Nov 2025) expands the metric set to include:
  • Quantum Readiness Level (QRL): Workflow checklist weighted by evidence and calibration drift.
  • Utility of Quantumness (UQ): Normalized speedup at fixed quality thresholds.
  • Timing and drift audit: Per-stage duration profiling and calibration drift statistics.

3. Workflow Management and Compiler Optimizations

HQPEF systems codify comprehensive hybrid workflows, integrating multiple layers:

1. Authoring: Quantum kernels are written in high-level DSLs and marked for compilation (e.g., __qpu__).
2. Compilation and IR Construction: The framework compiler parses source to IR, exposing a polymorphic, serializable structure for further compiler passes.
3. Preprocessing/Error Mitigation: IR passes inject calibration circuits for SPAM error estimation and attach classical postprocessors.
4. Optimization and Transformation: Includes constant propagation/folding, liveness and dead code analyses, hybrid-dependency analysis, and instruction reordering for maximizing parallelism.
5. Target Mapping: The lowered IR is mapped to the target hardware's ISA.
6. Execution: Quantum instructions are dispatched to the QPU or simulator; classical/quantum measurements are collected.
7. Postprocessing/Evaluation: Error-mitigation postprocessors adjust outputs; metrics are collected for audit and benchmarking (McCaskey et al., 2018, Remme et al., 19 May 2025, Osei et al., 23 Nov 2025).

Optimization routines in HQPEF commonly comprise:

• Constant propagation/folding across classical and quantum domains.
• Live-variable and dead-code elimination.
• Hybrid-dependency analysis for barrier alignment.
• Instruction reordering and latest-possible quantum execution for device utilization and coherence minimization (Remme et al., 19 May 2025).

4. Type Systems, Language Integration, and HPC Compatibility

HQPEFs emphasize strict typing and seamless integration with classical languages and high-performance environments:

• Type Safety and Language Bindings: HQPEF frameworks like XACC and Q-Pragma provide strong typing for quantum data types (e.g., qbool, quint_t<N>) and support for parameterizing quantum routines, preserving safe uncomputation and reversibility via RAII idioms. Kernel signatures translate directly into strongly typed C/C++/Fortran interfaces.
• HPC-Oriented Extensions: Q-Pragma introduces #pragma-based integration into C++17, enabling scope-based dispatch of both quantum and classical code to QPU controllers, manual memory movement between host and QPU, fine-grained control constructs, and streaming of quantum instructions across classical-quantum boundaries.
• LLVM/QIR Ecosystem: Full-stack HQPEFs support compilation from multiple high-level languages into LLVM IR augmented with QIR instructions, allowing hardware-agnostic lowering and reuse of mature classical compiler optimization passes. This approach underpins both flexible backend selection and cross-architecture compatibility (Gazda et al., 2023, Zhan et al., 23 Oct 2025).

5. Evaluation Protocols, Auditing, and Best Practices

HQPEF implementations deploy auditable workflow executions using rigorous metrics, instrumentation, and reporting standards:

• Metric-Guided Optimization Feedback: Integrated pipelines monitor wall-time, quantum instruction number, and coherence time as primary metrics, directing pass selection in real time or at compile time.
• Pythonic and Domain-Specific Auditing: HQPEF-Py (Osei et al., 23 Nov 2025) offers concise Python reference implementations for QRL assignment, UQ benchmarking under strict budget/matched-resource constraints, and timing/drift audit routines suited to reproducible, workflow-level validation.
• Best Practice Recommendations: Emphasis is placed on matched-budget benchmarking (identical time/cost/energy budgets for solvers), predeclared quality thresholds, strict random seed control, exhaustive reporting of timing and calibration drift, and versioned QRL rubrics to facilitate transparent and auditable comparisons.

Metric/Score	Definition/Formula	Purpose
QRL (Readiness Level)	$S=\sum_{i}w_i c_i + g(\delta)$; QRL(S) via staged thresholds	Workflow completeness/auditing
UQ (Speedup)	$$S_{\textrm{norm}} = \min\{T_A : Q_A \geq \tau\}/\min\{T_B : Q_B \geq \tau\}$$	Comparative solver efficiency
Coherence Time	$$\tau_Q = n_{q,\textrm{before}} + \Delta t_\textrm{between} + n_{q,\textrm{after}}$$	Noise minimization target

A tabular summary (see above) structures the core metrics, reflecting their explicit definitions and evaluation purposes (Remme et al., 19 May 2025, Osei et al., 23 Nov 2025).

6. Workflow Examples and Comparative Implementations

Comprehensive HQPEF exemplars demonstrate end-to-end workflow execution, metric tracking, and optimization:

• XACC VQE Example: Illustrates quantum kernel compilation, device-aware IR optimization, QPU execution, expectation value measurement, and metric collection in variational loops for physics simulations (McCaskey et al., 2018).
• Hybrid Program Optimization: (Remme et al., 19 May 2025) demonstrates that seven interleaved optimizations, guided by formal metrics, reduce wall time by up to 22% and coherence time by 14% on benchmark quantum-classical algorithms.
• Cross-Framework Comparison: Tierkreis and full-stack approaches (HPC-QC) extend HQPEF principles to pure dataflow and high-performance computing environments, emphasizing asynchronous, distributed runtime, and multi-SDK, multi-language support with hardware abstraction and partitioned circuit execution (Sivarajah et al., 2022, Zhan et al., 23 Oct 2025).

Framework	Compile Target(s)	Workflow/Abstraction Highlight
XACC	QMI, various IRs	Modular passes, kernel registration
Q-Pragma	OpenQASM3, QIR	C++ pragma DSL, HPC primitives
Tierkreis	Dataflow graphs	Higher-order dataflow, static typing
HPC-QC Stack	QIR/LLVM IR	Multi-node, circuit knitting, SDK-agn.

7. Identified Challenges and Future Directions

HQPEF usage reveals several open research challenges:

• Low-latency Local QPU Models: Mitigating remote queuing delays to enhance tight integration in variational and feedback loops.
• Device-Aware, Noise-Adaptive Compilation: Automatic extraction and exploitation of backend-specific noise and calibration metadata for optimal placement, scheduling, and error compensation.
• Dynamic Circuits and Feedback: Support for in-program mid-circuit measurement, classical-to-quantum feedback, and dynamic control flow within a unified execution session.
• Cross-Platform Benchmarking: Unified metrics and IR-level abstractions enabling systematic, reproducible comparison and benchmarking of quantum hardware and simulators.

This suggests that HQPEF designs will increasingly emphasize auditability, workflow generality, back-end agnosticism, and real-time, metric-guided adaptation for robust evaluation and optimization of hybrid quantum applications, particularly as quantum-classical integration matures in both scientific and enterprise contexts (McCaskey et al., 2018, Remme et al., 19 May 2025, Osei et al., 23 Nov 2025, Gazda et al., 2023, Zhan et al., 23 Oct 2025).