Quantum Structural Benchmark (QSB): Evaluating Quantum Devices via π-Reconstruction Fidelity Overview We propose a novel quantum device benchmark—the Quantum Structural Benchmark (QSB)—based on the reconstruction accuracy of π from GHZ state measurements. Unlike conventional benchmarks (T₁/T₂, gate error rates, etc.), QSB measures how faithfully a quantum device reproduces fundamental geometric structure constants embedded in quantum mechanics. Key Metric: Structural Constant Fidelity (SCF) SCF = 1 - |π̂ - π| / π Where π̂ = √(3/2λ₃) is derived from Mermin inequality measurements on GHZ states. SCF Value Interpretation 1.000 Perfect (ideal simulator) 0.99+ Excellent (best hardware) 0.95-0.99 Good (typical NISQ) < 0.95 Structural degradation Main Results Measurement Value Mermin violation >700σ above classical bound Structure constant λ₃ 0.1482 ± 0.0006 Reconstructed π 3.181 SCF 0.9875 Platform IBM Quantum ibm_torino Paradigm Shift Aspect Conventional QSB/SCF Evaluates Gate quality Structural fidelity Question "How fast/quiet?" "How faithful to reality?" Type Engineering metric Physics metric Companion Paper This work builds upon: Quantum Buffon's Needle: Deriving π from the GHZ Structure Constant λ₃*DOI: 10.5281/zenodo.17855223 Files Included quantum_structural_benchmark.pdf — Full manuscript qsb.py — Complete QSB library (Python) README.md — Documentation Significance SCF could become the "LINPACK of quantum computing" — a universal metric for comparing quantum devices by their ability to reproduce fundamental physical constants. This represents a paradigm shift from hardware-centric to physics-centric quantum device evaluation.
Quantum Structural Benchmark (QSB): Evaluating Quantum Devices via π-Reconstruction Fidelity Overview We propose a novel quantum device benchmark—the Quantum Structural Benchmark (QSB)—based on the reconstruction accuracy of π from GHZ state measurements. Unlike conventional benchmarks (T₁/T₂, gate error rates, etc.), QSB measures how faithfully a quantum device reproduces fundamental geometric structure constants embedded in quantum mechanics. Key Metric: Structural Constant Fidelity (SCF) SCF = 1 - |π̂ - π| / π Where π̂ = √(3/2λ₃) is derived from Mermin inequality measurements on GHZ states. SCF Value Interpretation 1.000 Perfect (ideal simulator) 0.99+ Excellent (best hardware) 0.95-0.99 Good (typical NISQ) < 0.95 Structural degradation Main Results Measurement Value Mermin violation >700σ above classical bound Structure constant λ₃ 0.1482 ± 0.0006 Reconstructed π 3.181 SCF 0.9875 Platform IBM Quantum ibm_torino Paradigm Shift Aspect Conventional QSB/SCF Evaluates Gate quality Structural fidelity Question "How fast/quiet?" "How faithful to reality?" Type Engineering metric Physics metric Companion Paper This work builds upon: Quantum Buffon's Needle: Deriving π from the GHZ Structure Constant λ₃*DOI: 10.5281/zenodo.17855223 Files Included quantum_structural_benchmark.pdf — Full manuscript qsb.py — Complete QSB library (Python) README.md — Documentation Significance SCF could become the "LINPACK of quantum computing" — a universal metric for comparing quantum devices by their ability to reproduce fundamental physical constants. This represents a paradigm shift from hardware-centric to physics-centric quantum device evaluation.
Quantum Buffon's Needle: Deriving π from the GHZ Structure Constant Overview We demonstrate that the fundamental mathematical constant π can be derived from the quantum structure constant λ₃* = 3/(2π²), which characterizes the phase-space capacity of three-qubit entangled systems. By measuring the structural coherence of GHZ states on IBM Quantum hardware (ibm_torino), we obtained: λ3≈0.1482⇒π^=2λ33≈3.181 with only 1.25% deviation from the true value. Key Equation π=2λ3∗3 This "Quantum Buffon's Needle" experiment establishes π as a measurable property of quantum geometry, paralleling Buffon's classical probability-based derivation while revealing deeper connections between quantum information theory, spherical geometry, and physical reality. Main Results Measurement Value Mermin inequality violation >700σ above classical bound Measured structure constant λ₃ = 0.1482 ± 0.0006 Reconstructed π 3.181 Relative error 1.25% Platform IBM Quantum ibm_torino (Heron r2) Files Included quantum_buffons_needle_pi_derivation.pdf — Full manuscript quantum_pi_scan.py — Python script for multi-backend π derivation experiments README.md — Documentation Significance This result establishes a novel paradigm: π is not merely an abstract mathematical entity but a measurable physical constant embedded in the geometric fabric of quantum state space. The method enables evaluation of quantum devices by their ability to reproduce fundamental geometric constants—a new direction in quantum benchmarking.
Abstract In this report, we explore benchmarking gate-based quantum devices based on the certification of quantum measurements, which can be viewed as an extension of quantum hypothesis testing. Here, we are interested in a binary certification scheme in which the null and alternative hypotheses are qubit von Neumann measurements. The certification procedure can be used to evaluate the accuracy of Noisy Intermediate-Scale Quantum devices. To support this methodology, we contribute benchmarks to PyQBench, an open-source Python library for benchmarking gate-based quantum computers. We provide a user-friendly command-line interface for certifying measurements from the Fourier family. For more advanced scenarios, PyQBench can also be used as a Python library, allowing users to define custom measurement schemes and error models. The latest version of PyQBench is designed to support IBM Q devices through integration with the Qiskit library, enabling seamless benchmarking on real quantum hardware. By providing flexible benchmarking tools, PyQBench addresses the critical need for reliable performance metrics in the NISQ era, contributing to the development of error mitigation techniques and the verification of quantum measurement fidelity.
In the near-term "NISQ"-era of noisy, intermediate-scale, quantum hardware and beyond, reliably determining the quality of quantum devices becomes increasingly important: users need to be able to compare them with one another, and make an estimate whether they are capable of performing a given task ahead of time. In this work, we develop and release an advanced quantum benchmarking framework in order to help assess the state of the art of current quantum devices. Our testing framework measures the performance of universal quantum devices in a hardware-agnostic way, with metrics that are aimed to facilitate an intuitive understanding of which device is likely to outperform others on a given task. This is achieved through six structured tests that allow for an immediate, visual assessment of how devices compare. Each test is designed with scalability in mind, making this framework not only suitable for testing the performance of present-day quantum devices, but also of those released in the foreseeable future. The series of tests are motivated by real-life scenarios, and therefore emphasise the interplay between various relevant characteristics of quantum devices, such as qubit count, connectivity, and gate and measurement fidelity. We present the benchmark results of twenty-one different quantum devices from IBM, Rigetti and IonQ.
The rapid advancement of quantum technologies has led to a growing and diverse landscape of quantum computing devices, each with varying architectures and capabilities. Most of them are evaluated using hardware-centric benchmarks such as gate fidelity, quantum volume, or coherence time. However, these metrics often fail to capture performance in problem-specific contexts, particularly in applications involving quantum image processing. In this work, we address this gap by introducing the Quantum Image Encoding Fidelity (QIEF) metric, a novel task-specific benchmark designed to evaluate how accurately quantum devices can encode classical image data into quantum representations. By focusing on image-specific criteria rather than device-agnostic parameters, QIEF offers a more application-relevant assessment of device capability, enabling a direct comparison of quantum hardware based on their effectiveness in real-world image-related tasks. We present the theoretical formulation of the QIEF, validate its relevance through quantum simulators and experiments on real quantum devices, and discuss its implications for guiding future hardware development tailored to quantum image processing applications.
Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire applications, have been proposed over the years. Objective comparisons are further hampered in practice as different variations of the same metric are used, and the data disclosed together with a reported metric value is often not sufficient to reproduce the measurements. In this poster, we present our recent article, where we address these challenges by providing a review of metrics and benchmarks for quantum computers [1], including 1) a comprehensive collection of benchmarks allowing holistic comparisons of quantum computers, 2) a consistent format of the definitions across all metrics including a transparent description of the methodology and of the main assumptions and limitations, and 3) a reproducible approach by linking the metrics to open-source software used to evaluate them . We identify five areas where international standardization working groups could be established, namely: i) the identification and agreement on the categories of metrics that comprehensively benchmark device performance; ii) the identification and agreement on a set of well-established metrics that together comprehensively benchmark performance; iii) the identification of metrics specific to hardware platforms, including non-gate-based quantum computers; iv) inter-laboratory comparison studies to develop best practice guides for measurement methodology; and v) agreement on what data and software should be reported together with a metric value to ensure trust, transparency and reproducibility. We provide potential routes to advancing these areas. We expect that this work will accelerate the progress of quantum computing hardware towards quantum advantage. [1] D. Lall et al., A Review and Collection of Metrics and Benchmarks for Quantum Computers: Definitions, Methodologies and Software, arXiv:2502.06717.
We present an updated version of PyQBench, an open-source Python library designed for benchmarking gate-based quantum computers, with a focus on certifying qubit von Neumann measurements. This version extends PyQBench's capabilities by incorporating a certification scheme of quantum measurements that evaluates the accuracy on Noisy Intermediate-Scale Quantum devices, alongside its original functionality of von Neumann measurements' discrimination. PyQBench offers a user-friendly command-line interface and Python library integration, allowing users to implement custom measurement schemes and error models for more advanced benchmarking tasks. The new version is specifically designed to support IBM Q devices through integration with the Qiskit library, enabling seamless benchmarking on real quantum hardware. By providing flexible benchmarking tools, PyQBench addresses the critical need for reliable performance metrics in the NISQ era, contributing to the development of error mitigation techniques and the verification of quantum measurement fidelity. The source code is available on GitHub under an open-source license, encouraging community collaboration and further advancements in quantum hardware benchmarking.