[Paper] Randomized and Diverse Input State Generation for Quantum Program Testing

Source: arXiv - 2605.03957v1

Overview

The paper presents a new framework for testing quantum programs by generating random, diverse quantum input states that better explore the huge quantum state space. By introducing quantitative “diversity scores” and a hardware‑friendly Brick‑Circuit (BC) generator, the authors show how to produce test inputs that are both more uniformly distributed and more entangled than those created by existing methods.

Key Contributions

• Diversity metrics for quantum state coverage – a suite of local and global scores that capture how well a set of test states spans magnitudes, phases, and entanglement across the Hilbert space.
• Brick‑Circuit (BC) test‑input generator – a construction using only native, low‑depth gates that approximates ideal random states while staying compatible with current quantum hardware.
• Comprehensive empirical evaluation – the BC generator is benchmarked against several state‑of‑the‑art generators, demonstrating superior expressibility (uniform coverage) and entangling power at shallower circuit depths.

Methodology

1. Define coverage criteria – The authors extend classical input‑coverage ideas to quantum programs, focusing on three properties:

   • Magnitude (probability amplitudes)
   • Phase (relative complex angles)
   • Entanglement (correlations between qubits)

2. Design diversity scores –

   • Local scores (e.g., pairwise distance, nearest‑neighbor correlation) measure how tightly test states cluster.
   • Global scores (e.g., distribution uniformity, spectral spread) assess overall spread across the state space.

3. Build the Brick‑Circuit generator –

   • Starts from a brick‑layer pattern of single‑qubit rotations and two‑qubit entangling gates (CNOT or CZ).
   • Parameters are sampled uniformly, producing a circuit that is shallow (few layers) yet expressive enough to approximate a Haar‑random state.

4. Benchmarking protocol – For each generator (BC and four baselines), the authors:

   • Sample a large set of test states (e.g., 10 000).
   • Compute all diversity scores.
   • Derive expressibility (how close the empirical distribution is to the ideal Haar distribution) and entangling capability (average entanglement entropy).

Results & Findings

• The BC generator reaches near‑optimal uniformity with significantly fewer gate layers, meaning less exposure to noise on real devices.
• Entanglement scores show the BC circuits generate states that are more highly entangled, a crucial property for many quantum algorithms.
• Diversity scores confirm that BC‑generated states are both globally spread and locally uncorrelated, satisfying the authors’ coverage criteria better than the alternatives.

Practical Implications

In short, the work gives the quantum community a practical, low‑overhead method to assess and improve the robustness of quantum programs before they run on noisy, near‑term hardware.

Limitations & Future Work

• Scalability of metrics – Computing global diversity scores scales quadratically with the number of test states; approximations may be needed for very large test suites.
• Hardware noise model – Experiments were performed on simulators with ideal gates; real‑device validation (including decoherence and gate errors) is left for future studies.
• Extension to mixed states – The current framework assumes pure states; handling density matrices (e.g., for noisy channels) would broaden applicability.
• Automated parameter tuning – Future work could explore adaptive schemes that automatically adjust BC parameters to target specific coverage goals or hardware constraints.

Authors

• Maryse Ernzer
• Seung Yeob Shin
• Fabrizio Pastore
• Domenico Bianculli

Paper Information

• arXiv ID: 2605.03957v1
• Categories: cs.SE
• Published: May 5, 2026
• PDF: Download PDF