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Equivalence, Identity, and Unitarity Checking in Black-Box Testing of Quantum Programs

Peixun Long, Jianjun Zhao

TL;DR

The paper tackles black-box testing of quantum programs by introducing three novel checking algorithms for equivalence, identity, and unitarity, all built around the Swap Test and Pauli-input-state analysis. It provides theoretical foundations, concrete algorithms with complexity bounds, and optimization strategies that leverage purity checks to accelerate detection. An extensive experimental evaluation on a Q# benchmark suite demonstrates effective bug detection and notable runtime improvements from optimization, while also acknowledging limitations and cases needing careful parameter tuning. The work advances practical black-box testing for quantum software, offering concrete guidelines and a benchmark ecosystem to assess future methods. Overall, the methods enable rigorous equivalence, identity, and unitarity verification in quantum programs, contributing to reliable quantum software development.

Abstract

Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often overlook fundamental questions in black-box testing. In this paper, we bridge this gap by presenting three novel algorithms specifically designed to address the challenges of equivalence, identity, and unitarity checking in black-box testing of quantum programs. We also explore optimization techniques for these algorithms, including specialized versions for equivalence and unitarity checking, and provide valuable insights into parameter selection to maximize performance and effectiveness. To evaluate the effectiveness of our proposed methods, we conducted comprehensive experimental evaluations, which demonstrate that our methods can rigorously perform equivalence, identity, and unitarity checking, offering robust support for black-box testing of quantum programs.

Equivalence, Identity, and Unitarity Checking in Black-Box Testing of Quantum Programs

TL;DR

The paper tackles black-box testing of quantum programs by introducing three novel checking algorithms for equivalence, identity, and unitarity, all built around the Swap Test and Pauli-input-state analysis. It provides theoretical foundations, concrete algorithms with complexity bounds, and optimization strategies that leverage purity checks to accelerate detection. An extensive experimental evaluation on a Q# benchmark suite demonstrates effective bug detection and notable runtime improvements from optimization, while also acknowledging limitations and cases needing careful parameter tuning. The work advances practical black-box testing for quantum software, offering concrete guidelines and a benchmark ecosystem to assess future methods. Overall, the methods enable rigorous equivalence, identity, and unitarity verification in quantum programs, contributing to reliable quantum software development.

Abstract

Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often overlook fundamental questions in black-box testing. In this paper, we bridge this gap by presenting three novel algorithms specifically designed to address the challenges of equivalence, identity, and unitarity checking in black-box testing of quantum programs. We also explore optimization techniques for these algorithms, including specialized versions for equivalence and unitarity checking, and provide valuable insights into parameter selection to maximize performance and effectiveness. To evaluate the effectiveness of our proposed methods, we conducted comprehensive experimental evaluations, which demonstrate that our methods can rigorously perform equivalence, identity, and unitarity checking, offering robust support for black-box testing of quantum programs.
Paper Structure (46 sections, 4 theorems, 40 equations, 4 figures, 8 tables, 7 algorithms)

This paper contains 46 sections, 4 theorems, 40 equations, 4 figures, 8 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Basic Concepts of Quantum Computation
  4. Evolution of Quantum States
  5. Quantum Operations and Quantum Programs
  6. Swap Test
  7. Quantum Tomography
  8. Questions and Motivations
  9. Modelling Black-Box Quantum Programs
  10. Questions
  11. Motivations
  12. Checking Algorithms
  13. Implementation of Swap Test
  14. Equivalence Checking
  15. Theoretical foundations
  16. ...and 31 more sections

Key Result

Theorem 1

Let $\mathcal{H}$ be a $d$-dimensional Hilbert space and $\{\left|1\right>,\dots,\left|d\right>\}$ is a group of standard orthogonal basis of $\mathcal{H}$. Let $\left|+_{mn}\right> = \frac{1}{\sqrt{2}}(\left|m\right>+\left|n\right>)$ and $\left|-_{mn}\right> = \frac{1}{\sqrt{2}}(\left|m\right>-\lef

Figures (4)

  • Figure 1: A SWAP gate that can be implemented by three CNOT gates.
  • Figure 3: Two sets of equivalent circuits
  • Figure 4: The number of PASS with different $s$ for expected-pass programs in EQ and UN under $k=4, \epsilon=0.15$
  • Figure 5: The Q# implementation for programs Cir2A, Cir2B, and QFT and their mutant operators in the evaluation.

Theorems & Definitions (6)

  • Theorem 1
  • Proposition 1
  • Corollary 1
  • Lemma 1
  • proof
  • proof : for Theorem \ref{['TheoremUcheck']}