Testing Multi-Subroutine Quantum Programs: From Unit Testing to Integration Testing

TL;DR

This paper presents a holistic framework for testing multi-subroutine quantum programs, spanning unit and integration testing. It identifies core properties of quantum programs, surveys languages and projects, and introduces seven novel testing principles plus three criteria to guide test design, including the SCAQ input strategy and density-matrix-based state selection. The authors propose IO-analysis, state-generation/checking methods, and subtask decomposition (relation, structural, behavioral testing) tailored for quantum contexts, and validate them through 17 subroutines and three case studies (QPE, Shor’s factoring, and a linear system solver). The findings demonstrate that careful consideration of endian modes, quantum-classical coupling, and transform-based output checks can substantially improve bug detection and testing efficiency on both simulators and, potentially, NISQ devices. Overall, the work offers practical guidelines and a test-driven roadmap for robust quantum software development.

Abstract

Quantum computing has emerged as a promising field with the potential to revolutionize various domains by harnessing the principles of quantum mechanics. As quantum hardware and algorithms continue to advance, developing high-quality quantum software has become crucial. However, testing quantum programs poses unique challenges due to the distinctive characteristics of quantum systems and the complexity of multi-subroutine programs. This paper addresses the specific testing requirements of multi-subroutine quantum programs. We begin by investigating critical properties by surveying existing quantum libraries and providing insights into the challenges of testing these programs. Building upon this understanding, we focus on testing criteria and techniques based on the whole testing process perspective, spanning from unit testing to integration testing. We delve into various aspects, including IO analysis, quantum relation checking, structural testing, behavior testing, integration of subroutine pairs, and test case generation. We also introduce novel testing principles and criteria to guide the testing process. We conduct comprehensive testing on typical quantum subroutines, including diverse mutants and randomized inputs, to evaluate our proposed approach. The analysis of failures provides valuable insights into the effectiveness of our testing methodology. Additionally, we present case studies on representative multi-subroutine quantum programs, demonstrating the practical application and effectiveness of our proposed testing principles and criteria.

Figures (21)

• Figure 1: A quantum circuit for preparing the Bell state.
• Figure 2: The quantum circuit for QPE algorithm.
• Figure 3: The quantum circuit for quantum teleportation.
• Figure 4: The corresponding circuits of QFT program with $n=$ 1, 2, 3, 4 respectively ($n$ is the number of qubits).
• Figure 5: The decomposition of the Controlled-X gate is controlled by 1001. On the left is the note in the quantum circuit, where 0-controlling qubits are with hollow circles. It can be decomposed to the right with a standard controlled-X gate between the two X gates on the 0-controlling qubits.

Theorems & Definitions (13)

• Example 5.1
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• Example 5.3
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• Example 5.6
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• Example 6.1
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• Example 6.3