Faster and Better Quantum Software Testing through Specification Reduction and Projective Measurements

TL;DR

This work introduces a QST approach, which applies a reduction algorithm to a quantum program specification, which alleviates the limitations of existing quantum software testing approaches by enabling faster sampling through quantum parallelism and by performing projective measurements in the mixed Hadamard basis.

Abstract

Quantum computing promises polynomial and exponential speedups in many domains, such as unstructured search and prime number factoring. However, quantum programs yield probabilistic outputs from exponentially growing distributions and are vulnerable to quantum-specific faults. Existing quantum software testing (QST) approaches treat quantum superpositions as classical distributions. This leads to two major limitations when applied to quantum programs: (1) an exponentially growing sample space distribution and (2) failing to detect quantum-specific faults such as phase flips. To overcome these limitations, we introduce a QST approach, which applies a reduction algorithm to a quantum program specification. The reduced specification alleviates the limitations (1) by enabling faster sampling through quantum parallelism and (2) by performing projective measurements in the mixed Hadamard basis. Our evaluation of 143 quantum programs across four categories demonstrates significant improvements in test runtimes and fault detection with our reduction approach. Average test runtimes improved from 169.9s to 11.8s, with notable enhancements in programs with large circuit depths (383.1s to 33.4s) and large program specifications (464.8s to 7.7s). Furthermore, our approach increases mutation scores from 54.5% to 74.7%, effectively detecting phase flip faults that non-reduced specifications miss. These results underline our approach's importance to improve QST efficiency and effectiveness.

Figures (4)

• Figure 1: Illustration of the background concepts. In the theoretical circuit 1), we demonstrate the following concepts: (a) state vectors $\ket{\psi_{init}}$ and $\ket{\psi_{final}}$, (b) qubits denoted by $\ket{x_j}$ for $j=0,1,\dots, n-1$, (c) the main program $\mathcal{U}$, (d) the basis transformation $\mathcal{T}$, measurement $M$, and the output $O_m=\ket{m}$ resulting from measurement $M$. In the coded Qiskit example 2), we illustrate additional concepts: (a) quantum gates such as H and X, (b) faults representing incorrectly inserted quantum gates, and (c) the basis transformation with $H$ gates, providing an example of a mixed Hadamard basis in a coded circuit.
• Figure 2: Overview and Application Context of the Reduction Approach.
• Figure 3: Directional graph representation of the Greedy reduction \ref{['alg:reduction_algorithm']} for the running example in \ref{['eq:approach_running_example']}.
• Figure 4: Boxplots of runtime improvement over Default when we apply reduction to by the number of qubits. Speedups are above the x-axis, and Slowdowns are below.