  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.
