Quantum algorithm

Quantum mechanics

Algorithm

Debugging

Quantum computer

Pure mathematics

Theoretical computer science

Soundness

Computer science

Projection (relational algebra)

Linear subspace

Physics

Mathematics

Quantum

Programming language

Executable

Assertion

Quantum state

State (computer science)

Proceedings of the ACM on Programming Languages

In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic. The satisfaction of a projection by a quantum state can be directly checked upon a small number of projective measurements rather than a large number of repeated executions. On the theory side, we rigorously prove that checking projection-based assertions can help locate bugs or statistically assure that the semantic function of the tested program is close to what we expect, for both exact and approximate quantum programs. On the practice side, we consider hardware constraints and introduce several techniques to transform the assertions, making them directly executable on the measurement-restricted quantum computers. We also propose to achieve simplified assertion implementation using local projection technique with soundness guaranteed. We compare Proq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Proq by its applications to assert two sophisticated quantum algorithms, the Harrow-Hassidim-Lloyd algorithm and Shor’s algorithm.

Projection-based runtime assertions for testing and debugging Quantum programs