[Paper Review] Poq: Projection-based Runtime Assertions for Debugging on a Quantum Computer

Gushu Li, Li Zhou+4 more|arXiv (Cornell University)|Nov 28, 2019

Quantum Computing Algorithms and Architecture30 references4 citations

TL;DR

Proq introduces a projection-based runtime assertion framework for debugging quantum programs by representing predicates as projections in quantum logic, enabling efficient verification via few projective measurements. It ensures correctness for both exact and approximate quantum programs and demonstrates effectiveness in asserting Shor's and the Harrow-Hassidim-Lloyd algorithms on measurement-restricted hardware.

ABSTRACT

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 ingenious quantum algorithms, the Harrow-Hassidim-Lloyd algorithm and Shor's algorithm.

Motivation & Objective

• To address the challenge of debugging quantum programs due to the lack of direct observation and high measurement cost.
• To provide a formal framework for runtime assertions that are semantically grounded in quantum logic and verifiable with minimal measurements.
• To adapt assertions for execution on near-term quantum computers with limited measurement capabilities.
• To simplify assertion implementation using local projection techniques with formal soundness guarantees.
• To evaluate Proq's effectiveness and efficiency on complex quantum algorithms like Shor's and HHL.

Proposed method

• Represent program assertions as projections (closed subspaces) in the state space, aligning with Birkhoff-von Neumann quantum logic.
• Use a small number of projective measurements to check whether a quantum state satisfies a given projection-based assertion.
• Apply transformation techniques to assertions to comply with hardware constraints such as limited measurement bases and qubit connectivity.
• Introduce a local projection technique to simplify assertion implementation while preserving correctness and soundness.
• Formalize the semantics of assertions to ensure they can detect bugs or statistically confirm program correctness for both exact and approximate quantum programs.
• Integrate the assertion framework into quantum program execution pipelines for runtime checking during algorithm execution.

Experimental results

Research questions

• RQ1 Can projection-based assertions be used to efficiently verify quantum program correctness with minimal measurement overhead?
• RQ2 How can assertions be transformed to be executable on current quantum hardware with restricted measurement capabilities?
• RQ3 To what extent can projection-based assertions detect semantic bugs in quantum programs?
• RQ4 Can the framework provide statistical confidence in the correctness of approximate quantum programs?
• RQ5 How does Proq compare in efficiency and effectiveness to existing quantum program assertion techniques?

Key findings

• Proq enables efficient runtime verification of quantum programs using only a small number of projective measurements per assertion, significantly reducing overhead compared to repeated execution.
• The framework provides formal guarantees that checking projection-based assertions can locate bugs or statistically assure semantic correctness for both exact and approximate quantum programs.
• Transformation techniques allow Proq assertions to be directly executed on measurement-restricted quantum computers, enhancing practical applicability.
• The local projection technique enables simplified and sound assertion implementation without sacrificing verification accuracy.
• Proq was successfully applied to assert two complex quantum algorithms—Shor’s algorithm and the Harrow-Hassidim-Lloyd algorithm—demonstrating its practical effectiveness.
• The evaluation shows that Proq outperforms existing assertion schemes in terms of measurement efficiency and verification reliability on real-world quantum programs.