[Paper Review] Proq: 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 Architecture4 citations

TL;DR

Proq introduces a projection-based runtime assertion framework for debugging quantum programs on actual quantum hardware. By representing assertions as quantum projections (orthogonal projectors), Proq enables efficient, single-execution verification via projective measurements, significantly reducing overhead compared to statistical or ancilla-based methods, and demonstrates effectiveness on Shor’s and HHL algorithms with theoretical guarantees on correctness and bug detection.

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

• Address the critical need for effective debugging in quantum program development due to the high likelihood of subtle bugs in counterintuitive quantum logic.
• Overcome limitations of prior quantum assertions that rely on classical logic, statistical sampling, or ancilla qubits, which restrict expressiveness and increase runtime cost.
• Develop a theoretically grounded, hardware-executable assertion scheme that supports complex quantum state properties using projections from Birkhoff-von Neumann quantum logic.
• Ensure practical feasibility on measurement-restricted quantum computers through assertion transformation and local projection techniques with soundness guarantees.
• Demonstrate the framework’s effectiveness on real-world quantum algorithms, including Shor’s and HHL algorithms, under realistic hardware constraints.

Proposed method

• Represent program assertions as projection operators (closed subspaces of Hilbert space), enabling logical reasoning over quantum states using quantum logic.
• Use projective measurements to check assertion satisfaction in a single execution, avoiding repeated runs required by statistical methods.
• Apply unitary transformations and measurement basis changes to adapt arbitrary projections into hardware-executable form on NISQ devices.
• Introduce local projection approximation to simplify complex projective measurements while preserving soundness and reducing qubit overhead.
• Design assertion transformation techniques to handle measurement restrictions in current quantum hardware, ensuring direct executability.
• Leverage the mathematical structure of orthomodular lattices and projection algebras to ensure logical consistency and correctness of assertions.

Experimental results

Research questions

• RQ1 Can projection-based assertions provide a more expressive and efficient alternative to classical-logic-based or statistical assertions in quantum program debugging?
• RQ2 How can projection-based assertions be transformed into executable circuits that respect the measurement constraints of current quantum hardware?
• RQ3 What is the theoretical foundation for ensuring that checking projection-based assertions reliably detects bugs or confirms semantic closeness in both exact and approximate quantum programs?
• RQ4 To what extent can local projection approximation simplify complex assertions without compromising soundness or detection capability?
• RQ5 How does Proq’s approach compare in efficiency and effectiveness to existing assertion schemes on real quantum algorithms like Shor’s and HHL?

Key findings

• Proq enables single-execution verification of complex quantum state properties using projective measurements, drastically reducing the number of required program runs compared to statistical assertion methods.
• The framework supports assertions on arbitrary quantum states through projection operators, overcoming the limited expressiveness of prior approaches restricted to specific state types.
• Assertion transformations allow direct execution on measurement-restricted quantum hardware, making the approach practical for current NISQ devices.
• Local projection approximation enables simplified, scalable assertion implementation with provable soundness, reducing resource overhead while maintaining detection capability.
• Proq successfully asserts and debugs two complex quantum algorithms—Shor’s and HHL—demonstrating its effectiveness in real-world scenarios with meaningful verification.
• Theoretical analysis confirms that projection-based assertions can statistically assure semantic correctness and locate bugs in both exact and approximate quantum programs.