quantum-hoare-logic

name	quantum-hoare-logic
description	Quantum Hoare Logic with Integer Hybrid Path-Sums (IHPS) for formal verification and resource estimation of hybrid quantum-classical programs with unbounded loops. Bridges formal methods, quantum programming, and static analysis.
category	quantum
trigger_words	["quantum hoare logic","hybrid quantum program verification","quantum resource estimation","path-sum quantum","quantum program static analysis","unbounded loop quantum"]

Quantum Hoare Logic with Integer Hybrid Path-Sums

Core Idea

Combine effective functional verification and resource estimation (termination, cost) for hybrid quantum-classical programs with unbounded loops using Integer Hybrid Path-Sums (IHPS).

Key Innovation

• Integer Hybrid Path-Sums (IHPS): Extension of path-sums to handle unbounded while loops as a representation of possible program executions
• First semi-automated static analysis solution for hybrid quantum programs
• Bridges functional verification with resource (termination/cost) estimation

Methodology

Step 1: Path-Sum Representation

• Represent quantum program executions as path-sums
• Extend to IHPS for handling unbounded while loops

Step 2: Loop Invariant Strategy

• Propose generic strategy for determining termination via loop invariants
• Compute expected resource consumption using invariant-based analysis
• Illustrate on several hybrid quantum program examples

Step 3: Semi-Automated Implementation

• Implement as semi-automatic Haskell program
• Combines equational reasoning with invariant checking

Applications

• Verifying correctness of VQA and QAOA programs with iterative loops
• Estimating quantum resource consumption (circuit depth, qubit count)
• Static analysis of hybrid quantum-classical algorithms
• Automated verification tools for quantum software engineering

Pitfalls

• Current gap: symbolic execution has largely left out hybridization and unbounded recursion
• Existing quantum Hoare logics lack expressiveness for computational equational reasoning
• Semi-automated: requires some human guidance for loop invariant discovery

Verification

• Apply to known hybrid quantum programs (VQA, QAOA loops)
• Compare resource estimates with actual execution costs
• Verify termination guarantees for iterative quantum algorithms

References

• arXiv:2607.08548 - An Effective Quantum Hoare Logic for Hybrid Quantum Programs with Unbounded Loops
• Authors: Christophe Chareton, Jad Issa, Romain Péchoux