Quantum Weakest Preconditions Revisited: Pre-expectations for Expected Runtime Analysis

2026-07-14

AI Summary

This work addresses a critical limitation in existing quantum program verification methods, which typically rely on upper-bound assumptions and struggle to handle programs containing reward statements or those with potentially infinite expected running times. For the first time, the paper introduces expected reward calculus into quantum program verification by leveraging the theory of quantum weakest preconditions. It establishes a framework for analyzing expected running times without requiring any upper-bound assumptions. Through program transformation and a set of inference rules, the approach expresses expected running times as weakest expected reward forms incorporating rewards, enabling precise reasoning about quantum programs that may exhibit infinite expected running times. This significantly broadens the scope and applicability of quantum program verification.

Abstract

Quantum weakest preconditions are a fundamental tool for program verification of quantum programs. Many variations have been reported in the literature. We revisit quantum weakest preconditions from the perspective of expected runtime analysis of quantum programs and introduce a novel pre-expectation framework that enables to reason about the preconditions of quantum programs without the need of an upper bound. This is particularly interesting for quantum programs involving reward statements. The overall goal is to analyze runtime behavior even in the case of programs with potentially infinite expected runtime. This paper presents several ways to do so, e.g., a program transformation such that the expected runtime of a quantum program can be expressed using the weakest pre-expectation calculus with rewards.

Problem

• quantum weakest preconditions
• expected runtime analysis
• pre-expectation
• quantum programs
• reward statements

Innovation

• quantum weakest preconditions
• pre-expectation
• expected runtime analysis
• reward statements
• program transformation