Runtime Analysis of Quantum Programs: A Formal Approach

TL;DR

This paper introduces a formal calculus for analyzing the expected runtime of quantum programs, enabling systematic derivation of exact runtimes and upper bounds, demonstrated on a quantum key distribution protocol.

Contribution

It presents a novel weakest precondition calculus for quantum programs to analyze their expected runtime and loop invariants for upper bound derivation.

Findings

Successfully derived exact expected runtimes for quantum programs.

Developed a method to compute upper bounds using loop invariants.

Applied the calculus to analyze a simplified BB84 protocol.

Abstract

In this abstract we study the resource consumption of quantum programs. Specifically, we focus on the expected runtime of programs and, inspired by recent methods for probabilistic programs, we develop a calculus \`a la weakest precondition to formally and systematically derive the (exact) expected runtime of quantum programs. Notably, the calculus admits a notion of loop runtime invariant that can be readily used to derive upper bounds of their runtime. Finally, we show the applicability of our calculus analyzing the runtime of (a simplified version of) the BB84 quantum key distribution protocol.