Branch Sequentialization in Quantum Polytime

TL;DR

This paper introduces a new compilation technique for quantum programs that avoids exponential circuit growth caused by branch sequentialization, enabling more efficient quantum algorithms within polynomial time.

Contribution

It presents a novel compilation method for quantum control flow that preserves polynomial size and overcomes the limitations of existing strategies.

Findings

The technique avoids exponential circuit size growth.

It maintains soundness and completeness for quantum polynomial time.

Improves efficiency of quantum control flow compilation.

Abstract

Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes. Current compilation strategies for quantum control flow involve compiling the branches of a quantum conditional, either in-depth or in-width, which in general leads to circuits of exponential size. This problem is coined as the branch sequentialization problem. We introduce and study a compilation technique for avoiding branch sequentialization on a language that is sound and complete for quantum polynomial time, thus, improving on existing polynomial-size-preserving compilation techniques.