Compositional Quantum Control Flow with Efficient Compilation in Qunity

TL;DR

This paper presents an efficient compiler for the Qunity quantum programming language, enabling high-level quantum control flow abstractions to be compiled into optimized OpenQASM 3 code, improving practicality and resource usage.

Contribution

It introduces a complete implementation of a Qunity compiler with advanced optimization techniques, addressing previous inefficiencies and expanding control flow abstractions.

Findings

Significantly reduced circuit size and gate count.

Enhanced compilation efficiency for high-level quantum control flow.

Broader range of abstractions with favorable trade-offs.

Abstract

Most existing quantum programming languages are based on the quantum circuit model of computation, as higher-level abstractions are particularly challenging to implement - especially ones relating to quantum control flow. The Qunity language, proposed by Voichick et al., offered such an abstraction in the form of a quantum control construct, with great care taken to ensure that the resulting language is still realizable. However, Qunity lacked a working implementation, and the originally proposed compilation procedure was very inefficient, with even simple quantum algorithms compiling to unreasonably large circuits. In this work, we focus on the efficient compilation of high-level quantum control flow constructs, using Qunity as our starting point. We introduce a wider range of abstractions on top of Qunity's core language that offer compelling trade-offs compared to its existing control construct. We create a complete implementation of a Qunity compiler, which converts high-level Qunity code into the quantum assembly language OpenQASM 3. We develop optimization techniques for multiple stages of the Qunity compilation procedure, including both low-level circuit optimizations as well as methods that consider the high-level structure of a Qunity program, greatly reducing the number of qubits and gates used by the compiler.