Reversible circuit compilation with space constraints

TL;DR

This paper presents REVS, a compiler that efficiently translates higher-level programs into reversible circuits with minimal memory use, crucial for quantum computing where qubits are limited.

Contribution

The paper introduces a novel framework and techniques for space-efficient reversible circuit compilation, including in-place functions, data dependency tracking, and pebble game transformations.

Findings

REVS reduces space complexity by a factor of 4 or more compared to Bennett's method.

The approach maintains moderate increases in circuit size and compilation time.

Reversible implementations of cryptographic functions and arithmetic demonstrate practical benefits.

Abstract

We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate representation is introduced that allows to trace data dependencies within the program, allowing to clean up qubits early. This realizes an analog to "garbage collection" for reversible circuits. Third, we use the concept of so-called pebble games to transform irreversible programs into reversible programs under space constraints, allowing for data to be erased and recomputed if needed. We introduce REVS, a compiler for reversible circuits that can translate a subset of the functional programming language F# into Toffoli networks which can then be further interpreted for instance in LIQui|>, a domain-specific language for quantum computing and which is also embedded into F#. We discuss a number of test cases that illustrate the advantages of our approach including reversible implementations of SHA-2 and other cryptographic hash-functions, reversible integer arithmetic, as well as a test-bench of combinational circuits used in classical circuit synthesis. Compared to Bennett's method, REVS can reduce space complexity by a factor of $4$ or more, while having an only moderate increase in circuit size as well as in the time it takes to compile the reversible networks.