Best Approximate Quantum Compiling Problems

TL;DR

This paper investigates the problem of approximating quantum circuits with hardware constraints, providing mathematical insights and efficient solutions, including a new Toffoli decomposition and circuit compression techniques.

Contribution

It offers a mathematical framework for approximate quantum compiling and demonstrates novel decompositions and compression methods for quantum circuits.

Findings

Derived a 14-CNOT 4-qubit Toffoli decomposition from scratch.

Showed Quantum Shannon Decomposition can be compressed by a factor of two.

Provided insights into the mathematics of approximate quantum circuit synthesis.

Abstract

We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity.