Optimizing Gate Decomposition for High-Level Quantum Programming

TL;DR

This paper introduces new methods for optimizing multi-controlled quantum gates, significantly reducing the number of CNOT gates needed, which improves the efficiency of quantum algorithms on NISQ devices.

Contribution

The authors develop a novel gate decomposition technique that reduces CNOT counts from quadratic to linear in the number of qubits, and implement it in the Ket platform.

Findings

CNOT gates reduced from 101,252 to 2,684 for a 114-qubit Grover layer

Decomposition reduces CNOT count from O(n^2) to O(n)

Implementation in Ket demonstrates practical efficiency gains

Abstract

This paper presents novel methods for optimizing multi-controlled quantum gates, which naturally arise in high-level quantum programming. Our primary approach involves rewriting $U(2)$ gates as $SU(2)$ gates, utilizing one auxiliary qubit for phase correction. This reduces the number of CNOT gates required to decompose any multi-controlled quantum gate from $O(n^2)$ to at most $32n$. Additionally, we can reduce the number of CNOTs for multi-controlled Pauli gates from $16n$ to $12n$ and propose an optimization to reduce the number of controlled gates in high-level quantum programming. We have implemented these optimizations in the Ket quantum programming platform and demonstrated significant reductions in the number of gates. For instance, for a Grover's algorithm layer with 114 qubits, we achieved a reduction in the number of CNOTs from 101,252 to 2,684. This reduction in the number of gates significantly impacts the execution time of quantum algorithms, thereby enhancing the feasibility of executing them on NISQ computers.