Compiling Quantum Circuits using the Palindrome Transform

TL;DR

This paper introduces the Palindrome Transform and Palindromic Optimization Algorithm, novel methods for reducing the gate count in quantum circuit compilation of arbitrary unitary matrices, enhancing efficiency in quantum computation.

Contribution

The paper presents new algebraic and algorithmic techniques, the Palindrome Transform and Palindromic Optimization Algorithm, for minimizing self-inverting gates in quantum circuit synthesis.

Findings

Significant reduction in gate count compared to conventional methods.

Effective optimization for circuits of (n-1)-controlled single-qubit and CNOT gates.

Enhanced efficiency in quantum circuit compilation.

Abstract

The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2^n x 2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit and (n-1)-controlled-NOT gates. We first present a general algebraic optimization technique, which we call the Palindrome Transform, that can be used to minimize the number of self-inverting gates in quantum circuits consisting of concatenations of palindromic subcircuits. For a fixed column ordering of two-level decomposition, we then give an numerative algorithm for minimal (n-1)-controlled-NOT circuit construction, which we call the Palindromic Optimization Algorithm. Our work dramatically reduces the number of gates generated by the conventional two-level decomposition method for constructing quantum circuits of (n-1)-controlled single-qubit and (n-1)-controlled-NOT gates.