Quantum comparator circuit on superconducting quantum computer

Abstract

In this thesis, we present an optimised quantum comparator circuit based on Cuccaro's ripple-carry quantum adder using relative phase techniques from Maslov's multiple control Toffoli optimisation. We extend the cost function from simply counting C-Not and Toffoli gate to Qiskit cost which defines arbitrary single qubit gate cost as unity and C-Not as the only two qubit gate cost as ten. We report the comparison result between our comparator circuit with previous comparator circuits from literature using optimal Toffoli implementation with Qiskit cost, C-Not count, and circuit depth. We also report our experiment of implementing a two-bit comparator on IBM QX devices.