Intelligent and Soft Computing Systems for Green Energy

20T-Count Optimized Quantum Comparator Circuit

Gayathri S. S., R. Kumar* and Samiappan Dhanalakshmi

Department of Electronics and Communication Engineering, SRM Institute of Science and Technology, Kattankulathur, Chengalpet, Tamil Nadu, India

Abstract

Quantum circuits that solve arithmetic problems find immense application in many quantum algorithms like Grover’s search algorithm, quantum cryptography, and quantum image processing applications. In this paper, a T-count optimized quantum comparator structure for single-qubit and two-qubit input is proposed. When compared to previous works, the proposed quantum structures show a better reduction in the number of T gates count and offer less T-depth.

Keywords: Quantum circuit, T-gates, quantum comparator, quantum gates, fault-tolerant, quantum computing

20.1 Introduction

Qubits are units of data that operate on quantum gates that can take |0⟩ state, |1⟩ state and superposition of both states represented as |ψ⟩ = α |0⟩+β |1⟩ where, α and β are satisfying ||α||² + ||β||² = 1. The output states can be measured by finding the values of α and β. Upon measurement the output state collapses to one of its measurement in standard basis states 0 and 1 [1]. To maintain unique mapping between input and output vectors, quantum circuits consume ancillary qubits and garbage outputs in the input and output section, respectively [2–4]. To employ the quantum circuits completely on quantum algorithms the garbage generated by the circuit has to ...