9、Parameterised Quantum Circuits and Data Encoding: A Comprehensive Guide

Parameterised Quantum Circuits and Data Encoding: A Comprehensive Guide

1. Introduction

After building quantum hardware, two key questions arise: what problems can be solved on NISQ computers, and how to encode classical data into quantum states? The focus here is on the concept of Parameterised Quantum Circuits (PQCs) as a generic quantum machine - learning model and various data - encoding methods.

2. Parameterised Quantum Circuits

A quantum circuit transforms an initial quantum state (|\psi\rangle) into a final quantum state (|\psi’\rangle) through a sequence of unitary operators:
[|\psi’\rangle = U_m(\theta_m)\cdots U_2(\theta_2)U_1(\theta_1)|\psi\rangle]
Here, ((U_i) {i = 1,\cdots,m}) are individual gates, and ((\theta_i