Quantum Circuits: Designing Quantum Operations

Introduction

A quantum circuit is a model for quantum computation in which a computation is a sequence of quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register.

Structure of a Circuit

In a quantum circuit diagram:

• Wires: Horizontal lines represent qubits (or classical bits for measurements).
• Time Flow: Flows from left to right.
• Boxes/Symbols: Represent quantum gates acting on the qubits.
• Meter Icons: Represent measurement operations.

Universality

A set of gates is called universal if any unitary operation on a finite number of qubits can be approximated to arbitrary accuracy by a circuit composed of gates only from this set. A common universal gate set consists of:

1. The CNOT gate (multi-qubit).
2. Single-qubit rotations (specifically Hadamard, Phase, and T-gates).