Overview of Quantum Gates and Circuits
๐ง Overview of Quantum Gates and Circuits
In classical computing, we use logic gates (AND, OR, NOT) to build circuits. In quantum computing, we use quantum gates to manipulate qubits. These gates are unitary operations (reversible linear transformations) applied to the state of qubits.
๐น What Is a Qubit?
A qubit is the quantum version of a classical bit.
It can be in a state |0⟩, |1⟩, or a superposition:
∣
๐
⟩
=
๐ผ
∣
0
⟩
+
๐ฝ
∣
1
⟩
∣ฯ⟩=ฮฑ∣0⟩+ฮฒ∣1⟩
where
๐ผ
ฮฑ and
๐ฝ
ฮฒ are complex numbers and
∣
๐ผ
∣
2
+
∣
๐ฝ
∣
2
=
1
∣ฮฑ∣
2
+∣ฮฒ∣
2
=1
๐ง Basic Quantum Gates
Here are the most common single-qubit and multi-qubit gates:
✅ Single-Qubit Gates
Gate Symbol Description
Pauli-X X Bit flip (like NOT gate):
Pauli-Y Y Bit and phase flip
Pauli-Z Z Phase flip (flips sign of
Hadamard (H) H Creates superposition:
Phase (S) S Adds phase of i to
T (ฯ/8 gate) T Adds a ฯ/4 phase to
✅ Multi-Qubit Gates
Gate Symbol Description
CNOT (Controlled NOT) CX Flips target qubit if control is
Toffoli (CCNOT) CCX Flips third qubit if both controls are
SWAP — Swaps two qubits
Controlled-Z CZ Applies Z to target if control is
๐ Gate Properties
Reversible: All quantum gates are reversible (unitary matrices).
Compositional: Gates can be chained together to build circuits.
No Cloning: You cannot duplicate qubit states (unlike classical bits).
๐ Quantum Circuits
A quantum circuit is a sequence of quantum gates applied to qubits, followed by measurement.
๐ Example:
Create a superposition and apply a CNOT gate:
|0⟩ ──H────■─────
│
|0⟩ ───────X─────
Apply Hadamard to the first qubit → superposition
Apply CNOT to entangle the two qubits → creates a Bell state
๐งฎ Measurement
Collapses a qubit into either |0⟩ or |1⟩ based on probability.
Used to extract classical information from quantum states.
๐งฐ Tools to Build and Visualize Circuits
Tool Description
Qiskit IBM's Python SDK for quantum computing
Cirq Google's framework for quantum circuits
Q# Microsoft's quantum language
Quantum Composer (IBM) Drag-and-drop circuit builder in browser
QuTiP Python toolkit for simulating quantum systems
๐ง Real-World Uses of Quantum Circuits
Quantum teleportation
Quantum key distribution
Shor’s algorithm (factoring)
Grover’s algorithm (search)
Quantum machine learning (QNNs, variational circuits)
๐ Summary Table
Feature Classical Gate Quantum Gate
Data Unit Bit (0 or 1) Qubit (
Operation Irreversible Reversible (unitary)
Parallelism No Yes (due to superposition & entanglement)
Measurement Not needed Collapses quantum state
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