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Quantum Gates Reference Guide

·535 words·3 mins

This guide explains the most common quantum gates, how they work, and includes simple examples using the Cirq library.

1. Identity Gate (I)
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  • What It Does: Leaves the qubit unchanged.
  • When to Use: To hold a qubit in its current state or as a placeholder.

Sample Code:

import cirq

q0 = cirq.NamedQubit("q0")
circuit = cirq.Circuit(cirq.I(q0))  # Apply Identity gate
print("Identity Gate Circuit:")
print(circuit)

2. NOT Gate (X)
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  • What It Does: Flips the state of a qubit:
    • If the qubit is off (0), it turns on (1).
    • If the qubit is on (1), it turns off (0).

Sample Code:

circuit = cirq.Circuit(cirq.X(q0))  # Apply NOT gate
print("NOT Gate Circuit:")
print(circuit)

3. Hadamard Gate (H)
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  • What It Does: Creates a superposition:
    • The qubit becomes “partly on and partly off.”
  • When to Use: To start quantum algorithms or prepare for interference.

Sample Code:

circuit = cirq.Circuit(cirq.H(q0))  # Apply Hadamard gate
print("Hadamard Gate Circuit:")
print(circuit)

4. Z Gate
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  • What It Does: Tweaks the “on” state (1) of the qubit without flipping it.
  • When to Use: To prepare for interference or phase-based algorithms.

Sample Code:

circuit = cirq.Circuit(cirq.Z(q0))  # Apply Z gate
print("Z Gate Circuit:")
print(circuit)

5. RY Gate (Rotation-Y)
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  • What It Does: Rotates the qubit state around the Y-axis of the Bloch sphere by a specified angle.
  • When to Use: To create arbitrary superpositions with real amplitudes.

Sample Code:

import numpy as np
circuit = cirq.Circuit(cirq.ry(np.pi/4)(q0))  # Apply RY gate with π/4 rotation
print("RY Gate Circuit:")
print(circuit)

6. CNOT Gate (Controlled-NOT)
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  • What It Does: Flips the target qubit only if the control qubit is on (1).
  • When to Use: To link two qubits or create entanglement.

Sample Code:

q1 = cirq.NamedQubit("q1")
circuit = cirq.Circuit(cirq.CNOT(q0, q1))  # Apply CNOT gate
print("CNOT Gate Circuit:")
print(circuit)

7. Toffoli Gate (Controlled-Controlled-NOT)
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  • What It Does: Flips the target qubit only if both control qubits are on.
  • When to Use: For more complex logic like an AND operation.

Sample Code:

q2 = cirq.NamedQubit("q2")
circuit = cirq.Circuit(cirq.TOFFOLI(q0, q1, q2))  # Apply Toffoli gate
print("Toffoli Gate Circuit:")
print(circuit)

8. Phase Gates (S and T)
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  • What They Do: Subtly adjust the qubit’s behavior without flipping it.
  • When to Use: To fine-tune circuits for interference effects.

Sample Code:

circuit = cirq.Circuit(cirq.S(q0))  # Apply S gate (90-degree phase shift)
circuit.append(cirq.T(q0))  # Apply T gate (45-degree phase shift)
print("Phase Gates Circuit:")
print(circuit)

9. Swap Gate
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  • What It Does: Swaps the states of two qubits.
  • When to Use: To rearrange qubits in a circuit.

Sample Code:

circuit = cirq.Circuit(cirq.SWAP(q0, q1))  # Apply Swap gate
print("Swap Gate Circuit:")
print(circuit)

10. Controlled Gates
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  • What They Do: Perform an operation on a target qubit only if a control qubit is in a certain state.
  • When to Use: For conditional logic or dependencies between qubits.

Sample Code:

circuit = cirq.Circuit(cirq.ControlledGate(cirq.X)(q0, q1))  # Custom controlled gate
print("Controlled Gate Circuit:")
print(circuit)

Key Rules for Quantum Gates
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  1. Reversible: Every gate can be undone (e.g., applying the same gate twice).
  2. Superposition: Gates like Hadamard make qubits partly “on” and “off.”
  3. Entanglement: Multi-qubit gates (like CNOT) create dependencies between qubits.
  4. Interference: Phase gates adjust probabilities in subtle ways.

Use these gates to build quantum circuits and explore powerful quantum algorithms.