Quantum Gates

Quantum gates are the building blocks of quantum circuits. This guide covers the basic gates available in LeafSheep QVU.

Single-Qubit Only Gates

These gates cannot be used as controlled operations.

Basic Gates

• H (Hadamard): Creates superposition states
  • No parameters
  • Color: Gold (#FFD700)

• I (Identity): Does nothing to the qubit state
  • No parameters
  • Color: Light Pink (#FFB6C1)

Phase Gates

• S Gate: Fixed π/2 phase rotation
  • No parameters (equivalent to P(π/2))
  • Color: Turquoise (#00CED1)

• T Gate: Fixed π/4 phase rotation
  • No parameters (equivalent to P(π/4))
  • Color: Tomato (#FF6347)

Special Operations

• Reset to |0⟩: Resets qubit to ground state
  • No parameters
  • Color: Light Gray (#D3D3D3)

Controllable Gates

These gates can be used with control qubits.

Pauli Gates

• X (NOT Gate): Flips the state of a qubit
  • No parameters
  • Control qubits: Up to maximum qubit number
  • Color: Light Green (#98FB98)

• Y Gate: Rotates the state around Y-axis
  • No parameters
  • Control qubits: Up to 1
  • Color: Light Pink (#FFB6C1)

• Z Gate: Adds a phase difference
  • No parameters
  • Control qubits: Up to 2
  • Color: Silver (#B8C0C0)

Rotation Gates

• RX(θ): Rotation around X-axis
  • Parameter θ (theta): Value from -2 to 2 (multiplied by π)
  • Control qubits: Up to 1
  • Color: Yellow (#FFFF00)

• RY(θ): Rotation around Y-axis
  • Parameter θ (theta): Value from -2 to 2 (multiplied by π)
  • Control qubits: Up to 1
  • Color: Yellow (#FFFF00)

• RZ(φ): Rotation around Z-axis
  • Parameter φ (phi): Value from -2 to 2 (multiplied by π)
  • Control qubits: Up to 1
  • Color: Yellow (#FFFF00)

Phase Gates

• P(θ): Phase rotation
  • Parameter θ (theta): Value from -2 to 2 (multiplied by π)
  • Control qubits: Up to 1
  • Color: Light Green (#98FB98)

Universal Gate

• U3(θ,φ,λ): General single-qubit rotation
  • Parameter θ (theta): Value from 0 to 1 (multiplied by π)
  • Parameter φ (phi): Value from -2 to 2 (multiplied by π)
  • Parameter λ (lambda): Value from -2 to 2 (multiplied by π)
  • Control qubits: Up to 1
  • Color: Bisque (#FFE4C4)

Parameter Panel

When you select and hover a gate, the parameter panel appears next to the gate:

• Enter values between -2 and 2 (these are multiplied by π)
• Values are multipliers of π (e.g., 0.5 means 0.5π)

Common Parameter Values

Here are some frequently used parameter values:

• 0.5: Means 0.5π (π/2), used in S gates
• 0.25: Means 0.25π (π/4), used in T gates
• 1.0: Means π, full phase rotation
• -0.5: Means -0.5π (-π/2), inverse rotation

note

All angle parameters are multipliers of π. For example:

• Entering 0.5 means 0.5π (or π/2)
• Entering 0.25 means 0.25π (or π/4)
• Entering 1 means π
• Entering -2 means -2π

Tips for Working with Parameters

• Use mathematical expressions for precise values (e.g., "1/2" for π/2)
• Parameters update the circuit in real-time

Using Gates in LeafSheep QVU

1. Select a gate from the left panel
2. Drag it onto your circuit

Example: Creating a CNOT Gate

1. Add an X gate to your circuit
2. Hover over the X gate to reveal control points
3. Click and drag from the control point to another qubit
4. The X gate is now controlled by the other qubit (CNOT)