Quantum

A quantum computing simulator in Julia. Implements qubit state vectors, quantum gates, measurement, entanglement, and circuit visualization.

Features

• State Vectors: Represent quantum states as complex amplitude vectors
• Quantum Gates: Pauli (X, Y, Z), Hadamard, Phase (S, T), CNOT, SWAP, and rotations
• Measurement: Born rule probabilities, partial measurement, repeated sampling
• Entanglement: Tensor products, partial trace, concurrence, entropy
• Circuits: Compose gates into circuits, execute on states
• Visualization: ASCII circuit diagrams and state display

Installation

using Pkg
Pkg.develop(path="path/to/quantum")

Quick Start

using Quantum

# Create a Bell state |Φ+⟩ = (|00⟩ + |11⟩) / √2
c = Circuit(2)
add!(c, H, 1)
add!(c, CNOT, 1, 2)

# View the circuit
show_circuit(c)
# q1: [H]─●─
# q2: ───⊕─

# Execute and show results
state = execute(c)
show_state(state)
# |00⟩: 0.7071
# |11⟩: 0.7071

# Sample measurements
counts = simulate(c, 1000)
# Dict(0 => 512, 3 => 488)

Using Circuits

# Build a circuit
c = Circuit(3)
add!(c, H, 1)           # Hadamard on qubit 1
add!(c, CNOT, 1, 2)     # CNOT: control 1, target 2
add!(c, X, 3)           # Pauli-X on qubit 3

# Convenience methods
add_h!(c, 1)
add_x!(c, 2)
add_cnot!(c, 1, 3)

# Circuit info
gate_count(c)  # Number of operations
depth(c)       # Circuit depth

Available Gates

Single-Qubit

• I_GATE - Identity
• X, Y, Z - Pauli gates
• H - Hadamard
• S, T - Phase gates
• Rx(θ), Ry(θ), Rz(θ) - Rotation gates

Two-Qubit

• CNOT - Controlled-NOT
• CZ - Controlled-Z
• SWAP - Swap qubits
• iSWAP - iSWAP gate

Controlled Gates

# Create controlled version of any single-qubit gate
add_controlled!(circuit, X, [1], [2])  # Controlled-X
add_controlled!(circuit, Z, [1, 2], [3])  # Toffoli-like

Measurement

state = execute(circuit)

# Get probability distribution
probs = probabilities(state)

# Measure all qubits (collapses state)
result, collapsed = measure(state)

# Measure single qubit
bit, collapsed = measure_qubit(state, 1)

# Sample without collapse
counts = sample(state, 1000)

# Expectation value
expectation(state, Z)

Entanglement

# Tensor product of states
combined = tensor(state_a, state_b)

# Check if entangled
is_separable(state)  # false for entangled states

# Entanglement measure (2 qubits)
concurrence(state)  # 0 = separable, 1 = maximally entangled

# Partial trace (reduced density matrix)
rho = partial_trace(state, [1])  # Keep qubit 1

# Von Neumann entropy
von_neumann_entropy(rho)

Visualization

# Circuit diagram
show_circuit(circuit)

# State in ket notation
show_state(state)

# Probability histogram
show_probabilities(state)

# Bloch sphere (single qubit)
show_bloch(state)

Examples

See examples/ for:

• bell_state.jl - Bell state preparation and measurement
• teleportation.jl - Quantum teleportation protocol
• grover.jl - Grover's search algorithm
• qft.jl - Quantum Fourier Transform

Run an example:

julia --project=. examples/bell_state.jl

API Reference

States

• zero_state(n) - Create |0⟩^⊗n
• one_state(n) - Create |1⟩^⊗n
• basis_state(n, i) - Create |i⟩
• is_normalized(state) - Check normalization

Operations

• apply(state, gate, target) - Apply gate
• apply(state, gate, [targets]) - Multi-qubit gate

Circuits

• Circuit(n) - Create n-qubit circuit
• add!(circuit, gate, targets...) - Add operation
• execute(circuit) - Run from |0⟩^n
• simulate(circuit, shots) - Sample results

Limitations

• Maximum ~20 qubits (2^20 amplitudes ≈ 1M complex numbers)
• Ideal gates only (no noise model)
• No circuit optimization passes

Running Tests

julia --project=. test/runtests.jl

License

MIT