# Summary¶

QCircuits is a lightweight Python package for simulating the operation of small-scale quantum computers, based on the quantum circuit model. It uses type (d, 0) and type (d, d) tensors to represent state vectors for and operators on d-qubit systems, rather than using straight vectors and matrices produced by Kronecker products, as is more typical.

# Documentation, tutorial, and examples¶

# Installation¶

Install with pip:

`pip install qcircuits`

or from the source at github.com/grey-area/qcircuits.

# Example usage: quantum teleportation¶

See the examples page for more examples.

Quantum teleportation example:

Quantum circuit:

Code:

```
import qcircuits as qc
# Quantum Teleportation: transmitting two classical bits to transport a qubit state
# Alice has a qubit in a given quantum state.
# Alice and Bob have previously prepared a Bell state, and have since
# physically separated the qubits.
# Alice manipulates her hidden qubit and her half of the Bell state, and then
# measures both qubits.
# She sends the result (two classical bits) to Bob, who is able to reconstruct
# Alice's state by applying operators based on the measurement outcomes.
def quantum_teleportation(alice_state):
# Get operators we will need
CNOT = qc.CNOT()
H = qc.Hadamard()
X = qc.PauliX()
Z = qc.PauliZ()
# The prepared, shared Bell state
bell = qc.bell_state(0, 0)
# The whole state vector
phi = alice_state * bell
# Apply CNOT and Hadamard gate
phi = CNOT(phi, qubit_indices=[0, 1])
phi = H(phi, qubit_indices=[0])
# Measure the first two bits
# The only uncollapsed part of the state vector is Bob's
M1, M2 = phi.measure(qubit_indices=[0, 1], remove=True)
# Apply X and/or Z gates to third qubit depending on measurements
if M2:
phi = X(phi)
if M1:
phi = Z(phi)
return phi
if __name__ == '__main__':
# Alice's original state to be teleported to Bob
alice = qc.qubit(theta=1.5, phi=0.5, global_phase=0.2)
# Bob's state after quantum teleportation
bob = quantum_teleportation(alice)
print('Original state:', alice)
print('\nTeleported state:', bob)
```