1. qib Basics

In this basic example, we construct and “run” a quantum circuit which prepares a Bell state.

1.1. Circuit construction

# import the qib package; see the README for installation instructions
import qib

As first step, we define a qubit “field” with two sites, which is essentially a quantum register containing two qubits. Fields can also host fermionic particles, for example, which will become relevant for defining chemistry Hamiltonians.

field = qib.field.Field(qib.field.ParticleType.QUBIT, qib.lattice.IntegerLattice((2,)))

# retrieve the two qubits of the field
qa = qib.field.Qubit(field, 0)
qb = qib.field.Qubit(field, 1)

Next, we define standard Hadamard and CNOT quantum gates and associate the qubits with them. In qib, gates contain a reference to the qubits which they act on.

# Hadamard gate
hadamard = qib.HadamardGate(qa)
# CNOT gate
cnot = qib.ControlledGate(qib.PauliXGate(qb), 1).set_control(qa)

We now construct a circuit out of the gates. The gates “know” already which qubits they are applied to.

circuit = qib.Circuit()
circuit.append_gate(hadamard)
circuit.append_gate(cnot)

The following code generates the matrix representation of the circuit. The list of fields passed as argument determines the logical ordering of the qubits.

circuit.as_matrix([field]).toarray()

array([[ 0.70710678,  0.        ,  0.70710678,  0.        ],
       [ 0.        ,  0.70710678,  0.        ,  0.70710678],
       [ 0.        ,  0.70710678,  0.        , -0.70710678],
       [ 0.70710678,  0.        , -0.70710678,  0.        ]])

1.2. Running the circuit

We use qib’s built-in statevector simulator to “run” the quantum circuit:

statesim = qib.simulator.StatevectorSimulator()

ψ = statesim.run(circuit, [field], None)

As expected, ψ is a Bell state:

ψ

array([0.70710678, 0.        , 0.        , 0.70710678])

Alternatively, qib also implements a tensor network simulator:

netsim = qib.simulator.TensorNetworkSimulator()

ψn = netsim.run(circuit, [field], None)

The output quantum state is represented as tensor, using a tensor “leg” (or axis) for each qubit wire.

ψn

array([[0.70710678, 0.        ],
       [0.        , 0.70710678]])

We obtain the usual statevector by flattening the tensor:

ψn.reshape(-1)

array([0.70710678, 0.        , 0.        , 0.70710678])