# qrisp.tensordot#

tensordot(a, b, axes)[source]#

Port of numpy tensordot with similar semantics.

Parameters
aQuantumArray

The first operand.

bQuantumArray

The second operand.

axestuple

The axes to contract.

Returns
QuantumArray

The QuantumArray containing the result of tensordot.

Examples

Using tensordot we can perform the arithmetic for simulating a quantum computer on a quantum computer.

>>> import numpy as np
>>> from qrisp import QuantumFloat, QuantumArray, tensordot


Initiate the QuantumArray holding the statevector. We initate the state of uniform superposition

$\ket{+} = \frac{1}{\sqrt{2^n}} \sum_{i = 0}^{2^n - 1} \ket{i}$
>>> qfloat_type = QuantumFloat(3, -2, signed = True)
>>> num_qubits = 4
>>> statevector = QuantumArray(shape = 2**num_qubits, qtype = qfloat_type)
>>> statevector[:] = [1/(2**num_qubits)**0.5]*2**num_qubits
>>> print(statevector)
{OutcomeArray([0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25]): 1.0}


Initiate the QuantumArray holding the unitary of a Z-gate

>>> z_gate = QuantumArray(shape = (2,2), qtype = qfloat_type)
>>> z_gate[:] = [[1,0], [0,-1]]
>>> print(z_gate)
{OutcomeArray([[ 1.,  0.],
[ 0., -1.]]): 1.0}


Perform the contraction

>>> statevector = statevector.reshape(num_qubits*[2])
>>> target_qubit = 3
>>> new_statevector = tensordot(z_gate, statevector, (1, target_qubit))
>>> new_statevector = new_statevector.reshape(2**num_qubits)
>>> print(new_statevector)
{OutcomeArray([ 0.25,  0.25,  0.25,  0.25,  0.25,  0.25,  0.25,  0.25,
-0.25, -0.25, -0.25, -0.25, -0.25, -0.25, -0.25, -0.25]): 1.0}


We perform a similar contraction using numpy arrays

>>> from numpy import tensordot
>>> statevector = 0.25*np.ones(2**num_qubits)
>>> print(statevector)
[0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25]
>>> statevector = statevector.reshape(num_qubits*[2])
>>> z_gate = np.zeros((2,2))
>>> z_gate[:] = [[1,0], [0,-1]]
>>> new_statevector = tensordot(z_gate, statevector, (1, target_qubit))
>>> print(new_statevector.reshape(2**num_qubits))
[ 0.25  0.25  0.25  0.25  0.25  0.25  0.25  0.25 -0.25 -0.25 -0.25 -0.25
-0.25 -0.25 -0.25 -0.25]