# cirq.targeted_left_multiply¶

cirq.targeted_left_multiply(left_matrix: numpy.ndarray, right_target: numpy.ndarray, target_axes: Sequence[int], out: Optional[numpy.ndarray] = None) → numpy.ndarray[source]

Left-multiplies the given axes of the target tensor by the given matrix.

Note that the matrix must have a compatible tensor structure.

For example, if you have an 6-qubit state vector input_state with shape
(2, 2, 2, 2, 2, 2), and a 2-qubit unitary operation op with shape
(2, 2, 2, 2), and you want to apply op to the 5’th and 3’rd qubits
within input_state, then the output state vector is computed as follows:
output_state = cirq.targeted_left_multiply(op, input_state, [5, 3])

This method also works when the right hand side is a matrix instead of a
vector. If a unitary circuit’s matrix is old_effect, and you append
a CNOT(q1, q4) operation onto the circuit, where the control q1 is the qubit
at offset 1 and the target q4 is the qubit at offset 4, then the appended
circuit’s unitary matrix is computed as follows:
new_effect = cirq.targeted_left_multiply(
left_matrix=cirq.unitary(cirq.CNOT).reshape((2, 2, 2, 2)),
right_target=old_effect,
target_axes=[1, 4])

Parameters
• left_matrix – What to left-multiply the target tensor by.

• right_target – A tensor to carefully broadcast a left-multiply over.

• target_axes – Which axes of the target are being operated on.

• out – The buffer to store the results in. If not specified or None, a new buffer is used. Must have the same shape as right_target.

Returns

The output tensor.