@@ -7,6 +7,7 @@ matrix written in the computational basis.

 import numpy as np

 __all__ = [

+    "apply",

     "n_qubits",

     "controlled",

     # -- Single qubit gates --

@@ -28,6 +29,38 @@ __all__ = [

 ]  # type: ignore

+def apply(gate, qubits, state):

+    n_gate_qubits = gate.shape[0].bit_length() - 1

+    n_state_qubits = state.shape[0].bit_length() - 1

+    assert len(qubits) == n_gate_qubits

+

+    # We can view an n-qubit gate as a 2*n-tensor (n contravariant and n contravariant

+    # indices) and an n-qubit state as an n-tensor (contravariant indices)

+    # with each axis having length 2 (the state space of a single qubit).

+    gate = gate.reshape((2,) * 2 * n_gate_qubits)

+    state = state.reshape((2,) * n_state_qubits)

+

+    # Our qubits are labeled from least significant to most significant, i.e. our

+    # computational basis (for e.g. 2 qubits) is ordered like |00⟩, |01⟩, |10⟩, |11⟩.

+    # We represent the state as a tensor in *row-major* order; this means that the

+    # axis ordering is *backwards* compared to the qubit ordering (the least significant

+    # qubit corresponds to the *last* axis in the tensor etc.)

+    qubit_axes = tuple(n_state_qubits - 1 - np.asarray(qubits))

+

+    # Applying the gate to the state vector is then the tensor product over the appropriate axes

+    axes = (np.arange(n_gate_qubits, 2 * n_gate_qubits), qubit_axes)

+    new_state = np.tensordot(gate, state, axes=axes)

+

+    # tensordot effectively re-orders the qubits such that the qubits we operated

+    # on are in the most-significant positions (i.e. their axes come first). We

+    # thus need to transpose the axes to place them back into their original positions.

+    untouched_axes = tuple(

+        idx for idx in range(n_state_qubits) if idx not in qubit_axes

+    )

+    inverse_permutation = np.argsort(qubit_axes + untouched_axes)

+    return np.transpose(new_state, inverse_permutation).reshape(-1)

+

+

 def _check_valid_gate(gate):

     if not (

         # is an array