Merge pull request #1492 from qiboteam/to_stinespring

Add `to_stinespring` to `quantum_info.superoperator_transformations`

Author: scarrazza

doc/source/api-reference/qibo.rst

@@ -2175,6 +2175,12 @@ To Chi
 .. autofunction:: qibo.quantum_info.to_chi
 
 
+To Stinespring
+""""""""""""""
+
+.. autofunction:: qibo.quantum_info.to_stinespring
+
+
 Choi to Liouville
 """""""""""""""""
 

src/qibo/quantum_info/superoperator_transformations.py

@@ -1,7 +1,7 @@
 """Module with the most commom superoperator transformations."""
 
 import warnings
-from typing import Optional
+from typing import List, Optional, Tuple, Union
 
 import numpy as np
 from scipy.optimize import minimize
@@ -303,6 +303,50 @@ def to_chi(
     return channel
 
 
+def to_stinespring(
+    channel,
+    partition: Optional[Union[List[int], Tuple[int, ...]]] = None,
+    nqubits: Optional[int] = None,
+    initial_state_env=None,
+    backend=None,
+):
+    """Convert quantum ``channel`` :math:`U` to its Stinespring representation :math:`U_{0}`.
+
+    It uses the Kraus representation as an intermediate step.
+
+    Args:
+        channel (ndarray): quantum channel.
+        nqubits (int, optional): total number of qubits in the system that is
+            interacting with the environment. Must be equal or greater than
+            the number of qubits ``channel`` acts on. If ``None``,
+            defaults to the number of qubits in ``channel``.
+            Defauts to ``None``.
+        initial_state_env (ndarray, optional): statevector representing the
+            initial state of the enviroment. If ``None``, it assumes the
+            environment in its ground state. Defaults to ``None``.
+        backend (:class:`qibo.backends.abstract.Backend`, optional): backend
+            to be used in the execution. If ``None``, it uses
+            :class:`qibo.backends.GlobalBackend`. Defaults to ``None``.
+
+    Returns:
+        ndarray: Quantum channel in its Stinespring representation :math:`U_{0}`.
+    """
+    backend = _check_backend(backend)
+
+    if partition is None:
+        nqubits_channel = int(np.log2(channel.shape[-1]))
+        partition = tuple(range(nqubits_channel))
+
+    channel = kraus_to_stinespring(
+        [(partition, channel)],
+        nqubits=nqubits,
+        initial_state_env=initial_state_env,
+        backend=backend,
+    )
+
+    return channel
+
+
 def choi_to_liouville(choi_super_op, order: str = "row", backend=None):
     """Converts Choi representation :math:`\\Lambda` of quantum channel
     to its Liouville representation :math:`\\mathcal{E}`.
@@ -320,7 +364,6 @@ def choi_to_liouville(choi_super_op, order: str = "row", backend=None):
         \\Lambda_{\\alpha\\beta, \\, \\gamma\\delta} \\mapsto
             \\Lambda_{\\delta\\beta, \\, \\gamma\\alpha} \\equiv \\mathcal{E}
 
-
     Args:
         choi_super_op: Choi representation of quantum channel.
         order (str, optional): If ``"row"``, reshuffling is performed
@@ -640,7 +683,7 @@ def choi_to_stinespring(
     if nqubits is None:
         nqubits = int(np.log2(kraus_ops[0].shape[0]))
 
-    nqubits_list = [tuple(range(nqubits)) for _ in range(len(kraus_ops))]
+    nqubits_list = [tuple(range(nqubits))] * len(kraus_ops)
 
     kraus_ops = list(zip(nqubits_list, kraus_ops))
 

tests/test_quantum_info_superoperator_transformations.py

@@ -3,6 +3,7 @@
 
 from qibo import matrices
 from qibo.config import PRECISION_TOL
+from qibo.quantum_info.linalg_operations import partial_trace
 from qibo.quantum_info.random_ensembles import random_density_matrix, random_statevector
 from qibo.quantum_info.superoperator_transformations import (
     chi_to_choi,
@@ -40,6 +41,7 @@
     to_choi,
     to_liouville,
     to_pauli_liouville,
+    to_stinespring,
     unvectorization,
     vectorization,
 )
@@ -363,6 +365,28 @@ def test_to_chi(backend, normalize, order, pauli_order):
     backend.assert_allclose(chi, test_chi, atol=PRECISION_TOL)
 
 
+@pytest.mark.parametrize("partition", [None, (0,)])
+@pytest.mark.parametrize("test_a0", [test_a0])
+def test_to_stinespring(backend, test_a0, partition):
+    test_a0_ = backend.cast(test_a0)
+    state = random_density_matrix(2, seed=8, backend=backend)
+
+    target = test_a0_ @ state @ backend.np.conj(test_a0_.T)
+
+    environment = (1, 2)
+
+    global_state = backend.identity_density_matrix(len(environment), normalize=True)
+    global_state = backend.np.kron(state, global_state)
+
+    stinespring = to_stinespring(
+        test_a0_, partition=partition, nqubits=len(environment) + 1, backend=backend
+    )
+    stinespring = stinespring @ global_state @ backend.np.conj(stinespring.T)
+    stinespring = partial_trace(stinespring, traced_qubits=environment, backend=backend)
+
+    backend.assert_allclose(stinespring, target, atol=PRECISION_TOL)
+
+
 @pytest.mark.parametrize("test_superop", [test_superop])
 @pytest.mark.parametrize("order", ["row", "column"])
 def test_choi_to_liouville(backend, order, test_superop):