Add circuit generation from set of stabilizers (Qiskit#11483)

* Add stabilizer_to_circuit function

* Fix verification test

* Mention `stabilizer_to_circuit` in `StabilizerState` documentation

* * Add `from_stabilizer_list` function to Stabilizer state
* Move to synthesis library and rename accordingly
* Add pseudo-random tests
* Fix docstrings

* doc fixes

* Allow any Collection and not just list, fix naming, tests, and docs accordingly.

* typo

* missed rename

* Documentation fixes

* fix indent

* fix indent 2

* fix indent 3

* Rewrite using `Pauli` instead of string.

qiskit/quantum_info/states/stabilizerstate.py

@@ -15,6 +15,9 @@
 """
 
 from __future__ import annotations
+
+from collections.abc import Collection
+
 import numpy as np
 
 from qiskit.exceptions import QiskitError
@@ -57,6 +60,17 @@ class StabilizerState(QuantumState):
         {'00': 0.5, '11': 0.5}
         1
 
+    Given a list of stabilizers, :meth:`qiskit.quantum_info.StabilizerState.from_stabilizer_list`
+    returns a state stabilized by the list
+
+    .. code-block:: python
+
+        from qiskit.quantum_info import StabilizerState
+
+        stabilizer_list = ["ZXX", "-XYX", "+ZYY"]
+        stab = StabilizerState.from_stabilizer_list(stabilizer_list)
+
+
     References:
         1. S. Aaronson, D. Gottesman, *Improved Simulation of Stabilizer Circuits*,
            Phys. Rev. A 70, 052328 (2004).
@@ -91,6 +105,36 @@ def __init__(
         # Initialize
         super().__init__(op_shape=OpShape.auto(num_qubits_r=self._data.num_qubits, num_qubits_l=0))
 
+    @classmethod
+    def from_stabilizer_list(
+        cls,
+        stabilizers: Collection[str],
+        allow_redundant: bool = False,
+        allow_underconstrained: bool = False,
+    ) -> StabilizerState:
+        """Create a stabilizer state from the collection of stabilizers.
+
+        Args:
+            stabilizers (Collection[str]): list of stabilizer strings
+            allow_redundant (bool): allow redundant stabilizers (i.e., some stabilizers
+                can be products of the others)
+            allow_underconstrained (bool): allow underconstrained set of stabilizers (i.e.,
+                the stabilizers do not specify a unique state)
+
+        Return:
+            StabilizerState: a state stabilized by stabilizers.
+        """
+
+        # pylint: disable=cyclic-import
+        from qiskit.synthesis.stabilizer import synth_circuit_from_stabilizers
+
+        circuit = synth_circuit_from_stabilizers(
+            stabilizers,
+            allow_redundant=allow_redundant,
+            allow_underconstrained=allow_underconstrained,
+        )
+        return cls(circuit)
+
     def __eq__(self, other):
         return (self._data.stab == other._data.stab).all()
 

qiskit/synthesis/__init__.py

@@ -73,6 +73,7 @@
 
 .. autofunction:: synth_stabilizer_layers
 .. autofunction:: synth_stabilizer_depth_lnn
+.. autofunction:: synth_circuit_from_stabilizers
 
 Discrete Basis Synthesis
 ========================
@@ -123,6 +124,10 @@
     synth_cnotdihedral_two_qubits,
     synth_cnotdihedral_general,
 )
-from .stabilizer import synth_stabilizer_layers, synth_stabilizer_depth_lnn
+from .stabilizer import (
+    synth_stabilizer_layers,
+    synth_stabilizer_depth_lnn,
+    synth_circuit_from_stabilizers,
+)
 from .discrete_basis import SolovayKitaevDecomposition, generate_basic_approximations
 from .qft import synth_qft_line

qiskit/synthesis/stabilizer/__init__.py

@@ -13,3 +13,4 @@
 """Module containing stabilizer state preparation circuit synthesis."""
 
 from .stabilizer_decompose import synth_stabilizer_layers, synth_stabilizer_depth_lnn
+from .stabilizer_circuit import synth_circuit_from_stabilizers

qiskit/synthesis/stabilizer/stabilizer_circuit.py

@@ -0,0 +1,149 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2024.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+"""
+Stabilizer to circuit function
+"""
+from __future__ import annotations
+
+from collections.abc import Collection
+
+import numpy as np
+
+from qiskit.quantum_info import PauliList
+from qiskit.exceptions import QiskitError
+from qiskit.circuit import QuantumCircuit
+from qiskit.quantum_info.operators.symplectic.clifford import Clifford
+
+
+def synth_circuit_from_stabilizers(
+    stabilizers: Collection[str],
+    allow_redundant: bool = False,
+    allow_underconstrained: bool = False,
+    invert: bool = False,
+) -> QuantumCircuit:
+    # pylint: disable=line-too-long
+    """Synthesis of a circuit that generates a state stabilized by the stabilziers
+    using Gaussian elimination with Clifford gates.
+    If the stabilizers are underconstrained, and `allow_underconstrained` is `True`,
+    the circuit will output one of the states stabilized by the stabilizers.
+    Based on stim implementation.
+
+    Args:
+        stabilizers (Collection[str]): list of stabilizer strings
+        allow_redundant (bool): allow redundant stabilizers (i.e., some stabilizers
+            can be products of the others)
+        allow_underconstrained (bool): allow underconstrained set of stabilizers (i.e.,
+            the stabilizers do not specify a unique state)
+        invert (bool): return inverse circuit
+
+    Return:
+        QuantumCircuit: a circuit that generates a state stabilized by `stabilizers`.
+
+    Raises:
+        QiskitError: if the stabilizers are invalid, do not commute, or contradict each other,
+                     if the list is underconstrained and `allow_underconstrained` is `False`,
+                     or if the list is redundant and `allow_redundant` is `False`.
+
+    Reference:
+        1. https://github.com/quantumlib/Stim/blob/c0dd0b1c8125b2096cd54b6f72884a459e47fe3e/src/stim/stabilizers/conversions.inl#L469
+        2. https://quantumcomputing.stackexchange.com/questions/12721/how-to-calculate-destabilizer-group-of-toric-and-other-codes
+
+    """
+    stabilizer_list = PauliList(stabilizers)
+    if np.any(stabilizer_list.phase % 2):
+        raise QiskitError("Some stabilizers have an invalid phase")
+    if len(stabilizer_list.commutes_with_all(stabilizer_list)) < len(stabilizer_list):
+        raise QiskitError("Some stabilizers do not commute.")
+
+    num_qubits = stabilizer_list.num_qubits
+    circuit = QuantumCircuit(num_qubits)
+
+    used = 0
+    for i in range(len(stabilizer_list)):
+        curr_stab = stabilizer_list[i].evolve(Clifford(circuit), frame="s")
+
+        # Find pivot.
+        pivot = used
+        while pivot < num_qubits:
+            if curr_stab[pivot].x or curr_stab[pivot].z:
+                break
+            pivot += 1
+
+        if pivot == num_qubits:
+            if curr_stab.x.any():
+                raise QiskitError(
+                    f"Stabilizer {i} ({stabilizer_list[i]}) anti-commutes with some of "
+                    "the previous stabilizers."
+                )
+            if curr_stab.phase == 2:
+                raise QiskitError(
+                    f"Stabilizer {i} ({stabilizer_list[i]}) contradicts "
+                    "some of the previous stabilizers."
+                )
+            if curr_stab.z.any() and not allow_redundant:
+                raise QiskitError(
+                    f"Stabilizer {i} ({stabilizer_list[i]}) is a product of the others "
+                    "and allow_redundant is False. Add allow_redundant=True "
+                    "to the function call if you want to allow redundant stabilizers."
+                )
+            continue
+
+        # Change pivot basis to the Z axis.
+        if curr_stab[pivot].x:
+            if curr_stab[pivot].z:
+                circuit.h(pivot)
+                circuit.s(pivot)
+                circuit.h(pivot)
+                circuit.s(pivot)
+                circuit.s(pivot)
+            else:
+                circuit.h(pivot)
+
+        # Cancel other terms in Pauli string.
+        for j in range(num_qubits):
+            if j == pivot or not (curr_stab[j].x or curr_stab[j].z):
+                continue
+            p = curr_stab[j].x + curr_stab[j].z * 2
+            if p == 1:  # X
+                circuit.h(pivot)
+                circuit.cx(pivot, j)
+                circuit.h(pivot)
+            elif p == 2:  # Z
+                circuit.cx(j, pivot)
+            elif p == 3:  # Y
+                circuit.h(pivot)
+                circuit.s(j)
+                circuit.s(j)
+                circuit.s(j)
+                circuit.cx(pivot, j)
+                circuit.h(pivot)
+                circuit.s(j)
+
+        # Move pivot to diagonal.
+        if pivot != used:
+            circuit.swap(pivot, used)
+
+        # fix sign
+        curr_stab = stabilizer_list[i].evolve(Clifford(circuit), frame="s")
+        if curr_stab.phase == 2:
+            circuit.x(used)
+        used += 1
+
+    if used < num_qubits and not allow_underconstrained:
+        raise QiskitError(
+            "Stabilizers are underconstrained and allow_underconstrained is False."
+            " Add allow_underconstrained=True  to the function call "
+            "if you want to allow underconstrained stabilizers."
+        )
+    if invert:
+        return circuit
+    return circuit.inverse()

releasenotes/notes/add-synth-circuit-from-stabilizer-list-4cf9cfa01bbc7ddf.yaml

@@ -0,0 +1,14 @@
+---
+features:
+  - |
+    Add :func:`qiskit.synthesis.synth_circuit_from_stabilizers` function that, given stabilizers,
+    returns a circuit that outputs the state stabilized by the stabilizers.
+
+  - |
+    Add :meth:`qiskit.quantum_info.StabilizerState.from_stabilizer_list` method
+    that generates a stabilizer state from a list of stabilizers::
+
+        from qiskit.quantum_info import StabilizerState
+
+        stabilizer_list = ["ZXX", "-XYX", "+ZYY"]
+        stab = StabilizerState.from_stabilizer_list(stabilizer_list)