Add Slater determinant and fermionic Gaussian state initial states

.pylintdict

@@ -52,6 +52,7 @@ cargs
 cartesian
 cbit
 ccx
+cdots
 cfg
 chc
 chiral
@@ -100,6 +101,7 @@ debye
 deepcopy
 dft
 diag
+diagonalization
 diagonalize
 diagonalizes
 diagonalizing
@@ -109,6 +111,7 @@ dimensionality
 discoverable
 distinguishability
 dll
+docstring
 dof
 doi
 dt
@@ -122,6 +125,7 @@ eigensolvers
 eigenstate
 eigenstateresult
 eigenstates
+eigenvector
 einact
 einsum
 endian
@@ -232,6 +236,7 @@ kwargs
 kwds
 labelled
 lda
+ldots
 len
 leucine
 levinthal
@@ -246,6 +251,7 @@ ljik
 lk
 logfile
 lookback
+lvert
 lysine
 macos
 majorana
@@ -322,6 +328,7 @@ ortho
 orthonormal
 otimes
 outpath
+overline
 pac
 param
 parameterized
@@ -374,6 +381,7 @@ qubit
 qubits
 qutrit
 radians
+rangle
 rcccx
 rccx
 readme
@@ -417,6 +425,7 @@ setia
 setted
 shende
 sklearn
+slater
 spinop
 springer
 spsa

qiskit_nature/circuit/library/__init__.py

@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2020, 2021.
+# (C) Copyright IBM 2020, 2022.
 #
 # 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
@@ -25,7 +25,9 @@
    :toctree: ../stubs/
    :nosignatures:
 
+   FermionicGaussianState
    HartreeFock
+   SlaterDeterminant
    VSCF
 
 Ansatzes
@@ -64,7 +66,7 @@
     UVCCSD,
 )
 
-from .initial_states import HartreeFock, VSCF
+from .initial_states import FermionicGaussianState, HartreeFock, SlaterDeterminant, VSCF
 
 __all__ = [
     "UCC",
@@ -76,4 +78,6 @@
     "UVCC",
     "UVCCSD",
     "VSCF",
+    "FermionicGaussianState",
+    "SlaterDeterminant",
 ]

qiskit_nature/circuit/library/initial_states/__init__.py

@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2020, 2021.
+# (C) Copyright IBM 2020, 2022.
 #
 # 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
@@ -11,7 +11,14 @@
 # that they have been altered from the originals.
 """Qiskit Nature Circuit Library Initial States."""
 
+from .fermionic_gaussian_state import FermionicGaussianState
 from .hartree_fock import HartreeFock
+from .slater_determinants import SlaterDeterminant
 from .vscf import VSCF
 
-__all__ = ["HartreeFock", "VSCF"]
+__all__ = [
+    "FermionicGaussianState",
+    "HartreeFock",
+    "SlaterDeterminant",
+    "VSCF",
+]

qiskit_nature/circuit/library/initial_states/fermionic_gaussian_state.py

@@ -0,0 +1,173 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021, 2022.
+#
+# 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.
+
+"""Fermionic Gaussian states."""
+
+from typing import Optional, Sequence
+
+import numpy as np
+from qiskit import QuantumCircuit, QuantumRegister
+from qiskit_nature.converters.second_quantization import QubitConverter
+from qiskit_nature.mappers.second_quantization import JordanWignerMapper
+
+from .utils.givens_rotations import _prepare_fermionic_gaussian_state_jordan_wigner
+
+
+def _validate_transformation_matrix(
+    mat: np.ndarray, rtol: float = 1e-5, atol: float = 1e-8
+) -> None:
+    if not len(mat.shape) == 2:
+        raise ValueError(
+            "transformation_matrix must be a 2-dimensional array. "
+            f"Instead, got shape {mat.shape}."
+        )
+
+    n, p = mat.shape  # pylint: disable=invalid-name
+    if p != n * 2:
+        raise ValueError(
+            "transformation_matrix must have shape (n_orbitals, 2 * n_orbitals). "
+            f"Instead, got shape {mat.shape}."
+        )
+
+    left = mat[:, :n]
+    right = mat[:, n:]
+    comm1 = left @ left.T.conj() + right @ right.T.conj()
+    comm2 = left @ right.T + right @ left.T
+    one = np.eye(n)
+    zero = np.zeros((n, n))
+    if not np.allclose(comm1, one, rtol=rtol, atol=atol) or not np.allclose(comm2, zero):
+        raise ValueError(
+            "transformation_matrix does not describe a valid transformation "
+            "of fermionic ladder operators. A valid matrix should have the block form "
+            "[W1 W2] where W1 @ W1.T.conj() + W2 @ W2.T.conj() = I and "
+            "W1 @ W2.T + W2 @ W1.T = 0."
+        )
+
+
+class FermionicGaussianState(QuantumCircuit):
+    r"""A circuit that prepares a fermionic Gaussian state.
+
+    A fermionic Gaussian state is a state of the form
+
+    .. math::
+        b^\dagger_1 \cdots b^\dagger_{N_p} \lvert \overline{\text{vac}} \rangle
+
+    where
+
+    .. math::
+        \begin{pmatrix}
+            b^\dagger_1 \\
+            \vdots \\
+            b^\dagger_N \\
+        \end{pmatrix}
+        = W
+        \begin{pmatrix}
+            a^\dagger_1 \\
+            \vdots \\
+            a^\dagger_N \\
+            a_1 \\
+            \vdots \\
+            a_N
+        \end{pmatrix},
+
+    - :math:`a^\dagger_1, \ldots, a^\dagger_{N}` are the fermionic creation operators
+    - :math:`W` is an :math:`N \times 2N` matrix such that
+      :math:`b^\dagger_1, \ldots, b^\dagger_{N}` also satisfy the
+      fermionic anticommutation relations
+    - :math:`\lvert \overline{\text{vac}} \rangle` is the mutual 0-eigenvector of
+      the operators :math:`\{b_j^\dagger b_j\}`
+
+    The matrix :math:`W` has the block form
+
+    .. math::
+        \begin{pmatrix}
+            W_1 & W_2
+        \end{pmatrix}
+
+    where :math:`W_1` and :math:`W_2` must satisfy
+
+    .. math::
+        W_1 W_1^\dagger + W_2 W_2^\dagger = I \\
+        W_1 W_2^T + W_2 W_1^T = 0
+
+    The matrix :math:`W` is commonly obtained by calling the
+    :meth:`~.QuadraticHamiltonian.diagonalizing_bogoliubov_transform`
+    method of the :class:`~.QuadraticHamiltonian` class.
+    This matrix is used to create circuits that prepare eigenstates of the
+    quadratic Hamiltonian.
+
+    Currently, only the Jordan-Wigner Transformation is supported.
+
+    Reference: `arXiv:1711.05395`_
+
+    .. _arXiv:1711.05395: https://arxiv.org/abs/1711.05395
+    """
+
+    def __init__(
+        self,
+        transformation_matrix: np.ndarray,
+        occupied_orbitals: Optional[Sequence[int]] = None,
+        qubit_converter: QubitConverter = None,
+        validate: bool = True,
+        rtol: float = 1e-5,
+        atol: float = 1e-8,
+        **circuit_kwargs,
+    ) -> None:
+        r"""
+        Args:
+            transformation_matrix: The matrix :math:`W` that specifies the coefficients of the
+                new creation operators in terms of the original creation and annihilation operators.
+                This matrix must satisfy special constraints; see the main body of the docstring
+                of this class.
+            occupied_orbitals: The pseudo-particle orbitals to fill. These refer to the indices
+                of the operators :math:`\{b^\dagger_j\}` from the main body of the docstring
+                of this function. The default behavior is to use the empty set of orbitals,
+                which corresponds to a state with zero pseudo-particles.
+            qubit_converter: a QubitConverter instance.
+            validate: Whether to validate the inputs.
+            rtol: Relative numerical tolerance for input validation.
+            atol: Absolute numerical tolerance for input validation.
+            circuit_kwargs: Keyword arguments to pass to the QuantumCircuit initializer.
+
+        Raises:
+            ValueError: transformation_matrix must be a 2-dimensional array.
+            ValueError: transformation_matrix must have shape (n_orbitals, 2 * n_orbitals).
+            NotImplementedError: Currently, only the Jordan-Wigner Transform is supported.
+                Please use
+                :class:`qiskit_nature.mappers.second_quantization.JordanWignerMapper`
+                to construct the qubit mapper used to construct `qubit_converter`.
+        """
+        if validate:
+            _validate_transformation_matrix(transformation_matrix, rtol=rtol, atol=atol)
+
+        if occupied_orbitals is None:
+            occupied_orbitals = []
+        if qubit_converter is None:
+            qubit_converter = QubitConverter(JordanWignerMapper())
+
+        n, _ = transformation_matrix.shape
+        register = QuantumRegister(n)
+        super().__init__(register, **circuit_kwargs)
+
+        if isinstance(qubit_converter.mapper, JordanWignerMapper):
+            operations = _prepare_fermionic_gaussian_state_jordan_wigner(
+                register, transformation_matrix, occupied_orbitals
+            )
+            for gate, qubits in operations:
+                self.append(gate, qubits)
+        else:
+            raise NotImplementedError(
+                "Currently, only the Jordan-Wigner Transform is supported. "
+                "Please use "
+                "qiskit_nature.mappers.second_quantization.JordanWignerMapper "
+                "to construct the qubit mapper used to construct qubit_converter."
+            )