Source code for pennylane.templates.subroutines.uccsd

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

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Contains the UCCSD template.
# pylint: disable-msg=too-many-branches,too-many-arguments,protected-access
import numpy as np
import pennylane as qml
from pennylane.operation import Operation, AnyWires
from pennylane.ops import BasisState

[docs]class UCCSD(Operation): r"""Implements the Unitary Coupled-Cluster Singles and Doubles (UCCSD) ansatz. The UCCSD ansatz calls the :func:`~.FermionicSingleExcitation` and :func:`~.FermionicDoubleExcitation` templates to exponentiate the coupled-cluster excitation operator. UCCSD is a VQE ansatz commonly used to run quantum chemistry simulations. The UCCSD unitary, within the first-order Trotter approximation, is given by: .. math:: \hat{U}(\vec{\theta}) = \prod_{p > r} \mathrm{exp} \Big\{\theta_{pr} (\hat{c}_p^\dagger \hat{c}_r-\mathrm{H.c.}) \Big\} \prod_{p > q > r > s} \mathrm{exp} \Big\{\theta_{pqrs} (\hat{c}_p^\dagger \hat{c}_q^\dagger \hat{c}_r \hat{c}_s-\mathrm{H.c.}) \Big\} where :math:`\hat{c}` and :math:`\hat{c}^\dagger` are the fermionic annihilation and creation operators and the indices :math:`r, s` and :math:`p, q` run over the occupied and unoccupied molecular orbitals, respectively. Using the `Jordan-Wigner transformation <>`_ the UCCSD unitary defined above can be written in terms of Pauli matrices as follows (for more details see `arXiv:1805.04340 <>`_): .. math:: \hat{U}(\vec{\theta}) = && \prod_{p > r} \mathrm{exp} \Big\{ \frac{i\theta_{pr}}{2} \bigotimes_{a=r+1}^{p-1} \hat{Z}_a (\hat{Y}_r \hat{X}_p - \mathrm{H.c.}) \Big\} \\ && \times \prod_{p > q > r > s} \mathrm{exp} \Big\{ \frac{i\theta_{pqrs}}{8} \bigotimes_{b=s+1}^{r-1} \hat{Z}_b \bigotimes_{a=q+1}^{p-1} \hat{Z}_a (\hat{X}_s \hat{X}_r \hat{Y}_q \hat{X}_p + \hat{Y}_s \hat{X}_r \hat{Y}_q \hat{Y}_p + \hat{X}_s \hat{Y}_r \hat{Y}_q \hat{Y}_p + \hat{X}_s \hat{X}_r \hat{X}_q \hat{Y}_p - \{\mathrm{H.c.}\}) \Big\}. Args: weights (tensor_like): Size ``(len(s_wires) + len(d_wires),)`` tensor containing the parameters :math:`\theta_{pr}` and :math:`\theta_{pqrs}` entering the Z rotation in :func:`~.FermionicSingleExcitation` and :func:`~.FermionicDoubleExcitation`. These parameters are the coupled-cluster amplitudes that need to be optimized for each single and double excitation generated with the :func:`~.excitations` function. wires (Iterable): wires that the template acts on s_wires (Sequence[Sequence]): Sequence of lists containing the wires ``[r,...,p]`` resulting from the single excitation :math:`\vert r, p \rangle = \hat{c}_p^\dagger \hat{c}_r \vert \mathrm{HF} \rangle`, where :math:`\vert \mathrm{HF} \rangle` denotes the Hartee-Fock reference state. The first (last) entry ``r`` (``p``) is considered the wire representing the occupied (unoccupied) orbital where the electron is annihilated (created). d_wires (Sequence[Sequence[Sequence]]): Sequence of lists, each containing two lists that specify the indices ``[s, ...,r]`` and ``[q,..., p]`` defining the double excitation :math:`\vert s, r, q, p \rangle = \hat{c}_p^\dagger \hat{c}_q^\dagger \hat{c}_r \hat{c}_s \vert \mathrm{HF} \rangle`. The entries ``s`` and ``r`` are wires representing two occupied orbitals where the two electrons are annihilated while the entries ``q`` and ``p`` correspond to the wires representing two unoccupied orbitals where the electrons are created. Wires in-between represent the occupied and unoccupied orbitals in the intervals ``[s, r]`` and ``[q, p]``, respectively. init_state (array[int]): Length ``len(wires)`` occupation-number vector representing the HF state. ``init_state`` is used to initialize the wires. .. details:: :title: Usage Details Notice that: #. The number of wires has to be equal to the number of spin orbitals included in the active space. #. The single and double excitations can be generated with the function :func:`~.excitations`. See example below. #. The vector of parameters ``weights`` is a one-dimensional array of size ``len(s_wires)+len(d_wires)`` An example of how to use this template is shown below: .. code-block:: python import pennylane as qml from pennylane import numpy as np # Define the molecule symbols = ['H', 'H', 'H'] geometry = np.array([[0.01076341, 0.04449877, 0.0], [0.98729513, 1.63059094, 0.0], [1.87262415, -0.00815842, 0.0]], requires_grad = False) electrons = 2 charge = 1 # Build the electronic Hamiltonian H, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry, charge=charge) # Define the HF state hf_state = qml.qchem.hf_state(electrons, qubits) # Generate single and double excitations singles, doubles = qml.qchem.excitations(electrons, qubits) # Map excitations to the wires the UCCSD circuit will act on s_wires, d_wires = qml.qchem.excitations_to_wires(singles, doubles) # Define the device dev = qml.device("default.qubit", wires=qubits) # Define the qnode @qml.qnode(dev) def circuit(params, wires, s_wires, d_wires, hf_state): qml.UCCSD(params, wires, s_wires, d_wires, hf_state) return qml.expval(H) # Define the initial values of the circuit parameters params = np.zeros(len(singles) + len(doubles)) # Define the optimizer optimizer = qml.GradientDescentOptimizer(stepsize=0.5) # Optimize the circuit parameters and compute the energy for n in range(21): params, energy = optimizer.step_and_cost(circuit, params, wires=range(qubits), s_wires=s_wires, d_wires=d_wires, hf_state=hf_state) if n % 2 == 0: print("step = {:}, E = {:.8f} Ha".format(n, energy)) .. code-block:: none step = 0, E = -1.24654994 Ha step = 2, E = -1.27016844 Ha step = 4, E = -1.27379541 Ha step = 6, E = -1.27434106 Ha step = 8, E = -1.27442311 Ha step = 10, E = -1.27443547 Ha step = 12, E = -1.27443733 Ha step = 14, E = -1.27443761 Ha step = 16, E = -1.27443765 Ha step = 18, E = -1.27443766 Ha step = 20, E = -1.27443766 Ha """ num_wires = AnyWires grad_method = None def __init__(self, weights, wires, s_wires=None, d_wires=None, init_state=None, id=None): if (not s_wires) and (not d_wires): raise ValueError( f"s_wires and d_wires lists can not be both empty; got ph={s_wires}, pphh={d_wires}" ) for d_wires_ in d_wires: if len(d_wires_) != 2: raise ValueError( f"expected entries of d_wires to be of size 2; got {d_wires_} of length {len(d_wires_)}" ) shape = qml.math.shape(weights) if shape != (len(s_wires) + len(d_wires),): raise ValueError( f"Weights tensor must be of shape {(len(s_wires) + len(d_wires),)}; got {shape}." ) init_state = qml.math.toarray(init_state) if init_state.dtype != np.dtype("int"): raise ValueError(f"Elements of 'init_state' must be integers; got {init_state.dtype}") self._hyperparameters = {"init_state": init_state, "s_wires": s_wires, "d_wires": d_wires} super().__init__(weights, wires=wires, id=id) @property def num_params(self): return 1
[docs] @staticmethod def compute_decomposition( weights, wires, s_wires, d_wires, init_state ): # pylint: disable=arguments-differ r"""Representation of the operator as a product of other operators. .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:`~.UCCSD.decomposition`. Args: weights (tensor_like): Size ``(len(s_wires) + len(d_wires),)`` tensor containing the parameters entering the Z rotation in :func:`~.FermionicSingleExcitation` and :func:`~.FermionicDoubleExcitation`. wires (Any or Iterable[Any]): wires that the operator acts on s_wires (Sequence[Sequence]): Sequence of lists containing the wires ``[r,...,p]`` resulting from the single excitation. d_wires (Sequence[Sequence[Sequence]]): Sequence of lists, each containing two lists that specify the indices ``[s, ...,r]`` and ``[q,..., p]`` defining the double excitation. init_state (array[int]): Length ``len(wires)`` occupation-number vector representing the HF state. ``init_state`` is used to initialize the wires. Returns: list[.Operator]: decomposition of the operator """ op_list = [] op_list.append(BasisState(init_state, wires=wires)) for i, (w1, w2) in enumerate(d_wires): op_list.append( qml.FermionicDoubleExcitation(weights[len(s_wires) + i], wires1=w1, wires2=w2) ) for j, s_wires_ in enumerate(s_wires): op_list.append(qml.FermionicSingleExcitation(weights[j], wires=s_wires_)) return op_list