qml.templates.subroutines.AllSinglesDoubles

class AllSinglesDoubles(weights, wires, hf_state, singles=None, doubles=None, do_queue=True)[source]

Bases: pennylane.operation.Operation

Builds a quantum circuit to prepare correlated states of molecules by applying all SingleExcitation and DoubleExcitation operations to the initial Hartree-Fock state.

The template initializes the \(n\)-qubit system to encode the input Hartree-Fock state and applies the particle-conserving SingleExcitation and DoubleExcitation operations which are implemented as Givens rotations that act on the subspace of two and four qubits, respectively. The total number of excitation gates and the indices of the qubits they act on are obtained using the excitations() function.

For example, the quantum circuit for the case of two electrons and six qubits is sketched in the figure below:


../../_images/all_singles_doubles.png

In this case, we have four single and double excitations that preserve the total-spin projection of the Hartree-Fock state. The SingleExcitation gate \(G\) act on the qubits [0, 2], [0, 4], [1, 3], [1, 5] as indicated by the squares, while the DoubleExcitation operation \(G^{(2)}\) is applied to the qubits [0, 1, 2, 3], [0, 1, 2, 5], [0, 1, 2, 4], [0, 1, 4, 5].

The resulting unitary conserves the number of particles and prepares the \(n\)-qubit system in a superposition of the initial Hartree-Fock state and other states encoding multiply-excited configurations.

Parameters
  • weights (tensor_like) – size (len(singles) + len(doubles),) tensor containing the angles entering the SingleExcitation and DoubleExcitation operations, in that order

  • wires (Iterable) – wires that the template acts on

  • hf_state (array[int]) – Length len(wires) occupation-number vector representing the Hartree-Fock state. hf_state is used to initialize the wires.

  • singles (Sequence[Sequence]) – sequence of lists with the indices of the two qubits the SingleExcitation operations act on

  • doubles (Sequence[Sequence]) – sequence of lists with the indices of the four qubits the DoubleExcitation operations act on

Notice that:

  1. The number of wires has to be equal to the number of spin orbitals included in the active space.

  2. The single and double excitations can be generated with the function excitations(). See example below.

An example of how to use this template is shown below:

import pennylane as qml
import numpy as np

electrons = 2
qubits = 4

# Define the HF state
hf_state = qml.qchem.hf_state(electrons, qubits)

# Generate all single and double excitations
singles, doubles = qml.qchem.excitations(electrons, qubits)

# Define the device
dev = qml.device('default.qubit', wires=qubits)

wires = range(qubits)

@qml.qnode(dev)
def circuit(weights, hf_state, singles, doubles):
    qml.templates.AllSinglesDoubles(weights, wires, hf_state, singles, doubles)
    return qml.expval(qml.PauliZ(0))

# Evaluate the QNode for a given set of parameters
params = np.random.normal(0, np.pi, len(singles) + len(doubles))
circuit(params, hf_state, singles=singles, doubles=doubles)

base_name

Get base name of the operator.

eigvals

Eigenvalues of an instantiated operator.

generator

Generator of the operation.

grad_method

Gradient computation method.

grad_recipe

Gradient recipe for the parameter-shift method.

id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

matrix

Matrix representation of an instantiated operator in the computational basis.

name

Get and set the name of the operator.

num_params

num_wires

par_domain

parameters

Current parameter values.

string_for_inverse

wires

Wires of this operator.

base_name

Get base name of the operator.

eigvals
generator

Generator of the operation.

A length-2 list [generator, scaling_factor], where

  • generator is an existing PennyLane operation class or \(2\times 2\) Hermitian array that acts as the generator of the current operation

  • scaling_factor represents a scaling factor applied to the generator operation

For example, if \(U(\theta)=e^{i0.7\theta \sigma_x}\), then \(\sigma_x\), with scaling factor \(s\), is the generator of operator \(U(\theta)\):

generator = [PauliX, 0.7]

Default is [None, 1], indicating the operation has no generator.

grad_method

Gradient computation method.

  • 'A': analytic differentiation using the parameter-shift method.

  • 'F': finite difference numerical differentiation.

  • None: the operation may not be differentiated.

Default is 'F', or None if the Operation has zero parameters.

grad_recipe = None

Gradient recipe for the parameter-shift method.

This is a tuple with one nested list per operation parameter. For parameter \(\phi_k\), the nested list contains elements of the form \([c_i, a_i, s_i]\) where \(i\) is the index of the term, resulting in a gradient recipe of

\[\frac{\partial}{\partial\phi_k}f = \sum_{i} c_i f(a_i \phi_k + s_i).\]

If None, the default gradient recipe containing the two terms \([c_0, a_0, s_0]=[1/2, 1, \pi/2]\) and \([c_1, a_1, s_1]=[-1/2, 1, -\pi/2]\) is assumed for every parameter.

Type

tuple(Union(list[list[float]], None)) or None

id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

matrix
name

Get and set the name of the operator.

num_params = 1
num_wires = -1
par_domain = 'A'
parameters

Current parameter values.

string_for_inverse = '.inv'
wires

Wires of this operator.

Returns

wires

Return type

Wires

adjoint([do_queue])

Create an operation that is the adjoint of this one.

decomposition(*params, wires)

Returns a template decomposing the operation into other quantum operations.

expand()

Returns a tape containing the decomposed operations, rather than a list.

get_parameter_shift(idx[, shift])

Multiplier and shift for the given parameter, based on its gradient recipe.

inv()

Inverts the operation, such that the inverse will be used for the computations by the specific device.

queue()

Append the operator to the Operator queue.

shape(singles, doubles)

Returns the expected shape of the tensor that contains the circuit parameters.

adjoint(do_queue=False)

Create an operation that is the adjoint of this one.

Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates.

Parameters

do_queue – Whether to add the adjointed gate to the context queue.

Returns

The adjointed operation.

static decomposition(*params, wires)

Returns a template decomposing the operation into other quantum operations.

expand()[source]

Returns a tape containing the decomposed operations, rather than a list.

Returns

Returns a quantum tape that contains the operations decomposition, or if not implemented, simply the operation itself.

Return type

JacobianTape

get_parameter_shift(idx, shift=1.5707963267948966)

Multiplier and shift for the given parameter, based on its gradient recipe.

Parameters

idx (int) – parameter index

Returns

list of multiplier, coefficient, shift for each term in the gradient recipe

Return type

list[[float, float, float]]

inv()

Inverts the operation, such that the inverse will be used for the computations by the specific device.

This method concatenates a string to the name of the operation, to indicate that the inverse will be used for computations.

Any subsequent call of this method will toggle between the original operation and the inverse of the operation.

Returns

operation to be inverted

Return type

Operator

queue()

Append the operator to the Operator queue.

static shape(singles, doubles)[source]

Returns the expected shape of the tensor that contains the circuit parameters.

Parameters
  • singles (Sequence[Sequence]) – sequence of lists with the indices of the two qubits the SingleExcitation operations act on

  • doubles (Sequence[Sequence]) – sequence of lists with the indices of the four qubits the DoubleExcitation operations act on

Returns

shape of the tensor containing the circuit parameters

Return type

tuple(int)