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
andDoubleExcitation
operations to the initial HartreeFock state.The template initializes the \(n\)qubit system to encode the input HartreeFock state and applies the particleconserving
SingleExcitation
andDoubleExcitation
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 theexcitations()
function.For example, the quantum circuit for the case of two electrons and six qubits is sketched in the figure below:
In this case, we have four single and double excitations that preserve the totalspin projection of the HartreeFock state. The
SingleExcitation
gate \(G\) act on the qubits[0, 2], [0, 4], [1, 3], [1, 5]
as indicated by the squares, while theDoubleExcitation
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 HartreeFock state and other states encoding multiplyexcited configurations.
 Parameters
weights (tensor_like) – size
(len(singles) + len(doubles),)
tensor containing the angles entering theSingleExcitation
andDoubleExcitation
operations, in that orderwires (Iterable) – wires that the template acts on
hf_state (array[int]) – Length
len(wires)
occupationnumber vector representing the HartreeFock 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 ondoubles (Sequence[Sequence]) – sequence of lists with the indices of the four qubits the
DoubleExcitation
operations act on
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
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)
Attributes
Get base name of the operator.
Eigenvalues of an instantiated operator.
Generator of the operation.
Gradient computation method.
Gradient recipe for the parametershift method.
String for the ID of the operator.
Boolean determining if the inverse of the operation was requested.
Matrix representation of an instantiated operator in the computational basis.
Get and set the name of the operator.
Current parameter values.
Wires of this operator.

base_name
¶ Get base name of the operator.

eigvals
¶

generator
¶ Generator of the operation.
A length2 list
[generator, scaling_factor]
, wheregenerator
is an existing PennyLane operation class or \(2\times 2\) Hermitian array that acts as the generator of the current operationscaling_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 parametershift method.'F'
: finite difference numerical differentiation.None
: the operation may not be differentiated.
Default is
'F'
, orNone
if the Operation has zero parameters.

grad_recipe
= None¶ Gradient recipe for the parametershift 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'¶
Methods
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

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 ondoubles (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)
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