qml.templates.subroutines.DoubleExcitationUnitary¶

class
DoubleExcitationUnitary
(weight, wires1=None, wires2=None, do_queue=True, id=None)[source]¶ Bases:
pennylane.operation.Operation
Circuit to exponentiate the tensor product of Pauli matrices representing the doubleexcitation operator entering the Unitary CoupledCluster Singles and Doubles (UCCSD) ansatz. UCCSD is a VQE ansatz commonly used to run quantum chemistry simulations.
The CC doubleexcitation operator is given by
\[\hat{U}_{pqrs}(\theta) = \mathrm{exp} \{ \theta (\hat{c}_p^\dagger \hat{c}_q^\dagger \hat{c}_r \hat{c}_s  \mathrm{H.c.}) \},\]where \(\hat{c}\) and \(\hat{c}^\dagger\) are the fermionic annihilation and creation operators and the indices \(r, s\) and \(p, q\) run over the occupied and unoccupied molecular orbitals, respectively. Using the JordanWigner transformation the fermionic operator defined above can be written in terms of Pauli matrices (for more details see arXiv:1805.04340):
\[\hat{U}_{pqrs}(\theta) = \mathrm{exp} \Big\{ \frac{i\theta}{8} \bigotimes_{b=s+1}^{r1} \hat{Z}_b \bigotimes_{a=q+1}^{p1} \hat{Z}_a (\hat{X}_s \hat{X}_r \hat{Y}_q \hat{X}_p + \hat{Y}_s \hat{X}_r \hat{Y}_q \hat{Y}_p + \hat{X}_s \hat{Y}_r \hat{Y}_q \hat{Y}_p + \hat{X}_s \hat{X}_r \hat{X}_q \hat{Y}_p  \mathrm{H.c.} ) \Big\}\]The quantum circuit to exponentiate the tensor product of Pauli matrices entering the latter equation is shown below (see arXiv:1805.04340):
As explained in Seely et al. (2012), the exponential of a tensor product of PauliZ operators can be decomposed in terms of \(2(n1)\) CNOT gates and a singlequbit Zrotation referred to as \(U_\theta\) in the figure above. If there are \(X\) or:math:Y Pauli matrices in the product, the Hadamard (\(H\)) or \(R_x\) gate has to be applied to change to the \(X\) or \(Y\) basis, respectively. The latter operations are denoted as \(U_1\), \(U_2\), \(U_3\) and \(U_4\) in the figure above. See the Usage Details section for more details.
 Parameters
weight (float or tensor_like) – angle \(\theta\) entering the Z rotation acting on wire
p
wires1 (Iterable) – Wires of the qubits representing the subset of occupied orbitals in the interval
[s, r]
. The first wire is interpreted ass
and the last wire asr
. Wires in between are acted on with CNOT gates to compute the parity of the set of qubits.wires2 (Iterable) – Wires of the qubits representing the subset of unoccupied orbitals in the interval
[q, p]
. The first wire is interpreted asq
and the last wire is interpreted asp
. Wires in between are acted on with CNOT gates to compute the parity of the set of qubits.
Usage Details
Notice that:
\(\hat{U}_{pqrs}(\theta)\) involves eight exponentiations where \(\hat{U}_1\), \(\hat{U}_2\), \(\hat{U}_3\), \(\hat{U}_4\) and \(\hat{U}_\theta\) are defined as follows,
\[\begin{split}[U_1, && U_2, U_3, U_4, U_{\theta}] = \\ && \Bigg\{\bigg[H, H, R_x(\frac{\pi}{2}), H, R_z(\theta/8)\bigg], \bigg[R_x(\frac{\pi}{2}), H, R_x(\frac{\pi}{2}), R_x(\frac{\pi}{2}), R_z(\frac{\theta}{8}) \bigg], \\ && \bigg[H, R_x(\frac{\pi}{2}), R_x(\frac{\pi}{2}), R_x(\frac{\pi}{2}), R_z(\frac{\theta}{8}) \bigg], \bigg[H, H, H, R_x(\frac{\pi}{2}), R_z(\frac{\theta}{8}) \bigg], \\ && \bigg[R_x(\frac{\pi}{2}), H, H, H, R_z(\frac{\theta}{8}) \bigg], \bigg[H, R_x(\frac{\pi}{2}), H, H, R_z(\frac{\theta}{8}) \bigg], \\ && \bigg[R_x(\frac{\pi}{2}), R_x(\frac{\pi}{2}), R_x(\frac{\pi}{2}), H, R_z(\frac{\theta}{8}) \bigg], \bigg[R_x(\frac{\pi}{2}), R_x(\frac{\pi}{2}), H, R_x(\frac{\pi}{2}), R_z(\frac{\theta}{8}) \bigg] \Bigg\}\end{split}\]For a given quadruple
[s, r, q, p]
with \(p>q>r>s\), seventytwo singlequbit and16*(len(wires1)1 + len(wires2)1 + 1)
CNOT operations are applied. Consecutive CNOT gates act on qubits with indices betweens
andr
andq
andp
while a single CNOT acts on wiresr
andq
. The operations performed across these qubits are shown in dashed lines in the figure above.
An example of how to use this template is shown below:
import pennylane as qml from pennylane.templates import DoubleExcitationUnitary dev = qml.device('default.qubit', wires=5) @qml.qnode(dev) def circuit(weight, wires1=None, wires2=None): DoubleExcitationUnitary(weight, wires1=wires1, wires2=wires2) return qml.expval(qml.PauliZ(0)) weight = 1.34817 print(circuit(weight, wires1=[0, 1], wires2=[2, 3, 4]))
Attributes
Get base name of the operator.
The basis of an operation, or for controlled gates, of the target operation.
For operations that are controlled, returns the set of control wires.
Eigenvalues of an instantiated operator.
Generator of the operation.
Gradient recipe for the parametershift method.
returns an integer hash uniquely representing the operator
String for the ID of the operator.
Boolean determining if the inverse of the operation was requested.
True
if composing multiple copies of the operation results in an addition (or alternative accumulation) of parameters.True
if the operation is its own inverse.True
if the operation is the same if you exchange the order of wires.True
if the operation is the same if you exchange the order of all but the last wire.Matrix representation of an instantiated operator in the computational basis.
Get and set the name of the operator.
Current parameter values.
The parameters required to implement a singlequbit gate as an equivalent
Rot
gate, up to a global phase.Wires of this operator.

base_name
¶ Get base name of the operator.

basis
= None¶ The basis of an operation, or for controlled gates, of the target operation. If not
None
, should take a value of"X"
,"Y"
, or"Z"
.For example,
X
andCNOT
havebasis = "X"
, whereasControlledPhaseShift
andRZ
havebasis = "Z"
. Type
str or None

control_wires
¶ For operations that are controlled, returns the set of control wires.
 Returns
The set of control wires of the operation.
 Return type

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
= 'A'¶

grad_recipe
= ([[0.4267766952966368, 1, 1.5707963267948966], [0.4267766952966368, 1, 1.5707963267948966], [0.07322330470336313, 1, 4.71238898038469], [0.07322330470336313, 1, 4.71238898038469]],)¶ 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

hash
¶ returns an integer hash uniquely representing the operator
 Type
int

id
¶ String for the ID of the operator.

inverse
¶ Boolean determining if the inverse of the operation was requested.

is_composable_rotation
= None¶ True
if composing multiple copies of the operation results in an addition (or alternative accumulation) of parameters.For example,
qml.RZ
is a composable rotation. Applyingqml.RZ(0.1, wires=0)
followed byqml.RZ(0.2, wires=0)
is equivalent to performing a single rotationqml.RZ(0.3, wires=0)
.If set to
None
, the operation will be ignored during compilation transforms that merge adjacent rotations. Type
bool or None

is_self_inverse
= None¶ True
if the operation is its own inverse.If
None
, all instances of the given operation will be ignored during compilation transforms involving inverse cancellation. Type
bool or None

is_symmetric_over_all_wires
= None¶ True
if the operation is the same if you exchange the order of wires.For example,
qml.CZ(wires=[0, 1])
has the same effect asqml.CZ(wires=[1, 0])
due to symmetry of the operation.If
None
, all instances of the operation will be ignored during compilation transforms that check for wire symmetry. Type
bool or None

is_symmetric_over_control_wires
= None¶ True
if the operation is the same if you exchange the order of all but the last wire.For example,
qml.Toffoli(wires=[0, 1, 2])
has the same effect asqml.Toffoli(wires=[1, 0, 2])
, but neither are the same asqml.Toffoli(wires=[0, 2, 1])
.If
None
, all instances of the operation will be ignored during compilation transforms that check for controlwire symmetry. Type
bool or None

matrix
¶

name
¶ Get and set the name of the operator.

num_params
= 1¶

num_wires
= 1¶

par_domain
= 'R'¶

parameters
¶ Current parameter values.

single_qubit_rot_angles
¶ The parameters required to implement a singlequbit gate as an equivalent
Rot
gate, up to a global phase. Returns
A list of values \([\phi, \theta, \omega]\) such that \(RZ(\omega) RY(\theta) RZ(\phi)\) is equivalent to the original operation.
 Return type
tuple[float, float, float]

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
([context])Append the operator to the Operator queue.

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
(context=<class 'pennylane.queuing.QueuingContext'>)¶ Append the operator to the Operator queue.
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