qml.GateFabric

class GateFabric(weights, wires, init_state, include_pi=False, do_queue=True, id=None)[source]

Bases: pennylane.operation.Operation

Implements a local, expressive, and quantum-number-preserving ansatz proposed by Anselmetti et al. in arXiv:2104.05692.

This template prepares the \(N\)-qubit trial state by applying \(D\) layers of gate-fabric blocks \(\hat{U}_{GF}(\vec{\theta},\vec{\phi})\) to the Hartree-Fock state in the Jordan-Wigner basis

\[\vert \Psi(\vec{\theta},\vec{\phi})\rangle = \hat{U}_{GF}^{(D)}(\vec{\theta}_{D},\vec{\phi}_{D}) \ldots \hat{U}_{GF}^{(2)}(\vec{\theta}_{2},\vec{\phi}_{2}) \hat{U}_{GF}^{(1)}(\vec{\theta}_{1},\vec{\phi}_{1}) \vert HF \rangle,\]

where each of the gate fabric blocks \(\hat{U}_{GF}(\vec{\theta},\vec{\phi})\) is comprised of two-parameter four-qubit gates \(\hat{Q}(\theta, \phi)\) that act on four nearest-neighbour qubits. The circuit implementing a single layer of the gate fabric block for \(N = 8\) is shown in the figure below:

../../_images/gate_fabric_layer.png

The gate element \(\hat{Q}(\theta, \phi)\) (arXiv:2104.05692) is composed of a four-qubit spin-adapted spatial orbital rotation gate, which is implemented by the OrbitalRotation() operation and a four-qubit diagonal pair-exchange gate, which is equivalent to the DoubleExcitation() operation. In addition to these two gates, the gate element \(\hat{Q}(\theta, \phi)\) can also include an optional constant \(\hat{\Pi} \in \{\hat{I}, \text{OrbitalRotation}(\pi)\}\) gate.

../../_images/q_gate_decompositon.png

The four-qubit DoubleExcitation() and OrbitalRotation() gates given here are equivalent to the \(\text{QNP}_{PX}(\theta)\) and \(\text{QNP}_{OR}(\phi)\) gates presented in arXiv:2104.05692, respectively. Moreover, regardless of the choice of \(\hat{\Pi}\), this gate fabric will exactly preserve the number of particles and total spin of the state.

Parameters
  • weights (tensor_like) – Array of weights of shape (D, L, 2), where D is the number of gate fabric layers and L = N/2-1 is the number of \(\hat{Q}(\theta, \phi)\) gates per layer with N being the total number of qubits.

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

  • init_state (tensor_like) – init_state (tensor_like): iterable of shape (len(wires),), representing the input Hartree-Fock state in the Jordan-Wigner representation.

  • include_pi (boolean) – If include_pi = True, the optional constant \(\hat{\Pi}\) gate is set to \(\text{OrbitalRotation}(\pi)\). Default value is \(\hat{I}\).

  1. The number of wires \(N\) has to be equal to the number of spin-orbitals included in the active space, and should be even.

  2. The number of trainable parameters scales linearly with the number of layers as \(2 D (N/2-1)\).

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

import numpy as np
import pennylane as qml

# Build the electronic Hamiltonian
symbols = ["H", "H"]
coordinates = np.array([0.0, 0.0, -0.6614, 0.0, 0.0, 0.6614])
H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)

# Define the Hartree-Fock state
electrons = 2
ref_state = qml.qchem.hf_state(electrons, qubits)

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

# Define the ansatz
@qml.qnode(dev)
def ansatz(weights):
    qml.GateFabric(weights, wires=[0,1,2,3],
                                init_state=ref_state, include_pi=True)
    return qml.expval(H)

# Get the shape of the weights for this template
layers = 2
shape = qml.GateFabric.shape(n_layers=layers, n_wires=qubits)

# Initialize the weight tensors
np.random.seed(42)
weights = np.random.random(size=shape)

# Define the optimizer
opt = qml.GradientDescentOptimizer(stepsize=0.4)

# Store the values of the cost function
energy = [ansatz(weights)]

# Store the values of the circuit weights
angle = [weights]

max_iterations = 100
conv_tol = 1e-06

for n in range(max_iterations):
    weights, prev_energy = opt.step_and_cost(ansatz, weights)
    energy.append(ansatz(weights))
    angle.append(weights)
    conv = np.abs(energy[-1] - prev_energy)

    if n % 2 == 0:
        print(f"Step = {n},  Energy = {energy[-1]:.8f} Ha")

    if conv <= conv_tol:
        break

print("\n" f"Final value of the ground-state energy = {energy[-1]:.8f} Ha")
print("\n" f"Optimal value of the circuit parameters = {angle[-1]}")
Step = 0,  Energy = -0.92629604 Ha
Step = 2,  Energy = -1.10724005 Ha
Step = 4,  Energy = -1.13307755 Ha
Step = 6,  Energy = -1.13587374 Ha
Step = 8,  Energy = -1.13615720 Ha
Step = 10,  Energy = -1.13618592 Ha
Step = 12,  Energy = -1.13618883 Ha

Final value of the ground-state energy = -1.13618883 Ha

Optimal value of the circuit parameters = [[[ 0.58835515  0.40801101]]
[[ 0.83842218 -0.24228264]]]

Parameter shape

The shape of the weights argument can be computed by the static method shape() and used when creating randomly initialised weight tensors:

shape = GateFabric.shape(n_layers=2, n_wires=4)
weights = np.random.random(size=shape)
>>> weights.shape
(2, 1, 2)

base_name

Get base name of the operator.

basis

The basis of an operation, or for controlled gates, of the target operation.

control_wires

Returns the control wires.

eigvals

Eigenvalues of an instantiated operator.

generator

Generator of the operation.

grad_method

grad_recipe

Gradient recipe for the parameter-shift method.

hash

returns an integer hash uniquely representing the operator

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

Number of trainable parameters that this operator expects to be fed via the dynamic *params argument.

num_wires

parameters

Current parameter values.

single_qubit_rot_angles

The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase.

string_for_inverse

wires

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 and CNOT have basis = "X", whereas ControlledPhaseShift and RZ have basis = "Z".

Type

str or None

control_wires

Returns the control wires. For operations that are not controlled, this is an empty Wires object of length 0.

Returns

The control wires of the operation.

Return type

Wires

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 = None
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

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.

matrix
name

Get and set the name of the operator.

num_params
num_wires = -1
parameters

Current parameter values.

single_qubit_rot_angles

The parameters required to implement a single-qubit 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'
wires

Wires of this operator.

Returns

wires

Return type

Wires

adjoint([do_queue])

Create an operation that is the adjoint of this one.

decompose()

Decomposes this operator into products of other operators.

decomposition(*params, wires)

Defines a decomposition of this operator into products of other operators.

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.

label([decimals, base_label])

A customizable string representation of the operator.

queue([context])

Append the operator to the Operator queue.

shape(n_layers, n_wires)

Returns the shape of the weight tensor required for this template.

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.

decompose()

Decomposes this operator into products of other operators.

Returns

list[Operation]

static decomposition(*params, wires)

Defines a decomposition of this operator into products of other operators.

Parameters
  • params (tuple[float, int, array]) – operator parameters

  • wires (Union(Sequence[int], Wires)) – wires the operator acts on

Returns

list[Operation]

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

label(decimals=None, base_label=None)

A customizable string representation of the operator.

Parameters
  • decimals=None (int) – If None, no parameters are included. Else, specifies how to round the parameters.

  • base_label=None (str) – overwrite the non-parameter component of the label

Returns

label to use in drawings

Return type

str

Example:

>>> op = qml.RX(1.23456, wires=0)
>>> op.label()
"RX"
>>> op.label(decimals=2)
"RX\n(1.23)"
>>> op.label(base_label="my_label")
"my_label"
>>> op.label(decimals=2, base_label="my_label")
"my_label\n(1.23)"
>>> op.inv()
>>> op.label()
"RX⁻¹"
queue(context=<class 'pennylane.queuing.QueuingContext'>)

Append the operator to the Operator queue.

static shape(n_layers, n_wires)[source]

Returns the shape of the weight tensor required for this template.

Parameters
  • n_layers (int) – number of layers

  • n_wires (int) – number of qubits

Returns

shape

Return type

tuple[int]

Contents

Using PennyLane

Development

API