qml.grouping¶
This subpackage defines functions and classes for Pauli-word partitioning functionality used in measurement optimization.
A Pauli word is defined as \(P_J = \prod_{i=1}^{N}\sigma_i^{(J)}\), where
\(\sigma_i^{(J)}\) is one of the Pauli operators (PauliX
,
PauliY
, PauliZ
) or identity
(Identity
) acting on the \(i^{th}\) qubit.
Pauli words can be used for expressing a qubit Hamiltonian
.
A qubit Hamiltonian has the form \(H_{q} = \sum_{J} C_J P_J\) where
\(C_{J}\) are numerical coefficients, and \(P_J\) are Pauli words.
A list of Pauli words can be partitioned according to certain grouping
strategies. As an example, the group_observables()
function partitions
a list of observables (Pauli operations and tensor products thereof) into
groupings according to a binary relation (e.g., qubit-wise commuting):
>>> observables = [qml.PauliY(0), qml.PauliX(0) @ qml.PauliX(1), qml.PauliZ(1)]
>>> obs_groupings = group_observables(observables)
>>> obs_groupings
[[Tensor(PauliX(wires=[0]), PauliX(wires=[1]))],
[PauliY(wires=[0]), PauliZ(wires=[1])]]
The \(C_{J}\) coefficients for each \(P_J\) Pauli word making up a Hamiltonian can also be specified along with further options, such as the Pauli-word grouping method (e.g., qubit-wise commuting) and the underlying graph-colouring algorithm (e.g., recursive largest first) used for creating the groups of observables:
>>> obs = [qml.PauliY(0), qml.PauliX(0) @ qml.PauliX(1), qml.PauliZ(1)]
>>> coeffs = [1.43, 4.21, 0.97]
>>> obs_groupings, coeffs_groupings = group_observables(obs, coeffs, 'qwc', 'rlf')
>>> obs_groupings
[[Tensor(PauliX(wires=[0]), PauliX(wires=[1]))],
[PauliY(wires=[0]), PauliZ(wires=[1])]]
>>> coeffs_groupings
[[4.21], [1.43, 0.97]]
pennylane.grouping Package¶
This subpackage defines functions and classes for Pauli-word partitioning functionality used in measurement optimization.
Functions¶
|
Performs a check if two Pauli words have the same |
|
Converts a binary vector of even dimension to an Observable instance. |
|
Transforms the Pauli word to diagonal form in the computational basis. |
|
Diagonalizes a list of qubit-wise commutative groupings of Pauli strings. |
|
Diagonalizes a list of mutually qubit-wise commutative Pauli words. |
|
Partitions a list of observables (Pauli operations and tensor products thereof) into groupings according to a binary relation (qubit-wise commuting, fully-commuting, or anticommuting). |
|
Checks if an observable instance is a Pauli word. |
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Checks if two Pauli words in the binary vector representation are qubit-wise commutative. |
|
Converts a list of Pauli words to the binary vector representation and yields a row matrix of the binary vectors. |
|
Partitions then diagonalizes a list of Pauli words, facilitating simultaneous measurement of all observables within a partition. |
|
Converts a Pauli word to the binary vector representation. |
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Obtains the adjacency matrix for the complementary graph of the qubit-wise commutativity graph for a given set of observables in the binary representation. |
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Performs circuit implementation of diagonalizing unitary for a Pauli word. |
Classes¶
|
Class for partitioning a list of Pauli words according to some binary symmetric relation. |
pennylane.grouping.graph_colouring Module¶
A module for heuristic algorithms for colouring Pauli graphs.
A Pauli graph is a graph where vertices represent Pauli words and edges denote if a specified symmetric binary relation (e.g., commutation) is satisfied for the corresponding Pauli words. The graph-colouring problem is to assign a colour to each vertex such that no vertices of the same colour are connected, using the fewest number of colours (lowest “chromatic number”) as possible.
Functions¶
|
Performs graph-colouring using the Largest Degree First heuristic. |
|
Performs graph-colouring using the Recursive Largest Degree First heuristic. |
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