clifford_group

chalmers_qubit.utils.randomized_benchmarking.clifford_group

Classes:

Name	Description
Clifford	Base class for Clifford operations.
SingleQubitClifford	Single Qubit Clifford gate class.
TwoQubitClifford	Two Qubit Clifford gate class.

Clifford

Clifford(idx: int)

Base class for Clifford operations.

Abstract base class for all Clifford operations.

Attributes:

Name	Type	Description
idx	int	Index of the Clifford operation.
GROUP_SIZE	ClassVar[int]	Size of the Clifford group.
CLIFFORD_HASH_TABLE	ClassVar[Dict[int, int]]	Hash table for fast lookup of Clifford indices.

Initialize the Clifford object with a given index.

Parameters:

Name	Type	Description	Default
idx	int	Index of the Clifford operation.	required

Raises:

Type	Description
ValueError	If the index is not valid (0 <= idx < GROUP_SIZE).

Methods:

Name	Description
find_clifford_index	Find the index of a Clifford matrix using hash lookup.
get_inverse	Get the inverse of this Clifford operation.

gate_decomposition property

gate_decomposition: List[Tuple[List[str], str]]

Returns the gate decomposition of the Clifford gate.

Returns:

Type	Description
list of tuple	Gate decomposition as a list of tuples (gate_name, qubit_identifier).

Raises:

Type	Description
NotImplementedError	If not implemented in subclass.

pauli_transfer_matrix property

pauli_transfer_matrix: ndarray

Returns the Pauli transfer matrix of the Clifford operation.

Returns:

Type	Description
ndarray	The Pauli transfer matrix.

Raises:

Type	Description
NotImplementedError	If not implemented in subclass.

find_clifford_index classmethod

find_clifford_index(matrix: ndarray) -> int

Find the index of a Clifford matrix using hash lookup.

Parameters:

Name	Type	Description	Default
matrix	ndarray	The Pauli transfer matrix.	required

Returns:

Type	Description
int	The index of the Clifford operation.

Raises:

Type	Description
ValueError	If the Clifford index is not found.

get_inverse

get_inverse() -> Clifford

Get the inverse of this Clifford operation.

Returns:

Type	Description
Clifford	The inverse operation.

SingleQubitClifford

SingleQubitClifford(idx: int)

Bases: Clifford

Single Qubit Clifford gate class.

The decomposition of the single qubit clifford group follows Epstein et al. Phys. Rev. A 89, 062321 (2014).

Attributes:

Name	Type	Description
CLIFFORD_HASH_TABLE	dict	Hash table for fast lookup.
GROUP_SIZE	int	Size of the single qubit Clifford group.

Initialize the Clifford object with a given index.

Parameters:

Name	Type	Description	Default
idx	int	Index of the Clifford operation.	required

Raises:

Type	Description
ValueError	If the index is not valid (0 <= idx < GROUP_SIZE).

Methods:

Name	Description
find_clifford_index	Find the index of a Clifford matrix using hash lookup.
get_inverse	Get the inverse of this Clifford operation.

gate_decomposition property

gate_decomposition: List[Tuple[List[str], str]]

Returns the gate decomposition of the single qubit Clifford group according to the decomposition by Epstein et al.

Returns:

Type	Description
list of tuple	Each tuple contains (gate_name, qubit_identifier).

pauli_transfer_matrix property

pauli_transfer_matrix: ndarray

Returns the Pauli transfer matrix of the single qubit Clifford operation.

Returns:

Type	Description
ndarray	Pauli transfer matrix.

find_clifford_index classmethod

find_clifford_index(matrix: ndarray) -> int

Find the index of a Clifford matrix using hash lookup.

Parameters:

Name	Type	Description	Default
matrix	ndarray	The Pauli transfer matrix.	required

Returns:

Type	Description
int	The index of the Clifford operation.

Raises:

Type	Description
ValueError	If the Clifford index is not found.

get_inverse

get_inverse() -> Clifford

Get the inverse of this Clifford operation.

Returns:

Type	Description
Clifford	The inverse operation.

TwoQubitClifford

TwoQubitClifford(idx: int)

Bases: Clifford

Two Qubit Clifford gate class.

The Clifford decomposition closely follows: 1. Corcoles et al. Process verification ... Phys. Rev. A. 2013. 2. Barends et al. Superconducting quantum circuits ... Nature 2014.

The two qubit Clifford group (C2) consists of 11520 two-qubit Cliffords, subdivided into four classes.

Attributes:

Name	Type	Description
CLIFFORD_HASH_TABLE	dict	Hash table for fast lookup.
_PTM_CACHE	dict	Cache for PTMs.
_GATE_DECOMP_CACHE	dict	Cache for gate decompositions.
GROUP_SIZE	int	Size of the two-qubit Clifford group.

Initialize the Clifford object with a given index.

Parameters:

Name	Type	Description	Default
idx	int	Index of the Clifford operation.	required

Raises:

Type	Description
ValueError	If the index is not valid (0 <= idx < GROUP_SIZE).

Methods:

Name	Description
CNOT_like_PTM	Returns the pauli transfer matrix for gates of the CNOT-like class.
CNOT_like_gates	Returns the gates for Cliffords of the CNOT-like class.
SWAP_like_PTM	Returns the pauli transfer matrix for gates of the SWAP-like class.
SWAP_like_gates	Returns the gates for Cliffords of the SWAP-like class.
find_clifford_index	Find the index of a Clifford matrix using hash lookup.
get_inverse	Get the inverse of this Clifford operation.
iSWAP_like_PTM	Returns the pauli transfer matrix for gates of the iSWAP-like class.
iSWAP_like_gates	Returns the gates for Cliffords of the iSWAP-like class.
single_qubit_like_PTM	Returns the pauli transfer matrix for gates of the single qubit like class.
single_qubit_like_gates	Returns the gates for Cliffords of the single qubit like class.

gate_decomposition property

gate_decomposition

Returns the gate decomposition of the two qubit Clifford group.

Returns:

Type	Description
list of tuple	Gate decomposition as a list of tuples (gate_name, qubit_identifier).

pauli_transfer_matrix property

pauli_transfer_matrix: ndarray

Returns the Pauli transfer matrix for the two-qubit Clifford operation.

Returns:

Type	Description
ndarray	Pauli transfer matrix.

CNOT_like_PTM classmethod

CNOT_like_PTM(idx: int) -> ndarray

Returns the pauli transfer matrix for gates of the CNOT-like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the CNOT-like class.	required

Returns:

Type	Description
ndarray	Pauli transfer matrix.

CNOT_like_gates classmethod

CNOT_like_gates(idx: int)

Returns the gates for Cliffords of the CNOT-like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the CNOT-like class.	required

Returns:

Type	Description
list of tuple	Each tuple contains (gate_name, qubit_identifier).

SWAP_like_PTM classmethod

SWAP_like_PTM(idx: int) -> ndarray

Returns the pauli transfer matrix for gates of the SWAP-like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the SWAP-like class.	required

Returns:

Type	Description
ndarray	Pauli transfer matrix.

SWAP_like_gates classmethod

SWAP_like_gates(idx: int)

Returns the gates for Cliffords of the SWAP-like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the SWAP-like class.	required

Returns:

Type	Description
list of tuple	Each tuple contains (gate_name, qubit_identifier).

find_clifford_index classmethod

find_clifford_index(matrix: ndarray) -> int

Find the index of a Clifford matrix using hash lookup.

Parameters:

Name	Type	Description	Default
matrix	ndarray	The Pauli transfer matrix.	required

Returns:

Type	Description
int	The index of the Clifford operation.

Raises:

Type	Description
ValueError	If the Clifford index is not found.

get_inverse

get_inverse() -> Clifford

Get the inverse of this Clifford operation.

Returns:

Type	Description
Clifford	The inverse operation.

iSWAP_like_PTM classmethod

iSWAP_like_PTM(idx: int) -> ndarray

Returns the pauli transfer matrix for gates of the iSWAP-like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the iSWAP-like class.	required

Returns:

Type	Description
ndarray	Pauli transfer matrix.

iSWAP_like_gates classmethod

iSWAP_like_gates(idx: int)

Returns the gates for Cliffords of the iSWAP-like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the iSWAP-like class.	required

Returns:

Type	Description
list of tuple	Each tuple contains (gate_name, qubit_identifier).

single_qubit_like_PTM classmethod

single_qubit_like_PTM(idx: int) -> ndarray

Returns the pauli transfer matrix for gates of the single qubit like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the single qubit like class.	required

Returns:

Type	Description
ndarray	Pauli transfer matrix.

single_qubit_like_gates classmethod

single_qubit_like_gates(idx: int) -> List[Tuple[str, str]]

Returns the gates for Cliffords of the single qubit like class.

Parameters:

Name	Type	Description	Default
idx	int	Index within the single qubit like class.	required

Returns:

Type	Description
list of tuple	Each tuple contains (gate_name, qubit_identifier).