Pattern Manipulation

graphix.pattern module

class graphix.pattern.Pattern(input_nodes: list[int] | None = None)

MBQC pattern class.

Pattern holds a sequence of commands to operate the MBQC (Pattern.seq), and provide modification strategies to improve the structure and simulation efficiency of the pattern accoring to measurement calculus.

ref: V. Danos, E. Kashefi and P. Panangaden. J. ACM 54.2 8 (2007)

list(self)

list of commands.

each command is a list [type, nodes, attr] which will be applied in the order of list indices.

type: one of {‘N’, ‘M’, ‘E’, ‘X’, ‘Z’, ‘S’, ‘C’}

nodes: int for {‘N’, ‘M’, ‘X’, ‘Z’, ‘S’, ‘C’} commands, tuple (i, j) for {‘E’} command

attr for N: none

attr for M: meas_plane, angle, s_domain, t_domain

attr for X: signal_domain

attr for Z: signal_domain

attr for S: signal_domain

attr for C: clifford_index, as defined in graphix.clifford

n_node

total number of nodes in the resource state

Type:

int

__init__(input_nodes: list[int] | None = None) → None

Construct a pattern.

Parameters:

input_nodes – optional, list of input qubits

add(cmd: N | M | E | C | X | Z | S | T) → None

Add command to the end of the pattern.

An MBQC command is an instance of graphix.command.Command.

Parameters:

cmd (graphix.command.Command) – MBQC command.

extend(cmds: list[N | M | E | C | X | Z | S | T]) → None

Add a list of commands.

Parameters:

cmds – list of commands

clear() → None

Clear the sequence of pattern commands.

replace(cmds: list[N | M | E | C | X | Z | S | T], input_nodes=None) → None

Replace pattern with a given sequence of pattern commands.

Parameters:

• cmds – list of commands

• input_nodes – optional, list of input qubits (by default, keep the same input nodes as before)

reorder_output_nodes(output_nodes: list[int])

Arrange the order of output_nodes.

Parameters:

output_nodes (list of int) – output nodes order determined by user. each index corresponds to that of logical qubits.

reorder_input_nodes(input_nodes: list[int])

Arrange the order of input_nodes.

Parameters:

input_nodes (list of int) – input nodes order determined by user. each index corresponds to that of logical qubits.

simulate_pattern(backend: str = 'statevector', input_state: BasicStates = graphix.states.PlanarState(Plane.XY, 0.0), **kwargs) → State

Simulate the execution of the pattern by using graphix.simulator.PatternSimulator.

Available backend: [‘statevector’, ‘densitymatrix’, ‘tensornetwork’]

Parameters:

• backend (str) – optional parameter to select simulator backend.

• kwargs (keyword args for specified backend.)

Returns:

• state – quantum state representation for the selected backend.

• See also

  graphix.simulator.PatternSimulator

get_max_degree()

Get max degree of a pattern.

Returns:

max_degree – max degree of a pattern

Return type:

int

get_angles()

Get measurement angles of the pattern.

Returns:

angles – measurement angles of the each node.

Return type:

dict

get_vops(conj=False, include_identity=False)

Get local-Clifford decorations from measurement or Clifford commands.

Parameters:

• (False) (include_identity) – Apply conjugations to all local Clifford operators.

• (False) – Whether or not to include identity gates in the output

Returns:

vops

Return type:

dict

connected_nodes(node, prepared=None)

Find nodes that are connected to a specified node.

These nodes must be in the statevector when the specified node is measured, to ensure correct computation. If connected nodes already exist in the statevector (prepared), then they will be ignored as they do not need to be prepared again.

Parameters:

• node (int) – node index

• prepared (list) – list of node indices, which are to be ignored

Returns:

node_list – list of nodes that are entangled with specified node

Return type:

list

run_pattern(backend, **kwargs)

Run the pattern on cloud-based quantum devices and their simulators.

Available backend: [‘ibmq’]

Parameters:

• backend (str) – parameter to select executor backend.

• kwargs (keyword args for specified backend.)

Returns:

the measurement result, in the representation depending on the backend used.

Return type:

result

perform_pauli_measurements(leave_input: bool = False, ignore_pauli_with_deps: bool = False) → None

Perform Pauli measurements in the pattern using efficient stabilizer simulator.

Parameters:

• leave_input (bool) – Optional (False by default). If True, measurements on input nodes are preserved as-is in the pattern.

• ignore_pauli_with_deps (bool) – Optional (False by default). If True, Pauli measurements with domains depending on other measures are preserved as-is in the pattern. If False, all Pauli measurements are preprocessed. Formally, measurements are swapped so that all Pauli measurements are applied first, and domains are updated accordingly.

• seealso: (..) – measure_pauli():

print_pattern(lim=40, target: list[CommandKind] | None = None) → None

Print the pattern sequence (Pattern.seq).

Parameters:

• lim (int, optional) – maximum number of commands to show

• target (list of CommandKind, optional) – show only specified commands, e.g. [CommandKind.M, CommandKind.X, CommandKind.Z]

standardize(method='direct') → None

Execute standardization of the pattern.

‘standard’ pattern is one where commands are sorted in the order of ‘N’, ‘E’, ‘M’ and then byproduct commands (‘X’ and ‘Z’).

Parameters:

method (str, optional) – ‘mc’ corresponds to a conventional standardization defined in original measurement calculus paper, executed on Pattern class. ‘direct’ fast standardization implemented as standardize_direct() defaults to ‘direct’

shift_signals(method='direct') → dict[int, list[int]]

Perform signal shifting procedure.

Extract the t-dependence of the measurement into ‘S’ commands and commute them to the end of the command sequence where it can be removed. This procedure simplifies the dependence structure of the pattern.

Ref for the original ‘mc’ method:

22. Danos, E. Kashefi and P. Panangaden. J. ACM 54.2 8 (2007)

Parameters:

method (str, optional) – ‘direct’ shift_signals is executed on a conventional Pattern sequence. ‘mc’ shift_signals is done using the original algorithm on the measurement calculus paper.

Returns:

signal_dict – For each node, the signal that have been shifted.

Return type:

dict[int, list[int]]

is_standard()

Determine whether the command sequence is standard.

Returns:

is_standard – True if the pattern is standard

Return type:

bool

get_graph() → tuple[list[int], list[tuple[int, int]]]

Return the list of nodes and edges from the command sequence, extracted from ‘N’ and ‘E’ commands.

Returns:

• node_list (list) – list of node indices.

• edge_list (list) – list of tuples (i,j) specifying edges

parallelize_pattern()

Optimize the pattern to reduce the depth of the computation by gathering measurement commands that can be performed simultaneously.

This optimized pattern runs efficiently on GPUs and quantum hardwares with depth (e.g. coherence time) limitations.

minimize_space() → None

Optimize the pattern to minimize the max_space property of the pattern.

The optimized pattern has significantly reduced space requirement (memory space for classical simulation, and maximum simultaneously prepared qubits for quantum hardwares).

draw_graph(flow_from_pattern: bool = True, show_pauli_measurement: bool = True, show_local_clifford: bool = False, show_measurement_planes: bool = False, show_loop: bool = True, node_distance: tuple[int, int] = (1, 1), figsize: tuple | None = None, save: bool = False, filename: str | None = None) → None

Visualize the underlying graph of the pattern with flow or gflow structure.

Parameters:

• flow_from_pattern (bool) – If True, the command sequence of the pattern is used to derive flow or gflow structure. If False, only the underlying graph is used.

• show_pauli_measurement (bool) – If True, the nodes with Pauli measurement angles are colored light blue.

• show_local_clifford (bool) – If True, indexes of the local Clifford operator are displayed adjacent to the nodes.

• show_measurement_planes (bool) – If True, measurement planes are displayed adjacent to the nodes.

• show_loop (bool) – whether or not to show loops for graphs with gflow. defaulted to True.

• node_distance (tuple) – Distance multiplication factor between nodes for x and y directions.

• figsize (tuple) – Figure size of the plot.

• save (bool) – If True, the plot is saved as a png file.

• filename (str) – Filename of the saved plot.

max_space() → int

Compute the maximum number of nodes that must be present in the graph (graph space) during the execution of the pattern.

For statevector simulation, this is equivalent to the maximum memory needed for classical simulation.

Returns:

n_nodes – max number of nodes present in the graph during pattern execution.

Return type:

int

get_layers()

Construct layers(l_k) from dependency information.

kth layer must be measured before measuring k+1th layer and nodes in the same layer can be measured simultaneously.

Returns:

• depth (int) – depth of graph

• layers (dict of set) – nodes grouped by layer index(k)

to_qasm3(filename)

Export measurement pattern to OpenQASM 3.0 file.

Parameters:

filename (str) – file name to export to. example: “filename.qasm”

graphix.pattern.measure_pauli(pattern, leave_input, copy=False)

Perform Pauli measurement of a pattern by fast graph state simulator.

Uses the decorated-graph method implemented in graphix.graphsim to perform the measurements in Pauli bases, and then sort remaining nodes back into pattern together with Clifford commands.

TODO: non-XY plane measurements in original pattern

Parameters:

• pattern (graphix.pattern.Pattern object)

• leave_input (bool) – True: input nodes will not be removed False: all the nodes measured in Pauli bases will be removed

• copy (bool) – True: changes will be applied to new copied object and will be returned False: changes will be applied to the supplied Pattern object

Returns:

new_pattern – pattern with Pauli measurement removed. only returned if copy argument is True.

Return type:

graphix.Pattern object

See also

graphix.graphsim.GraphState