Pattern Optimization

graphix.pattern module

class graphix.pattern.Pattern(input_nodes=[])

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

Nnode

total number of nodes in the resource state

Type:

int

__init__(input_nodes=[])

Parameters:

input_nodes – optional, list of input qubits

add(cmd: Command)

add command to the end of the pattern. an MBQC command is specified by a list of [type, node, attr], where

type : ‘N’, ‘M’, ‘E’, ‘X’, ‘Z’, ‘S’ or ‘C’ nodes : int for ‘N’, ‘M’, ‘X’, ‘Z’, ‘S’, ‘C’ commands nodes : tuple (i, j) for ‘E’ command attr for N (node preparation):

none

attr for E (entanglement):

none

attr for M (measurement):

meas_plane : ‘XY’,’YZ’ or ‘XZ’ angle : float, in radian / pi s_domain : list t_domain : list

attr for X:

signal_domain : list

attr for Z:

signal_domain : list

attr for S:

signal_domain : list

attr for C:

clifford_index : int

Parameters:

cmd (list) – MBQC command.

extend(cmds: list[Command])

Add a list of commands.

Parameters:

cmds – list of commands

clear()

Clear the sequence of pattern commands.

replace(cmds: list[Command], input_nodes=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='statevector', **kwargs)

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:

dict

Return type:

vops

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=False, use_rustworkx=False)

Perform Pauli measurements in the pattern using efficient stabilizer simulator.

See also

measure_pauli()

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

print the pattern sequence (Pattern.seq).

Parameters:

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

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

standardize(method='local')

Executes 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) – ‘global’ corresponds to a conventional standardization executed on Pattern class. ‘local’ standardization is executed on LocalPattern class. In all cases, local pattern standardization is significantly faster than conventional one. defaults to ‘local’

shift_signals(method='local')

Performs 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 ‘global’ method:

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

Ref for the ‘local’ method:

19. Sunami and M. Fukushima, in preparation

Parameters:

method (str, optional) – ‘global’ shift_signals is executed on a conventional Pattern sequence. ‘local’ shift_signals is done on a LocalPattern class which is faster but results in equivalent pattern. defaults to ‘local’

is_standard()

determines whether the command sequence is standard

Returns:

is_standard – True if the pattern is standard

Return type:

bool

get_graph()

returns 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()

Optimize the pattern to minimize the max_space property of the pattern i.e. 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=True, show_pauli_measurement=True, show_local_clifford=False, show_measurement_planes=False, show_loop=True, node_distance=(1, 1), figsize=None, save=False, filename=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()

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”

class graphix.pattern.CommandNode(node_index, seq, Mprop, Zsignal, input, output, Xsignal=[], Xsignals=[])

A node decorated with a distributed command sequence.

index

node index

Type:

int

seq

command sequence. In this class, a command sequence follows the rules noted below.

E: pair node’s index(>=0) M: -1 X: -2 Z: -3 C: -4

Type:

list

Mprop

attributes for a measurement command. consists of [meas_plane, angle, s_domain, t_domain, vop]

Type:

list

result

measurement result of the node

Type:

int

Xsignal

signal domain

Type:

list

Xsignals

signal domain. Xsignals may contains lists. For standardization, this variable is used.

Type:

list

Zsignal

signal domain

Type:

list

vop

value for clifford index

Type:

int

input

whether the node is an input or not

Type:

bool

output

whether the node is an output or not

Type:

bool

__init__(node_index, seq, Mprop, Zsignal, input, output, Xsignal=[], Xsignals=[])

Parameters:

• node_index (int) – node index

• seq (list) – distributed command sequence

• Mprop (list) – attributes for measurement command

• Xsignal (list) – signal domain for X byproduct correction

• Xsignals (list of list) – signal domains for X byproduct correction Xsignal or Xsignals must be specified

• Zsignal (list) – signal domain for Z byproduct correction

• input (bool) – whether the node is an input or not

• output (bool) – whether the node is an output or not

print_pattern()

Print the local command sequence

class graphix.pattern.LocalPattern(nodes={}, input_nodes=[], output_nodes=[], morder=[])

MBQC Local Pattern class

Instead of storing commands as a 1D list as in Pattern class, here we distribute them to each node. This data structure is efficient for command operations such as commutation and signal propagation. This results in faster standardization and signal shifting.

nodes

set of nodes with distributed command sequences

Type:

set

input_nodes

list of input node indices.

Type:

list

output_nodes

list of output node indices.

Type:

list

morder

list of node indices in a measurement order.

Type:

list

signal_destination

Type:

dict

stores the set of nodes where dependent feedforward operations are performed, from the result of measurement at each node.

stored separately for each nodes, and for each kind of signal(Ms, Mt, X, Z).

__init__(nodes={}, input_nodes=[], output_nodes=[], morder=[])

Parameters:

• nodes (dict) – dict of command decorated nodes. defaults to an empty dict.

• output_nodes (list, optional) – list of output node indices. defaults to [].

• morder (list, optional) – list of node indices in a measurement order. defaults to [].

standardize()

Standardize pattern. In this structure, it is enough to move all byproduct corrections to the back

shift_signals()

Shift signals to the back based on signal destinations.

get_graph()

Get a graph from a local pattern

Returns:

• nodes (list) – list of node indices

• edges (list) – list of edges

get_pattern()

Convert a local pattern into a corresponding global pattern. Currently, only standardized pattern is supported.

Returns:

pattern – standardized global pattern

Return type:

Pattern

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