Pattern Simulation

graphix.simulator module

class graphix.simulator.PatternSimulator(pattern, backend='statevector', **kwargs)

MBQC simulator

Executes the measurement pattern.

__init__(pattern, backend='statevector', **kwargs)

pattern: graphix.pattern.Pattern object

MBQC pattern to be simulated.

backend: str, ‘statevector’ or ‘MPS’

simulation backend (optional), default is ‘statevector’.

kwargs: keyword args for specified backend.

See also

graphix.sim.statevec.StatevectorBackend graphix.sim.mps.MPS

run()

Perform the simulation.

Returns

the output quantum state, in the representation depending on the backend used.

Return type

state

Simulator backends

Matrix Product State (MPS)

class graphix.sim.mps.MPS(pattern, singular_value=None, max_truncation_err=None, graph_prep='opt')

Matrix Product Simulator for MBQC

Executes the measurement pattern. This is a simple implementation. Improved CPU/GPU MPS simulator will be released soon.

__init__(pattern, singular_value=None, max_truncation_err=None, graph_prep='opt')

Parameters

• pattern (graphix.Pattern) – MBQC command sequence to be simulated

• singular_value (int) – cut off threshold for SVD decomposition

• truncation_err (float) – cut off threshold for SVD decomposition. truncate maximum number of singular values within truncation_err

• graph_prep (str) – ‘sequential’ for standard method, ‘opt’ for faster method

add_node(n)

Internal method of run_cmd(). Add new qubit to a node set of MPS.

Parameters

(int) (n) –

add_nodes(cmds)

add qubits to node sets from command sequence

apply_clifford(cmd)

Apply single-qubit Clifford gate, specified by vop index specified in graphix.clifford.CLIFFORD

Parameters

(list) (cmd) –

apply_one_site_operator(loc, node_op)

Internal method for measure, correct_byproduct, and apply_clifford. Apply one site operator to a node.

Parameters

• (int) (loc) –

• (tn.Node) (node_op) –

correct_byproduct(cmd)

Perform byproduct correction.

Parameters

(list) (cmd) –

count_maxE()

Count the max number of edges per a node. When maxE is large number, huge memory(2^maxE) will be used.

Returns

int

Return type

The max number of edges.

entangle_nodes(edge)

Make entanglement between nodes specified by edge. Contract non-dangling edges in this process. Optimized contraction will be implemented in a later release.

Parameters

ints) (edge (taple of) –

expectation_value(op, qargs)

calculate expectation value of given operator.

Parameters

• (numpy.ndarray) (op) –

• ints) (qargs (list of) –

Returns

expectation_value

Return type

float

expectation_value_ops(ops, qargs)

calculate expectation value of given operators. This command is mainly used for retrieving a probability distribution.

Parameters

• numpy.ndarray) (ops (list of) – For constructing statevector, ops are projection operators fro each site.

• ints) (qargs (list of) –

Returns

expectation value

Return type

float

get_amplitude(number)

calculate a probability amplitude of the specified state.

Parameters

• (int) (number) –

• 10. (e.g. |0000> corresponds to 0. |1010> corresponds to) –

Returns

float

Return type

the probability amplitude of the specified state.

initialize()

initialize the internal MPS state

make_graph_state()

Prepare a graph state with efficient expression, instead of using CZ gates. This is is an internal method of run_cmd().

See also

make_initial()

make_initial()

This is an internal method of run_cmd. Prepare a graph state sequentially by applying CZ gates.

measure(cmd)

Perform measurement of a node. In MPS, to apply measurement operator to the tensor, consisting Matrix Product State, equals to perform measurement.

Parameters

(list) (cmd) –

replicate_node_dict(node_dict, conjugate=False)

Replicate dictionary of nodes.

Parameters

tensornetwork.Node) (node_dict (dic of) –

Returns

dict of tensornetwork.Node

Return type

replicated node dictionary

set_singular_value(chi)

Set the number of singular values holding under singular value decomposition(SVD).

Note: If you choose ‘opt’ as a graph_prep, you don’t have to specify the singular_value.

Parameters

chi(int) (number of singular values holding when SVD executed) –

set_truncation_err(truncation_err)

Set the max truncation error under SVD.

Note: If you choose ‘opt’ as a graph_prep, you don’t have to specify the truncation_err.

Parameters

• (float) (truncation_err) –

• possessed. (Maximum number of singular values keeping truncation error under specified value will be) –

Statevector

class graphix.sim.statevec.StatevectorBackend(pattern, max_qubit_num=20)

MBQC simulator with statevector method.

__init__(pattern, max_qubit_num=20)

pattern: graphix.pattern.Pattern object

MBQC pattern to be simulated.

backend: str, ‘statevector’

optional argument for simulation.

max_qubit_numint

optional argument specifying the maximum number of qubits to be stored in the statevector at a time.

add_nodes(nodes)

add new qubit to internal statevector and assign the corresponding node number to list self.node_index.

Parameters

nodes (list of node indices) –

apply_clifford(cmd)

Apply single-qubit Clifford gate, specified by vop index specified in graphix.clifford.CLIFFORD

correct_byproduct(cmd)

Byproduct correction correct for the X or Z byproduct operators, by applying the X or Z gate.

entangle_nodes(edge)

Apply CZ gate to two connected nodes

Parameters

edge (tuple (i, j)) – a pair of node indices

finalize()

to be run at the end of pattern simulation.

initialize()

Initialize the internal statevector

measure(cmd)

Perform measurement of a node in the internal statevector and trace out the qubit :param cmd: measurement command : [‘M’, node, plane angle, s_domain, t_domain] :type cmd: list

qubit_dim()

Returns the qubit number in the internal statevector :returns: n_qubit :rtype: int

sort_qubits()

sort the qubit order in internal statevector

trace_out()

trace out the qubits buffered in self.to_trace from self.state

graphix.sim.statevec.meas_op(angle, vop=0, plane='XY', choice=0)

Returns the projection operator for given measurement angle and local Clifford op (VOP).

See also

graphix.clifford

Parameters

• angle (float) – original measurement angle in radian

• vop (int) – index of local Clifford (vop), see graphq.clifford.CLIFFORD

• plane ('XY', 'YZ' or 'ZX') – measurement plane on which angle shall be defined

• choice (0 or 1) – choice of measurement outcome. measured eigenvalue would be (-1)**choice.

Returns

op – projection operator

Return type

numpy array

class graphix.sim.statevec.Statevec(plus_states=True, nqubit=1)

Simple statevector simulator

CNOT(qubits)

apply CNOT

Parameters

qubits (tuple of ints) – (control, target) qubit indices

__init__(plus_states=True, nqubit=1)

Initialize statevector

Parameters

• plus_states (bool, optional) – whether or not to start all qubits in + state or 0 state. Defaults to +

• nqubit (int, optional) – number of qubits. Defaults to 1.

entangle(edge)

connect graph nodes

Parameters

edge (tuple of ints) – (control, target) qubit indices

evolve(op, qargs)

Multi-qubit operation

Parameters

• op (np.array) – 2^n*2^n matrix

• qargs (list of ints) – target qubits’ indexes

evolve_single(op, i)

Single-qubit operation

Parameters

• op (np.array) – 2*2 matrix

• i (int) – qubit index

expectation_single(op, loc)

Expectation value of single-qubit operator.

Parameters

• op (np.array) – 2*2 Hermite operator

• loc (int) – target qubit

Returns

expectation value.

Return type

complex

expectation_value(op, qargs)

Expectation value of multi-qubit operator.

Parameters

• op (np.array) – 2^n*2^n operator

• qargs (list of ints) – target qubit

Returns

expectation value

Return type

complex

flatten()

returns flattened statevector

normalize()

normalize the state

ptrace(qargs)

partial trace

Parameters

qargs (list of ints) – qubit inices to trace over

swap(qubits)

swap qubits

Parameters

qubits (tuple of ints) – (control, target) qubit indices

tensor(other)

Tensor product state with other qubits. Results in self \(\otimes\) other.

Parameters

other (_type_) – graphix.sim.statevec.Statevec instance