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 ‘tensornetwork’

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

kwargs: keyword args for specified backend.

See also

graphix.sim.statevec.StatevectorBackend graphix.sim.tensornet.TensorNetworkBackend

run()

Perform the simulation.

Returns

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

Return type

state

Simulator backends

Tensor Network

class graphix.sim.tensornet.TensorNetworkBackend(pattern, graph_prep='opt', **kwargs)

Tensor Network Simulator for MBQC

Executes the measurement pattern using TN expression of graph states.

__init__(pattern, graph_prep='opt', **kwargs)

Parameters

• pattern (graphix.Pattern) –

• graph_prep (str) –

  ‘opt’(default) :

  Faster and optimal method to prepare a tensornetwork representing graph state. The expression of the given graph state can be obtained from its geometry. See https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.052315 for example. Note that the ‘N’ and ‘E’ commands in the measurement pattern are ignored.

  ’sequential’ :

  Sequentially add nodes and edges, strictly following the measuremen pattern. In this strategy, All N and E commands executed sequentially.

• **kwargs (Additional keyword args to be passed to quimb.tensor.TensorNetwork.) –

add_nodes(nodes)

Add nodes to the network

Parameters

nodes (iterator of int) – index set of the new nodes.

apply_clifford(cmd)

Apply single-qubit Clifford gate

Parameters

cmd (list) – clifford command. See https://arxiv.org/pdf/2212.11975.pdf for the detail.

correct_byproduct(cmd)

Perform byproduct correction.

Parameters

cmd (list) – Byproduct command i.e. [‘X’ or ‘Z’, node, signal_domain]

entangle_nodes(edge)

Make entanglement between nodes specified by edge.

Parameters

edge (tuple of int) – edge specifies two target nodes of the CZ gate.

measure(cmd)

Perform measurement of the node. In the context of tensornetwork, performing measurement equals to applying measurement operator to the tensor. Here, directly contracted with the projected state.

Parameters

cmd (list) – measurement command i.e. [‘M’, node, plane angle, s_domain, t_domain]

graphix.sim.tensornet.gen_str()

Generate dummy string for einsum.

graphix.sim.tensornet.proj_basis(angle, vop, plane, choice)

the projected statevector.

Parameters

• angle (float) – measurement angle

• vop (int) – CLIFFORD index

• plane (str) – measurement plane

• choice (int) – measurement result

Returns

projected state

Return type

numpy.ndarray

graphix.sim.tensornet.outer_product(vectors)

outer product of the given vectors

Parameters

vectors (list of vector) – vectors

Returns

tensor object.

Return type

numpy.ndarray

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.

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