GraphState

class GraphState(adjacency_matrix)

Circuit to prepare a graph state.

Given a graph G = (V, E), with the set of vertices V and the set of edges E, the corresponding graph state is defined as

\[|G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V}\]

Such a state can be prepared by first preparing all qubits in the \(+\) state, then applying a \(CZ\) gate for each corresponding graph edge.

Graph state preparation circuits are Clifford circuits, and thus easy to simulate classically. However, by adding a layer of measurements in a product basis at the end, there is evidence that the circuit becomes hard to simulate [2].

Reference Circuit:

References:

[1] M. Hein, J. Eisert, H.J. Briegel, Multi-party Entanglement in Graph States,

arXiv:0307130

[2] D. Koh, Further Extensions of Clifford Circuits & their Classical Simulation Complexities.

arXiv:1512.07892

Create graph state preparation circuit.

Parameters

adjacency_matrix (Union[List, array]) – input graph as n-by-n list of 0-1 lists

The circuit prepares a graph state with the given adjacency matrix.

Attributes

GraphState.clbits	Returns a list of classical bits in the order that the registers were added.
GraphState.data	Return the circuit data (instructions and context).
GraphState.extension_lib
GraphState.header
GraphState.instances
GraphState.n_qubits	Deprecated, use num_qubits instead.
GraphState.num_clbits	Return number of classical bits.
GraphState.num_parameters	Convenience function to get the number of parameter objects in the circuit.
GraphState.num_qubits	Return number of qubits.
GraphState.parameters	Convenience function to get the parameters defined in the parameter table.
GraphState.prefix
GraphState.qubits	Returns a list of quantum bits in the order that the registers were added.

Methods

GraphState.AND(qr_variables, qb_target, …)	Build a collective conjunction (AND) circuit in place using mct.
GraphState.OR(qr_variables, qb_target, …)	Build a collective disjunction (OR) circuit in place using mct.
GraphState.__getitem__(item)	Return indexed operation.
GraphState.__len__()	Return number of operations in circuit.
GraphState.add_register(*regs)	Add registers.
GraphState.append(instruction[, qargs, cargs])	Append one or more instructions to the end of the circuit, modifying the circuit in place.
GraphState.assign_parameters(param_dict[, …])	Assign parameters to new parameters or values.
GraphState.barrier(*qargs)	Apply Barrier.
GraphState.bind_parameters(value_dict)	Assign numeric parameters to values yielding a new circuit.
GraphState.cast(value, _type)	Best effort to cast value to type.
GraphState.cbit_argument_conversion(…)	Converts several classical bit representations (such as indexes, range, etc.) into a list of classical bits.
GraphState.ccx(control_qubit1, …[, ctl1, …])	Apply CCXGate.
GraphState.ch(control_qubit, target_qubit, *)	Apply CHGate.
GraphState.cls_instances()	Return the current number of instances of this class, useful for auto naming.
GraphState.cls_prefix()	Return the prefix to use for auto naming.
GraphState.cnot(control_qubit, target_qubit, *)	Apply CXGate.
GraphState.combine(rhs)	Append rhs to self if self contains compatible registers.
GraphState.compose(other[, qubits, clbits, …])	Compose circuit with other circuit or instruction, optionally permuting wires.
GraphState.copy([name])	Copy the circuit.
GraphState.count_ops()	Count each operation kind in the circuit.
GraphState.crx(theta, control_qubit, …[, …])	Apply CRXGate.
GraphState.cry(theta, control_qubit, …[, …])	Apply CRYGate.
GraphState.crz(theta, control_qubit, …[, …])	Apply CRZGate.
GraphState.cswap(control_qubit, …[, …])	Apply CSwapGate.
GraphState.cu1(theta, control_qubit, …[, …])	Apply CU1Gate.
GraphState.cu3(theta, phi, lam, …[, …])	Apply CU3Gate.
GraphState.cx(control_qubit, target_qubit, *)	Apply CXGate.
GraphState.cy(control_qubit, target_qubit, *)	Apply CYGate.
GraphState.cz(control_qubit, target_qubit, *)	Apply CZGate.
GraphState.dcx(qubit1, qubit2)	Apply DCXGate.
GraphState.decompose()	Call a decomposition pass on this circuit, to decompose one level (shallow decompose).
GraphState.depth()	Return circuit depth (i.e., length of critical path).
GraphState.diag_gate(diag, qubit)	Deprecated version of QuantumCircuit.diagonal.
GraphState.diagonal(diag, qubit)	Attach a diagonal gate to a circuit.
GraphState.draw([output, scale, filename, …])	Draw the quantum circuit.
GraphState.extend(rhs)	Append QuantumCircuit to the right hand side if it contains compatible registers.
GraphState.fredkin(control_qubit, …[, …])	Apply CSwapGate.
GraphState.from_qasm_file(path)	Take in a QASM file and generate a QuantumCircuit object.
GraphState.from_qasm_str(qasm_str)	Take in a QASM string and generate a QuantumCircuit object.
GraphState.h(qubit, *[, q])	Apply HGate.
GraphState.hamiltonian(operator, time, qubits)	Apply hamiltonian evolution to to qubits.
GraphState.has_register(register)	Test if this circuit has the register r.
GraphState.i(qubit, *[, q])	Apply IGate.
GraphState.id(qubit, *[, q])	Apply IGate.
GraphState.iden(qubit, *[, q])	Deprecated identity gate.
GraphState.initialize(params, qubits)	Apply initialize to circuit.
GraphState.inverse()	Invert this circuit.
GraphState.iso(isometry, q_input, …[, …])	Attach an arbitrary isometry from m to n qubits to a circuit.
GraphState.isometry(isometry, q_input, …)	Attach an arbitrary isometry from m to n qubits to a circuit.
GraphState.iswap(qubit1, qubit2)	Apply iSwapGate.
GraphState.mcmt(gate, control_qubits, …[, …])	Apply a multi-control, multi-target using a generic gate.
GraphState.mcrx(theta, q_controls, q_target)	Apply Multiple-Controlled X rotation gate
GraphState.mcry(theta, q_controls, q_target, …)	Apply Multiple-Controlled Y rotation gate
GraphState.mcrz(lam, q_controls, q_target[, …])	Apply Multiple-Controlled Z rotation gate
GraphState.mct(control_qubits, target_qubit)	Apply MCXGate.
GraphState.mcu1(lam, control_qubits, …)	Apply MCU1Gate.
GraphState.mcx(control_qubits, target_qubit)	Apply MCXGate.
GraphState.measure(qubit, cbit)	Measure quantum bit into classical bit (tuples).
GraphState.measure_active([inplace])	Adds measurement to all non-idle qubits.
GraphState.measure_all([inplace])	Adds measurement to all qubits.
GraphState.mirror()	Mirror the circuit by reversing the instructions.
GraphState.ms(theta, qubits)	Apply MSGate.
GraphState.num_connected_components([…])	How many non-entangled subcircuits can the circuit be factored to.
GraphState.num_nonlocal_gates()	Return number of non-local gates (i.e.
GraphState.num_tensor_factors()	Computes the number of tensor factors in the unitary (quantum) part of the circuit only.
GraphState.num_unitary_factors()	Computes the number of tensor factors in the unitary (quantum) part of the circuit only.
GraphState.qasm([formatted, filename])	Return OpenQASM string.
GraphState.qbit_argument_conversion(…)	Converts several qubit representations (such as indexes, range, etc.) into a list of qubits.
GraphState.r(theta, phi, qubit, *[, q])	Apply RGate.
GraphState.rcccx(control_qubit1, …)	Apply RC3XGate.
GraphState.rccx(control_qubit1, …)	Apply RCCXGate.
GraphState.remove_final_measurements([inplace])	Removes final measurement on all qubits if they are present.
GraphState.reset(qubit)	Reset q.
GraphState.rx(theta, qubit, *[, label, q])	Apply RXGate.
GraphState.rxx(theta, qubit1, qubit2)	Apply RXXGate.
GraphState.ry(theta, qubit, *[, label, q])	Apply RYGate.
GraphState.ryy(theta, qubit1, qubit2)	Apply RYYGate.
GraphState.rz(phi, qubit, *[, q])	Apply RZGate.
GraphState.rzx(theta, qubit1, qubit2)	Apply RZXGate.
GraphState.rzz(theta, qubit1, qubit2)	Apply RZZGate.
GraphState.s(qubit, *[, q])	Apply SGate.
GraphState.sdg(qubit, *[, q])	Apply SdgGate.
GraphState.size()	Returns total number of gate operations in circuit.
GraphState.snapshot(label[, snapshot_type, …])	Take a statevector snapshot of the internal simulator representation.
GraphState.snapshot_density_matrix(label[, …])	Take a density matrix snapshot of simulator state.
GraphState.snapshot_expectation_value(label, …)	Take a snapshot of expectation value <O> of an Operator.
GraphState.snapshot_probabilities(label, qubits)	Take a probability snapshot of the simulator state.
GraphState.snapshot_stabilizer(label)	Take a stabilizer snapshot of the simulator state.
GraphState.snapshot_statevector(label)	Take a statevector snapshot of the simulator state.
GraphState.squ(unitary_matrix, qubit[, …])	Decompose an arbitrary 2*2 unitary into three rotation gates.
GraphState.swap(qubit1, qubit2)	Apply SwapGate.
GraphState.t(qubit, *[, q])	Apply TGate.
GraphState.tdg(qubit, *[, q])	Apply TdgGate.
GraphState.to_gate([parameter_map])	Create a Gate out of this circuit.
GraphState.to_instruction([parameter_map])	Create an Instruction out of this circuit.
GraphState.toffoli(control_qubit1, …[, …])	Apply CCXGate.
GraphState.u1(theta, qubit, *[, q])	Apply U1Gate.
GraphState.u2(phi, lam, qubit, *[, q])	Apply U2Gate.
GraphState.u3(theta, phi, lam, qubit, *[, q])	Apply U3Gate.
GraphState.uc(gate_list, q_controls, q_target)	Attach a uniformly controlled gates (also called multiplexed gates) to a circuit.
GraphState.ucg(angle_list, q_controls, q_target)	Deprecated version of uc.
GraphState.ucrx(angle_list, q_controls, q_target)	Attach a uniformly controlled (also called multiplexed) Rx rotation gate to a circuit.
GraphState.ucry(angle_list, q_controls, q_target)	Attach a uniformly controlled (also called multiplexed) Ry rotation gate to a circuit.
GraphState.ucrz(angle_list, q_controls, q_target)	Attach a uniformly controlled (also called multiplexed gates) Rz rotation gate to a circuit.
GraphState.ucx(angle_list, q_controls, q_target)	Deprecated version of ucrx.
GraphState.ucy(angle_list, q_controls, q_target)	Deprecated version of ucry.
GraphState.ucz(angle_list, q_controls, q_target)	Deprecated version of ucrz.
GraphState.unitary(obj, qubits[, label])	Apply unitary gate to q.
GraphState.width()	Return number of qubits plus clbits in circuit.
GraphState.x(qubit, *[, label, ctrl_state, q])	Apply XGate.
GraphState.y(qubit, *[, q])	Apply YGate.
GraphState.z(qubit, *[, q])	Apply ZGate.
GraphState.__getitem__(item)	Return indexed operation.
GraphState.__len__()	Return number of operations in circuit.