GMS

class GMS(num_qubits, theta)

Bases : QuantumCircuit

Global Mølmer–Sørensen gate.

Circuit symbol:

     ┌───────────┐
q_0: ┤0          ├
     │           │
q_1: ┤1   GMS    ├
     │           │
q_2: ┤2          ├
     └───────────┘

Expanded Circuit:

(Source code, png, hires.png, pdf)

The Mølmer–Sørensen gate is native to ion-trap systems. The global MS can be applied to multiple ions to entangle multiple qubits simultaneously [1].

In the two-qubit case, this is equivalent to an XX(theta) interaction, and is thus reduced to the RXXGate. The global MS gate is a sum of XX interactions on all pairs [2].

\[GMS(\chi_{12}, \chi_{13}, ..., \chi_{n-1 n}) = exp(-i \sum_{i=1}^{n} \sum_{j=i+1}^{n} X{\otimes}X \frac{\chi_{ij}}{2})\]

References:

[1] Sørensen, A. and Mølmer, K., Multi-particle entanglement of hot trapped ions. Physical Review Letters. 82 (9): 1835–1838. arXiv:9810040

[2] Maslov, D. and Nam, Y., Use of global interactions in efficient quantum circuit constructions. New Journal of Physics, 20(3), p.033018. arXiv:1707.06356

Create a new Global Mølmer–Sørensen (GMS) gate.

Paramètres

• num_qubits (int) – width of gate.

• theta (Union[List[List[float]], ndarray]) – a num_qubits x num_qubits symmetric matrix of interaction angles for each qubit pair. The upper triangle is considered.

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

Type renvoyé

List[AncillaQubit]

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}

Type renvoyé

dict

clbits

Returns a list of classical bits in the order that the registers were added.

Type renvoyé

List[Clbit]

data

Return the circuit data (instructions and context).

Renvoie

a list-like object containing the CircuitInstructions for each instruction.

Type renvoyé

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'

global_phase

Return the global phase of the circuit in radians.

Type renvoyé

Union[ParameterExpression, float]

header = 'OPENQASM 2.0;'

instances = 2021

metadata

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

Type renvoyé

dict

num_ancillas

Return the number of ancilla qubits.

Type renvoyé

int

num_clbits

Return number of classical bits.

Type renvoyé

int

num_parameters

The number of parameter objects in the circuit.

Type renvoyé

int

num_qubits

Return number of qubits.

Type renvoyé

int

op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

Type renvoyé

List[int]

Renvoie

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

Lève

AttributeError – When circuit is not scheduled.

parameters

The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

Exemples

The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])

Bear in mind that alphabetical sorting might be unituitive when it comes to numbers. The literal « 10 » comes before « 2 » in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])

To respect numerical sorting, a ParameterVector can be used.

>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])

Type renvoyé

ParameterView

Renvoie

The sorted Parameter objects in the circuit.

prefix = 'circuit'

qubits

Returns a list of quantum bits in the order that the registers were added.

Type renvoyé

List[Qubit]