GMS¶

class GMS(num_qubits, theta)[source]¶

Bases: qiskit.circuit.quantumcircuit.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)

../_images/qiskit-circuit-library-GMS-1.png

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.

Parameters

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.

Return type: List[AncillaQubit]

calibrations¶

Return calibration dictionary.

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

Return type: dict

clbits¶

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

Return type: List[Clbit]

data¶

Return the circuit data (instructions and context).

Returns: a list-like object containing the CircuitInstructions for each instruction.
Return type: QuantumCircuitData

extension_lib = 'include "qelib1.inc";'¶

global_phase¶

Return the global phase of the circuit in radians.

Return type: Union[ParameterExpression, float]

header = 'OPENQASM 2.0;'¶

instances = 2313¶

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.

Return type: dict

num_ancillas¶

Return the number of ancilla qubits.

Return type: int

num_clbits¶

Return number of classical bits.

Return type: int

num_parameters¶

The number of parameter objects in the circuit.

Return type: int

num_qubits¶

Return number of qubits.

Return type: 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.

Return type: List[int]
Returns: List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Raises: 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.

Examples

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])
])

Return type: ParameterView
Returns: The sorted Parameter objects in the circuit.

prefix = 'circuit'¶

qubits¶

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

Return type: List[Qubit]