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U2Gate

U2Gate(phi, lam, label=None) GitHub(opens in a new tab)

Single-qubit rotation about the X+Z axis.

Implemented using one X90 pulse on IBM Quantum systems:

U2(ϕ,λ)=RZ(ϕ+π/2).RX(π2).RZ(λπ/2)U2(\phi, \lambda) = RZ(\phi+\pi/2).RX(\frac{\pi}{2}).RZ(\lambda-\pi/2)

Circuit symbol:

     ┌─────────┐
q_0:U2(φ,λ)
     └─────────┘

Matrix Representation:

U2(ϕ,λ)=12(1eiλeiϕei(ϕ+λ))\begin{split}U2(\phi, \lambda) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -e^{i\lambda} \\ e^{i\phi} & e^{i(\phi+\lambda)} \end{pmatrix}\end{split}

Examples:

U2(0,π)=HU2(0, \pi) = H
See also

U3Gate: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses.

Create new U2 gate.


Attributes

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

label

str

Return gate label

Return type

str

params

return instruction params.


Methods

add_decomposition

U2Gate.add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

U2Gate.assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

broadcast_arguments

U2Gate.broadcast_arguments(qargs, cargs)

Validation and handling of the arguments and its relationship.

For example, cx([q[0],q[1]], q[2]) means cx(q[0], q[2]); cx(q[1], q[2]). This method yields the arguments in the right grouping. In the given example:

in: [[q[0],q[1]], q[2]],[]
outs: [q[0], q[2]], []
      [q[1], q[2]], []

The general broadcasting rules are:

  • If len(qargs) == 1:

    [q[0], q[1]] -> [q[0]],[q[1]]
  • If len(qargs) == 2:

    [[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
    [[q[0]], [r[0], r[1]]]       -> [q[0], r[0]], [q[0], r[1]]
    [[q[0], q[1]], [r[0]]]       -> [q[0], r[0]], [q[1], r[0]]
  • If len(qargs) >= 3:

    [q[0], q[1]], [r[0], r[1]],  ...] -> [q[0], r[0], ...], [q[1], r[1], ...]

Parameters

  • qargs (List) – List of quantum bit arguments.
  • cargs (List) – List of classical bit arguments.

Return type

Tuple[List, List]

Returns

A tuple with single arguments.

Raises

CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.

c_if

U2Gate.c_if(classical, val)

Add classical condition on register classical and value val.

control

U2Gate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return controlled version of gate. See ControlledGate for usage.

Parameters

  • num_ctrl_qubits (Optional[int]) – number of controls to add to gate (default=1)
  • label (Optional[str]) – optional gate label
  • ctrl_state (Union[int, str, None]) – The control state in decimal or as a bitstring (e.g. ‘111’). If None, use 2**num_ctrl_qubits-1.

Returns

Controlled version of gate. This default algorithm uses num_ctrl_qubits-1 ancillae qubits so returns a gate of size num_qubits + 2*num_ctrl_qubits - 1.

Return type

qiskit.circuit.ControlledGate

Raises

QiskitError – unrecognized mode or invalid ctrl_state

copy

U2Gate.copy(name=None)

Copy of the instruction.

Parameters

name (str) – name to be given to the copied circuit, if None then the name stays the same.

Returns

a copy of the current instruction, with the name

updated if it was provided

Return type

qiskit.circuit.Instruction

inverse

U2Gate.inverse()

Return inverted U2 gate.

U2(ϕ,λ)=U2(λπ,ϕ+π)U2(\phi, \lambda)^{\dagger} =U2(-\lambda-\pi, -\phi+\pi))

is_parameterized

U2Gate.is_parameterized()

Return True .IFF. instruction is parameterized else False

mirror

U2Gate.mirror()

For a composite instruction, reverse the order of sub-gates.

This is done by recursively mirroring all sub-instructions. It does not invert any gate.

Returns

a fresh gate with sub-gates reversed

Return type

qiskit.circuit.Instruction

power

U2Gate.power(exponent)

Creates a unitary gate as gate^exponent.

Parameters

exponent (float) – Gate^exponent

Returns

To which to_matrix is self.to_matrix^exponent.

Return type

qiskit.extensions.UnitaryGate

Raises

CircuitError – If Gate is not unitary

qasm

U2Gate.qasm()

Return a default OpenQASM string for the instruction.

Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).

repeat

U2Gate.repeat(n)

Creates an instruction with gate repeated n amount of times.

Parameters

n (int) – Number of times to repeat the instruction

Returns

Containing the definition.

Return type

qiskit.circuit.Instruction

Raises

CircuitError – If n < 1.

to_matrix

U2Gate.to_matrix()

Return a Numpy.array for the U2 gate.

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