LogicalQ.Library.Gates

Attributes

`UGate`
`zzgate`
`ZZGate_def`
`gates`
`clifford_gates`
`clifford_gates_1q`
`pauli_gates`
`gates_1q`
`gates_2q`
`gate_sets`

Classes

ZZGate

A parametric 2-qubit \(Z \otimes Z\) interaction (rotation about ZZ).

Functions

`string_to_gate_class`(_gate_string)
`string_to_gate_set`(_gate_set_string)
`get_num_params`(gate_class)

Module Contents

LogicalQ.Library.Gates.UGate

class LogicalQ.Library.Gates.ZZGate(label=None)

Bases: qiskit.circuit.library.RZZGate

A parametric 2-qubit \(Z \otimes Z\) interaction (rotation about ZZ).

This gate is symmetric, and is maximally entangling at \(\theta = \pi/2\).

Can be applied to a QuantumCircuit with the rzz() method.

Circuit Symbol:

q_0: ───■────
        │zz(θ)
q_1: ───■────

Matrix Representation:

\[ \begin{align}\begin{aligned}\newcommand{\rotationangle}{\frac{\theta}{2}}\\\begin{split}R_{ZZ}(\theta) = \exp\left(-i \rotationangle Z{\otimes}Z\right) = \begin{pmatrix} e^{-i \rotationangle} & 0 & 0 & 0 \\ 0 & e^{i \rotationangle} & 0 & 0 \\ 0 & 0 & e^{i \rotationangle} & 0 \\ 0 & 0 & 0 & e^{-i \rotationangle} \end{pmatrix}\end{split}\end{aligned}\end{align} \]

This is a direct sum of RZ rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RZ gate:

\[\begin{split}R_{ZZ}(\theta) = \begin{pmatrix} RZ(\theta) & 0 \\ 0 & RZ(-\theta) \end{pmatrix}\end{split}\]

Examples:

\[R_{ZZ}(\theta = 0) = I\]

\[R_{ZZ}(\theta = 2\pi) = -I\]

\[R_{ZZ}(\theta = \pi) = - i Z \otimes Z\]

\[\begin{split}R_{ZZ}\left(\theta = \frac{\pi}{2}\right) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1-i & 0 & 0 & 0 \\ 0 & 1+i & 0 & 0 \\ 0 & 0 & 1+i & 0 \\ 0 & 0 & 0 & 1-i \end{pmatrix}\end{split}\]

_standard_gate = None

name = 'zz': Return the name.

__eq__(other)

Two instructions are the same if they have the same name, same dimensions, and same params.

Parameters:: other (instruction) – other instruction
Returns:: are self and other equal.
Return type:: bool

LogicalQ.Library.Gates.zzgate

LogicalQ.Library.Gates.ZZGate_def

LogicalQ.Library.Gates.gates

LogicalQ.Library.Gates.string_to_gate_class(_gate_string)

LogicalQ.Library.Gates.clifford_gates

LogicalQ.Library.Gates.clifford_gates_1q

LogicalQ.Library.Gates.pauli_gates

LogicalQ.Library.Gates.gates_1q

LogicalQ.Library.Gates.gates_2q

LogicalQ.Library.Gates.gate_sets

LogicalQ.Library.Gates.string_to_gate_set(_gate_set_string)

LogicalQ.Library.Gates.get_num_params(gate_class)