c3/libraries/hamiltonians.py
"""Library of Hamiltonian functions."""
import numpy as np
hamiltonians = dict()
def hamiltonian_reg_deco(func):
"""
Decorator for making registry of functions
"""
hamiltonians[str(func.__name__)] = func
return func
@hamiltonian_reg_deco
def resonator(a):
"""
Harmonic oscillator hamiltonian given the annihilation operator.
Parameters
----------
a : Tensor
Annihilator.
Returns
-------
Tensor
Number operator.
"""
a_dag = a.T.conj()
return np.matmul(a_dag, a)
@hamiltonian_reg_deco
def duffing(a):
"""
Anharmonic part of the duffing oscillator.
Parameters
----------
a : Tensor
Annihilator.
Returns
-------
Tensor
Number operator.
"""
a_dag = a.T.conj()
n = np.matmul(a_dag, a)
return 1 / 2 * np.matmul(n - np.eye(int(n.shape[0]), dtype=np.complex128), n)
@hamiltonian_reg_deco
def third_order(a):
"""
Parameters
----------
a : Tensor
Annihilator.
Returns
-------
Tensor
Number operator.
return literally the Hamiltonian a_dag a a + a_dag a_dag a for the use in any Hamiltonian that uses more than
just a resonator or Duffing part. A more general type of quantum element on a physical chip can have this type of interaction.
One example is a three wave mixing element used in signal amplification called a Superconducting non-linear asymmetric inductive eLement
(SNAIL in short). The code is a simple modification of the Duffing function and written in the same style.
"""
a_dag = a.T.conj()
n = np.matmul(a_dag, a)
return np.matmul(n, a) + np.matmul(a_dag, n)
@hamiltonian_reg_deco
def int_XX(anhs):
"""
Dipole type coupling.
Parameters
----------
anhs : Tensor list
Annihilators.
Returns
-------
Tensor
coupling
"""
a = anhs[0]
b = anhs[1]
a_dag = a.T.conj()
b_dag = b.T.conj()
return np.matmul(a_dag + a, b_dag + b)
@hamiltonian_reg_deco
def int_YY(anhs):
"""
Dipole type coupling.
Parameters
----------
anhs : Tensor list
Annihilators.
Returns
-------
Tensor
coupling
"""
a = anhs[0]
b = anhs[1]
a_dag = a.T.conj()
b_dag = b.T.conj()
return -np.matmul(a_dag - a, b_dag - b)
@hamiltonian_reg_deco
def x_drive(a):
"""
Semiclassical drive.
Parameters
----------
a : Tensor
Annihilator.
Returns
-------
Tensor
Number operator.
"""
a_dag = a.T.conj()
return a_dag + a
@hamiltonian_reg_deco
def y_drive(a):
"""
Semiclassical drive.
Parameters
----------
a : Tensor
Annihilator.
Returns
-------
Tensor
Number operator.
"""
a_dag = a.T.conj()
return 1.0j * (a_dag - a)
@hamiltonian_reg_deco
def z_drive(a):
"""
Semiclassical drive.
Parameters
----------
a : Tensor
Annihilator.
Returns
-------
Tensor
Number operator.
"""
a_dag = a.T.conj()
return np.matmul(a_dag, a)