import numpy as np
from scipy.linalg import qr
import copy
from .TTsTwoLevelId import TTsTwoLevelId
from .tt import zCreMPS, zTT
from ..dynamics.tdevott import zRightOrth
[docs]
class TTs1Q(TTsTwoLevelId):
""" MPS and MPO for 1qubit systems
"""
def __init__(self, rhoIni, bondDim, V, depth, nu, coeff,
pulse, pulseMap):
"""
args:
rhoIni (numpy.ndarray): initial reduced density operator
bondDim (int): bondDimension of MPS
V (numpy.ndarray):
matrices for qubit-reservoir coupling (3d array)
nu (list): list of poles for FP-HEOM
coeff (list): list of residues for FP-HEOM
depth (list):
1d list of depth of hierarchy of FP-HEOM (from 0 to depth)
pulse (list[
list[list[int], pulse.abstract_pulse.abstractPulse]
]):
list for elemental gates
pulseMap (dict[tuple[int]: int]):
dictionary for a mapping from
qubit indeces to pulse indeces
keys (tuple[int]): qubit indedes
values (int): pulse indeces for self.pulse
"""
super().__init__(depth)
self.dim = [nu[0].shape[0]]
self.numQ = 1
self.numCore = 2 * self.dim[0] + 2
self.ptrKet = [0]
self.ptrBra = [2*self.dim[0]+1]
self.zGetMPS(rhoIni, bondDim, depth)
zRightOrth(self.rho)
self.numH = 4
self.zGetMPO(V, depth, nu, coeff)
# self.indices = self.getIndices()
self.pulse = pulse
self.map = pulseMap
[docs]
def zGetMPS(self, rhoIni, bondDim, depth):
"""create MPS
args:
rhoIni (numpy.ndarray): initial reduced density operator
bondDim (int): bondDimension of MPS
depth (list):
1d list of depth of hierarchy of FP-HEOM (from 0 to depth)
"""
levels = np.zeros(self.numCore, dtype=int)
levels[self.ptrKet[0]] = 2
levels[self.ptrKet[0] + 1:self.ptrBra[0]] = depth[0] + 1
levels[self.ptrBra[0]] = 2
rhoBondDims = self.getRhoBondDims(levels, bondDim)
self.rho = zCreMPS(self.numCore, rhoBondDims, levels)
ket0, bra0 = qr(rhoIni)
i = self.ptrKet[0]
coreTmp = np.zeros([self.rho[i].bondDimL,
self.rho[i].level,
self.rho[i].bondDimR],
dtype=np.complex128)
coreTmp[0, :2, :2] = ket0
self.rho[i].core = copy.deepcopy(coreTmp.flatten(order='F'))
i = self.ptrBra[0]
coreTmp = np.zeros([self.rho[i].bondDimL,
self.rho[i].level,
self.rho[i].bondDimR],
dtype=np.complex128)
coreTmp[:2, :2, 0] = bra0
self.rho[i].core = copy.deepcopy(coreTmp.flatten(order='F'))
# middle tensors
for i in range(self.ptrKet[0] + 1, self.ptrBra[0]):
coreTmp = np.zeros([self.rho[i].bondDimL,
self.rho[i].level,
self.rho[i].bondDimR],
dtype=np.complex128)
n = min(coreTmp.shape[0], coreTmp.shape[2])
for j in range(n):
coreTmp[j, 0, j] = 1.0 + 0.0j
self.rho[i].core = copy.deepcopy(coreTmp.flatten(order='F'))
[docs]
def zGetMPO(self, V, depth, nu, coeff):
"""create MPO
args:
V (numpy.ndarray):
matrices for qubit-reservoir coupling (3d array)
pol (list): list of poles for FP-HEOM
res (list): list of residues for FP-HEOM
depth (list):
1d list of depth of hierarchy of FP-HEOM (from 0 to depth)
"""
# creare array of MPO
self.H = np.array([[zTT() for _ in range(self.numCore)]
for _ in range(self.numH)])
# set values for MPO
# system part
# time-independent part
j = 0
i = self.ptrKet[0]
coreTmp = np.zeros([1, 2, 2, 4], dtype=np.complex128)
coreTmp[0, :, :, 1] = self.sysEye
coreTmp[0, :, :, 3] = V[0].T
self.setH(coreTmp, self.H[j, i])
i = self.ptrBra[0]
coreTmp = np.zeros([4, 2, 2, 1], dtype=np.complex128)
coreTmp[0, :, :, 0] = self.sysEye
coreTmp[2, :, :, 0] = V[0]
self.setH(coreTmp, self.H[j, i])
# time-dependent part
# Zeeman splitting for qubit 1
j = 1
i = self.ptrKet[0]
self.setRefH(self.shapeKet, self.coreKetSZ, self.H[j, i])
i = self.ptrBra[0]
self.setRefH(self.shapeBra, self.coreBraSZ, self.H[j, i])
# drive for qubit 0 (cos)
j = 2
i = self.ptrKet[0]
self.setRefH(self.shapeKet, self.coreKetSX, self.H[j, i])
i = self.ptrBra[0]
self.setRefH(self.shapeBra, self.coreBraSX, self.H[j, i])
# drive for qubit 0 (sin)
j = 3
i = self.ptrKet[0]
self.setRefH(self.shapeKet, self.coreKetSY, self.H[j, i])
i = self.ptrBra[0]
self.setRefH(self.shapeBra, self.coreBraSY, self.H[j, i])
# reservoir
# time-independent part
j = 0
for l in range(self.numQ):
self.setBathMPO(depth[l], nu[l], coeff[l], l, j)
l = 0
# time-dependent part
for j in range(1, 4):
for i in range(self.ptrKet[l]+1, self.ptrBra[l]):
self.setRefH(self.shapeBathEye2[l], self.coreBathEye2[l],
self.H[j, i])
def __getIndices(self):
"""compute MPS indices for output
returns:
indices (numpy.ndarray): 2d array of MPS indices
"""
indices = np.zeros([4, self.numCore], dtype=np.int32)
for i in range(4):
qWiseIdx = [i//2 % 2, i % 2]
indices[i, self.ptrKet[0]] = qWiseIdx[0]
indices[i, self.ptrBra[0]] = qWiseIdx[1]
return indices
[docs]
def getPrefactors(self, dt: float, time: float, stepNum: int)\
-> np.ndarray:
"""compute prefactor terms for Runge-Kutta update
args:
dt (float): step size for Runge-Kutta integration
time (float): current time
stepNum (int): current step number of the integration
returns:
numpy.ndarray: prefactors corresponding to MPO
"""
pulseIdx = self.map[(np.int64(0), )]
preSX, preSY = self.pulse[pulseIdx][1].getPrefactor(dt, time, stepNum)
return np.array(
[dt, dt * self.omegaQSeq[0][stepNum], dt * preSX, dt * preSY])