PyOR Quantum

Author: Vineeth Thalakottoor

Introduction to Quantum Library

[1]:

# Define the source path
SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/Source_Doc'

# Add source path
import sys
sys.path.append(SourcePath)

import numpy as np

# Import PyOR package
from PyOR_QuantumLibrary import QuantumLibrary
QLib = QuantumLibrary()

Make two states ket1 and ket2

[2]:

# Make two states ket1 and ket2
ket1 = QLib.Basis_Ket(2,0, PrintDefault=True)
ket2 = QLib.Basis_Ket(2,1, PrintDefault=True)

Quantum object initialized: shape=(2, 1), type='ket', dtype=complex128
Quantum object initialized: shape=(2, 1), type='ket', dtype=complex128

[3]:

# Matrix form of ket1
ket1.matrix

[3]:

$\displaystyle \left[\begin{matrix}1.0\\0\end{matrix}\right]$

[4]:

# Matrix form of ket2
ket2.matrix

[4]:

$\displaystyle \left[\begin{matrix}0\\1.0\end{matrix}\right]$

Create a state

[5]:

# Create a state
psi1 = 1 * ket1 + 2 * ket2

# Matrix form
psi1.matrix

[5]:

$\displaystyle \left[\begin{matrix}1.0\\2.0\end{matrix}\right]$

[6]:

# Create a state
psi2 = 10 * ket1 + 20 * ket2
psi2.matrix

[6]:

$\displaystyle \left[\begin{matrix}10.0\\20.0\end{matrix}\right]$

Outer Product

[7]:

# Outer Product
rho1 = QLib.OuterProduct(psi1,psi1)

# Matrix form
rho1.matrix

[7]:

$\displaystyle \left[\begin{matrix}1.0 & 2.0\\2.0 & 4.0\end{matrix}\right]$

[8]:

# Outer Product
rho2 = QLib.OuterProduct(psi2,psi2)

# Matrix form
rho2.matrix

[8]:

$\displaystyle \left[\begin{matrix}100.0 & 200.0\\200.0 & 400.0\end{matrix}\right]$

Conversion from density matrix to vector

[9]:

# Density matrix to vector
QLib.RowColOrder = "C" # Vectorize by row
#QLib.RowColOrder = "F" # Vectorize by col
vec1 = QLib.DMToVec(rho1)

[10]:

# Matrix form
vec1.matrix

[10]:

$\displaystyle \left[\begin{matrix}1.0\\2.0\\2.0\\4.0\end{matrix}\right]$

Conversion from vector to density matrix

[11]:

# Vector to DM
DM1 = QLib.VecToDM(vec1,shape=(2,2))

[12]:

# Matrix form
DM1.matrix

[12]:

$\displaystyle \left[\begin{matrix}1.0 & 2.0\\2.0 & 4.0\end{matrix}\right]$

Create a bra state

[13]:

# Bra state
bra1 = QLib.Basis_Bra(2,0, PrintDefault=True)

# Print matrix
bra1.matrix

Quantum object initialized: shape=(1, 2), type='bra', dtype=complex128

[13]:

$\displaystyle \left[\begin{matrix}1.0 & 0\end{matrix}\right]$

Import spin operators

[14]:

# Sx
Sx = QLib.SSpinOp(1/2,"x", PrintDefault=True)

# show matrix form (Sympy)
Sx.matrix

Quantum object initialized: shape=(2, 2), type='operator', dtype=complex128

[14]:

$\displaystyle \left[\begin{matrix}0 & 0.5\\0.5 & 0\end{matrix}\right]$

[15]:

# Sy
Sy = QLib.SSpinOp(1/2,"y")

[16]:

# Sz
Sz = QLib.SSpinOp(1/2,"z")

Creating Hamiltonian

[17]:

H1 = Sx + Sy + Sz
H1.matrix

[17]:

$\displaystyle \left[\begin{matrix}0.5 & 0.5 - 0.5 i\\0.5 + 0.5 i & -0.5\end{matrix}\right]$

[18]:

H2 = np.cos(np.pi) * Sz
H1.matrix

[18]:

$\displaystyle \left[\begin{matrix}0.5 & 0.5 - 0.5 i\\0.5 + 0.5 i & -0.5\end{matrix}\right]$

[19]:

H1.Positive()

False

[20]:

H1.Hermitian()

[20]:

True

Create Identity matrix

[21]:

Id = QLib.Identity(2)
Id.matrix

[21]:

$\displaystyle \left[\begin{matrix}1.0 & 0\\0 & 1.0\end{matrix}\right]$

[22]:

Id.Positive()

True

Tensor Product

[23]:

Sx1 = QLib.TensorProduct(Id,Sx)
Sx1.matrix

[23]:

$\displaystyle \left[\begin{matrix}0 & 0.5 & 0 & 0\\0.5 & 0 & 0 & 0\\0 & 0 & 0 & 0.5\\0 & 0 & 0.5 & 0\end{matrix}\right]$

[24]:

Sx2 = QLib.TensorProductMultiple(Id,Sx,Id)
Sx2.matrix

[24]:

$\displaystyle \left[\begin{matrix}0 & 0 & 0.5 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0.5 & 0 & 0 & 0 & 0\\0.5 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0.5 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0.5 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5\\0 & 0 & 0 & 0 & 0.5 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0.5 & 0 & 0\end{matrix}\right]$

Direct Sum

[25]:

DM4 = QLib.DirectSum(H1,H2)
DM4.matrix

[25]:

$\displaystyle \left[\begin{matrix}0.5 & 0.5 - 0.5 i & 0 & 0\\0.5 + 0.5 i & -0.5 & 0 & 0\\0 & 0 & -0.5 & 0\\0 & 0 & 0 & 0.5\end{matrix}\right]$

[26]:

ket4 = QLib.DirectSum(ket1,ket2)
ket4.matrix

[26]:

$\displaystyle \left[\begin{matrix}1.0\\0\\0\\1.0\end{matrix}\right]$

[27]:

DM5 = QLib.DirectSumMultiple(Sx,Sy,Sz)
DM5.matrix

[27]:

$\displaystyle \left[\begin{matrix}0 & 0.5 & 0 & 0 & 0 & 0\\0.5 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & - 0.5 i & 0 & 0\\0 & 0 & 0.5 i & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0.5 & 0\\0 & 0 & 0 & 0 & 0 & -0.5\end{matrix}\right]$

[28]:

ket5 = QLib.DirectSumMultiple(ket1,ket2,ket4)
ket5.matrix

[28]:

$\displaystyle \left[\begin{matrix}1.0\\0\\0\\1.0\\1.0\\0\\0\\1.0\end{matrix}\right]$

Block Extractor

[29]:

ket1.shape

[29]:

(2, 1)

[30]:

ket2.shape

[30]:

(2, 1)

[31]:

ket4.shape

[31]:

(4, 1)

[32]:

ket10 = QLib.BlockExtract(ket5,1,[(2,1),(2,1),(4,1)])
ket10.matrix

[32]:

$\displaystyle \left[\begin{matrix}0\\1.0\end{matrix}\right]$

[33]:

DM10 = QLib.BlockExtract(DM5,2,[(2,2),(2,2),(2,2)])
DM10.matrix

[33]:

$\displaystyle \left[\begin{matrix}0.5 & 0\\0 & -0.5\end{matrix}\right]$