Tensor Network in Python

Introduction

Syngular emerged in the context of my quantum computing project at CentraleSuépelec. I was working on the efficient simulation of quantum circuits on classical computers. The last work on the subject that tackled this issue was using Matrix Product State as a base to represent the 2^N parameters quantum state of a quantum system (What limits the simulation of quantum computers? Yiqing Zhou, E. Miles Stoudenmire, Xavier Waintal) with only a fraction of parameters at the price of approximation on the singular values. I dived into this world of Matrix Product State and Operator leading me to the theorisation of Tensor Network with Yvan Osedelets works and I created a simple simulator (too simple). Then, in my second year at CentraleSupélec in the same team project, I had the opportunity to work on how to use tensor networks that came from the quantum world to machine learning as to compress efficiently neural network.

As so, I developed this Python package to create easily Tensor Network and simulate as well Quantum Circuit as Neural Networks and optimization of function.

Getting Started

Installation

First, you will have to install the package

pip install syngular

MatrixProductState & MatrixProductOperator

from syngular.tensor import MatrixProductState
from syngular.tensor import MatrixProductOperator

import numpy as np

tensor_W = np.arange(16**6).reshape((16,16,16, 16,16,16))
tensor_X = np.arange(16**3).reshape((16,16,16))

W = MatrixProductOperator(tensor_W, bond_shape=(16,16,))
W.decompose()

X = MatrixProductState(tensor_X, bond_shape=(4,4,))
X.decompose()

T = MatrixProductOperator.random((16,16,16), (16,16,16), (8,8,))
O = MatrixProductOperator.zeros((16,16,16), (16,16,16), (4,4,))
U = MatrixProductState.random((16,16,16), (8,8,))

W = W >> 4
T = T >> 2

Z = ((T + W) @ T) @ X

print(X | U)
print(Z | X)

Z = Z >> 16
Z.left_orthonormalization()

print(np.diag(Z.left_orthogonality(0)))
print(np.diag(Z.left_orthogonality(1)))

Quantum Simulation

from syngular.quantum import Circuit, Qbit
import syngular.quantum.gate as gate

Qbit.LSB = False

circ = Circuit(size=15, structure=[
    (gate.X, 0),
    (gate.X, 2),
    (gate.H, 0),
    (gate.H, 2),
])

circ.run()
circ.add((gate.H, 1))
circ.run()

#########################################################

def verity_table(g, name):
    import itertools

    size = int(len(g.shape) // 2)
    length = ((3+size)*2+1)
    
    print('------------- Vertity Table --------------')
    print(f' > Gate : {name}')
    print("="*length)
    print("| inp > out |")
    print("="*length)

    for b in itertools.product([0, 1], repeat=size):
        qbit = Qbit(size)
        for i in range(len(b)): if b[i] == 1: qbit @= (gate.X, i)
        output = qbit @ (g, 0)

        print("|",qbit.to_binary(), '|', output.to_binary(), "|")
        print("-"*length)

verity_table(gate.TOFFOLI, "Toffoli")

######################################################

Qbit.LSB = True

qbit = Qbit(4)
qbit @= (gate.X, 0)
qbit @= (gate.X, 2)
print(qbit.to_binary())

qbit = qbit.swap(0,3)
print(qbit.to_binary())

qbit = qbit.swap(0,2)
print(qbit.to_binary())

qbit = qbit.swap(3,2)
print(qbit.to_binary())