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.
First, you will have to install the package
pip install syngularfrom 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)))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())
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