Using Tensor Network simulator

In this example, we simulate a circuit to create Greenberger-Horne-Zeilinger(GHZ) state with a tensor network simulator.

We will simulate the generation of 100-qubit GHZ state. Firstly, let us import relevant modules:

import matplotlib.pyplot as plt
import networkx as nx

from graphix import Circuit

n = 100
print(f"{n}-qubit GHZ state generation")
circuit = Circuit(n)

# initialize to ``|0>`` state.
for i in range(n):
    circuit.h(i)

# GHZ generation
circuit.h(0)
for i in range(1, n):
    circuit.cnot(i - 1, i)

100-qubit GHZ state generation

Transpile into pattern

pattern = circuit.transpile().pattern
pattern.standardize()

nodes, edges = pattern.get_graph()
g = nx.Graph()
g.add_nodes_from(nodes)
g.add_edges_from(edges)
print(f"Number of nodes: {len(nodes)}")
print(f"Number of edges: {len(edges)}")
pos = nx.spring_layout(g)
nx.draw(g, pos=pos, node_size=15)
plt.show()

Number of nodes: 399
Number of edges: 398

Calculate the amplitudes of |00...0> and |11...1> states.

tn = pattern.simulate_pattern(backend="tensornetwork")
print(f"The amplitude of |00...0>: {tn.get_basis_amplitude(0)}")
print(f"The amplitude of |11...1>: {tn.get_basis_amplitude(2**n - 1)}")

The amplitude of |00...0>: 0.49999999999999317
The amplitude of |11...1>: 0.49999999999999317