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:

from __future__ import annotations

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()

graph = pattern.extract_graph()
print(f"Number of nodes: {len(graph.nodes)}")
print(f"Number of edges: {len(graph.edges)}")
pos = nx.spring_layout(graph)
nx.draw(graph, 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.basis_amplitude(0)}")
print(f"The amplitude of |11...1>: {tn.basis_amplitude(2**n - 1)}")

/home/docs/checkouts/readthedocs.org/user_builds/graphix/checkouts/v0.3.5/examples/ghz_with_tn.py:48: UserWarning: Default random-number generator is used. Results may not be reproducible.
  tn = pattern.simulate_pattern(backend="tensornetwork")
The amplitude of |00...0>: 0.499999999999993
The amplitude of |11...1>: 0.499999999999993