Large-scale simulations with tensor network simulator

In this example, we demonstrate simulation of MBQC involving 10k+ nodes.

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Firstly, let us import relevant modules and define the circuit:

import numpy as np
from graphix import Circuit
import networkx as nx


def cp(circuit, theta, control, target):
    circuit.rz(control, theta / 2)
    circuit.rz(target, theta / 2)
    circuit.cnot(control, target)
    circuit.rz(target, -1 * theta / 2)
    circuit.cnot(control, target)


def swap(circuit, a, b):
    circuit.cnot(a, b)
    circuit.cnot(b, a)
    circuit.cnot(a, b)


def qft_rotations(circuit, n):
    circuit.h(n)
    for qubit in range(n + 1, circuit.width):
        cp(circuit, np.pi / 2 ** (qubit - n), qubit, n)


def swap_registers(circuit, n):
    for qubit in range(n // 2):
        swap(circuit, qubit, n - qubit - 1)
    return circuit


def qft(circuit, n):
    for i in range(n):
        qft_rotations(circuit, i)
    swap_registers(circuit, n)

We will simulate 45-qubit QFT, which requires graph states with more than 10000 nodes.

n = 45
print("{}-qubit QFT".format(n))
circuit = Circuit(n)

for i in range(n):
    circuit.h(i)
qft(circuit, n)

# standardize pattern
pattern = circuit.transpile()
pattern.standardize()
pattern.shift_signals()
nodes, edges = pattern.get_graph()
print(f"Number of nodes: {len(nodes)}")
print(f"Number of edges: {len(edges)}")

45-qubit QFT
Number of nodes: 10167
Number of edges: 12168

Using efficient graph state simulator graphix.GraphSim, we can classically preprocess Pauli measurements. We are currently improving the speed of this process by using rust-based graph manipulation backend.

pattern.perform_pauli_measurements()

You can easily check that the below code run without too much load on your computer. Also notice that we have not used graphix.pattern.Pattern.minimize_space(), which we know reduced the burden on the simulator. To specify TN backend of the simulation, simply provide as a keyword argument. here we do a very basic check that one of the statevector amplitudes is what it is expected to be:

import time
t1 = time.time()
tn = pattern.simulate_pattern(backend="tensornetwork")
value = tn.get_basis_amplitude(0)
t2 = time.time()
print("amplitude of |00...0> is ", value)
print("1/2^n (true answer) is", 1 / 2**n)
print("approximate execution time in seconds: ", t2 - t1)

amplitude of |00...0> is  2.8421709430405005e-14
1/2^n (true answer) is 2.842170943040401e-14
approximate execution time in seconds:  15.432862281799316