Large Statevector

A 20-qubit exact statevector: a million complex amplitudes, 16 MiB.

"""A larger exact statevector: 20 qubits, about 16 MiB of amplitudes."""

import math
import random

import numpy as np
from qiskit import QuantumCircuit

from menos.qiskit import MENOSBackend

n = 20
rng = random.Random(3)
qc = QuantumCircuit(n)
for _ in range(3):
    for q in range(n):
        qc.ry(rng.uniform(0, math.pi), q)
    for q in range(0, n - 1, 2):
        qc.cx(q, q + 1)
    for q in range(1, n - 1, 2):
        qc.cx(q, q + 1)

state = np.asarray(
    MENOSBackend().run(qc, shots=0, want_statevector=True).result().get_statevector()
)
print("amplitudes:", state.size, "| bytes:", state.nbytes)
assert state.size == 2**n
assert abs(np.linalg.norm(state) - 1.0) < 1e-12  # the state is normalised

Output

amplitudes: 1048576 | bytes: 16777216

The script checks that the state is normalized. On a CPU build this takes on the order of a second; on a CUDA-enabled build the planner moves it to the GPU (see CPU vs CUDA).

Scaling

Qubits	State size
20	16 MiB
25	512 MiB
30	16 GiB

Doubling the memory for each extra qubit is why dense simulation has a wall, and why other engines exist. See Memory Constraints.