Why does simulation time not scale linearly with circuit depth?

[OliverAh]

Observation

The following kernel applies a given number of controlled x gates to a qubit register. For a fixed number of qubits, I would have expected the runtime of the simulation to scale approx. linearly with the number of controlled x gates. However, I noticed when going from 1e4 to 1e5 gates, the runtime actually increases by a factor ~85, while I would have expected a factor ~10 as in the number of gates.

Questions

Am I missing something, and this is expected behaviour?
Or should I open an issue with that?

MWE: mwe.py

import cudaq
from typing import List
import time


@cudaq.kernel
def my_kernel(num_qubits: int,
              list_control_qubits: List[int],
              num_cnots: int):

    qvec = cudaq.qvector(num_qubits)
    h(qvec)

    for i in range(num_cnots):
        x.ctrl(qvec[list_control_qubits[i]], qvec[num_qubits-1])



num_qubits = 5
for l in (1e1, 1e1, 1e2, 1e3, 1e4, 1e5):
    num_cnots = int(l)
    print('num_cnots:', num_cnots)
    list_control_qubits = [i % (num_qubits-1) for i in range(num_cnots)]


    tic_comp = time.time()
    my_kernel.compile()
    toc_comp = time.time()
    print(f"  Compilation time: {toc_comp - tic_comp:.4f} seconds")

    tic_state = time.time()
    statevec = cudaq.get_state(my_kernel, num_qubits, list_control_qubits, num_cnots)
    toc_state = time.time()
    print(f"  State retrieval time: {toc_state - tic_state:.4f} seconds \n")

Output of python mwe.py

num_cnots: 10
  Compilation time: 0.1811 seconds
  State retrieval time: 0.6922 seconds 

num_cnots: 10
  Compilation time: 0.0002 seconds
  State retrieval time: 0.0012 seconds 

num_cnots: 100
  Compilation time: 0.0002 seconds
  State retrieval time: 0.0039 seconds 

num_cnots: 1000
  Compilation time: 0.0001 seconds
  State retrieval time: 0.0263 seconds 

num_cnots: 10000
  Compilation time: 0.0001 seconds
  State retrieval time: 1.5201 seconds 

num_cnots: 100000
  Compilation time: 0.0003 seconds
  State retrieval time: 126.5310 seconds 

Environment:

Apptainer container build from nvcr.io/nvidia/nightly/cuda-quantum:cu12-0.12.0
OS: Ubuntu 24.04.2 LTS
nvidia-smi info: NVIDIA-SMI 570.133.07, Driver Version: 570.133.07, CUDA Version: 12.8
GPU: 4x Nvidia L40S

Additional Info

Specifying the GPU-ID via CUDA_VISIBLE_DEVICES=..., so that only a single GPU is visible to the script, does not have an influence.