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quotonic

quotonic is a package created for studying nonlinear quantum photonic circuits, including yet not limited to, quantum photonic neural networks (QPNNs). It is designed to accommodate new circuit models that explore unknown capabilities, teaching all of us what can be accomplished when a handful of photons are combined with strong few-photon optical nonlinearities. We hope that you will use this package as a platform to begin answering pertinent research questions around nonlinear quantum photonic circuits like QPNNs. If you are able to do so, and would like to make additions here, please let us know! We would love for this package to grow, including many different models that can be explored in tandem.

When it comes to simulating quantum dynamics using classical computational resources, there is often a need to closely consider performance. Here, we write circuit models to be compatible with jax and thus owe a massive thank you to the developers at Google DeepMind. It is also necessary to mention and thank similar packages, each of which have inspired some of the code within quotonic.

Installation

You can install the latest release of quotonic from PyPI as 

pip install quotonic
or install the latest development version from GitHub 
pip install git+https://github.com/jewaniuk/quotonic.git

Getting Started

quotonic.qpnn contains a variety of models of QPNNs, the simplest of which is IdealQPNN, which follows their original proposal. Each model is accompanied by a trainer from quotonic.trainer, and can be trained to perform some task defined by a training set from quotonic.training_sets. In this example, we will train a two-layer, four-mode QPNN to act as a deterministic two-photon CNOT gate.

>>> from quotonic.qpnn import IdealQPNN
>>> from quotonic.trainer import IdealTrainer
>>> from quotonic.training_sets import CNOT

>>> n = 2  # number of photons
>>> m = 4  # number of optical modes
>>> L = 2  # number of network layers
We'll choose to perform one optimization trial that proceeds through 100 epochs. 
>>> num_trials = 1  # number of optimization trials to perform
>>> num_epochs = 100  # number of epochs to train for per trial
Now, we simply prepare the training set, instantiate a QPNN followed by a trainer, then train! 
>>> training_set = CNOT()
>>> qpnn = IdealQPNN(n, m, L, training_set=training_set)
>>> trainer = IdealTrainer(qpnn, num_trials, num_epochs)

>>> results = trainer.train()
Trial: 1
Epoch: 0     Cost: 9.3885e-01    Fidelity: 0.06115
Epoch: 10    Cost: 7.1853e-01    Fidelity: 0.2815
Epoch: 20    Cost: 6.6739e-01    Fidelity: 0.3326
Epoch: 30    Cost: 5.4786e-01    Fidelity: 0.4521
Epoch: 40    Cost: 4.2395e-01    Fidelity: 0.576
Epoch: 50    Cost: 3.0212e-01    Fidelity: 0.6979
Epoch: 60    Cost: 1.6486e-01    Fidelity: 0.8351
Epoch: 70    Cost: 7.8349e-02    Fidelity: 0.9217
Epoch: 80    Cost: 3.2369e-02    Fidelity: 0.9676
Epoch: 90    Cost: 1.2706e-02    Fidelity: 0.9873
Epoch: 100   Cost: 5.2117e-03    Fidelity: 0.9948
Epoch: 110   Cost: 2.0834e-03    Fidelity: 0.9979
Epoch: 120   Cost: 8.6629e-04    Fidelity: 0.9991
Epoch: 130   Cost: 3.8522e-04    Fidelity: 0.9996
Epoch: 140   Cost: 1.8960e-04    Fidelity: 0.9998
COMPLETE!    Cost: 1.1343e-04    Fidelity: 0.9999
This particular trial was able to tune the network parameters to achieve a fidelity of ~99.99%. The optimized parameters are passed back in results, so we can calculate the fidelity directly using them to check. 
>>> qpnn.calc_fidelity(results["phi"][0], results["theta"][0], results["delta"][0])
Array(0.99989176, dtype=float32)

Example Usage

Here, we provide example scripts that illustrate the methodology used in our previous research on QPNNs.

Imperfect Quantum Photonic Neural Networks

import os

os.environ["XLA_FLAGS"] = "--xla_force_host_platform_device_count=8"

import numpy as np
from jax import config

config.update("jax_enable_x64", True)

from quotonic.qpnn import ImperfectQPNN
from quotonic.trainer import ImperfectTrainer
from quotonic.training_sets import BSA

n = 2
m = 4
L = 2
varphi = np.pi / 2

ell_mzi = (0.00861, 0.00057)  # (0.00861 +/- 0.00057) dB loss per MZI, sota model
ell_ps = (0.0015, 0.0001)  # (0.0015 +/- 0.0001) dB loss per phase shifter, sota model
t_dc = (0.5000, 0.0508)  # (50.00 +/- 5.08) % T:R directional coupler splitting ratio

num_trials = 200
num_epochs = 1000
print_every = 100

tset = BSA()
qpnn = ImperfectQPNN(n, m, L, varphi=varphi, ell_mzi=ell_mzi, ell_ps=ell_ps, t_dc=t_dc, training_set=tset)
trainer = ImperfectTrainer(qpnn, num_trials, num_epochs, print_every=print_every)

results = trainer.train()

Large-Scale Tree-Type Photonic Cluster State Generation with Recurrent Quantum Photonic Neural Networks

import os

os.environ["XLA_FLAGS"] = "--xla_force_host_platform_device_count=8"

import numpy as np
from jax import config

config.update("jax_enable_x64", True)

from quotonic.qpnn import TreeQPNN
from quotonic.trainer import TreeTrainer
from quotonic.training_sets import Tree

b = 2
n = b + 1
m = 2 * n
L = 2
varphi = (0.0, np.pi)

ell_mzi = (0.0210, 0.0016)  # (0.0210 +/- 0.0016) dB loss per MZI, multi model
ell_ps = (0.0100, 0.0006)  # (0.0100 +/- 0.0006) dB loss per phase shifter, multi model
t_dc = (0.50, 0.005)  # (50 +/- 0.5) % T:R directional coupler splitting ratio

num_trials = 200
num_epochs = 1000
print_every = 100

tset = Tree(b)
qpnn = TreeQPNN(b, L, varphi=varphi, ell_mzi=ell_mzi, ell_ps=ell_ps, t_dc=t_dc, training_set=tset)
trainer = TreeTrainer(qpnn, num_trials, num_epochs, print_every=print_every)

results = trainer.train()

Citing

Rather than citing the package directly, please cite the following works that it was developed for: 

@article{Ewaniuk:23,
title   = {{Imperfect Quantum Photonic Neural Networks}},
author  = {Jacob Ewaniuk and Jacques Carolan and Bhavin J. Shastri and Nir Rotenberg},
journal = {Advanced Quantum Technologies},
volume  = {6},
pages   = {2200125},
year    = {2023},
doi     = {https://doi.org/10.1002/qute.202200125},
}

@misc{Ewaniuk:25,
title   = {{Large-Scale Tree-Type Photonic Cluster State Generation with Recurrent Quantum Photonic Neural Networks}},
author  = {Jacob Ewaniuk and Bhavin J. Shastri and Nir Rotenberg},
year    = {2025},
howpublished = {Preprint at https://arxiv.org/abs/2505.14628},
}

Authors

quotonic was initially created by Jacob Ewaniuk as part of his doctoral studies at Queen's University, working with the Quantum Nanophotonics Lab and Shastri Lab. Currently, it is in active use as a research tool by a number of graduate students in each of these research groups. As further contributions are made, additional authors will be listed here.