Here, we present two of our works focusing on Quantum Machine Learning. We discuss both about the capabilities of trained quantum optical chips, as well as about methods to train them eficiently. We also consider how the training process will be afected by limitations and imperfections in a possible physical implementation, and show how the performance of the trained circuit is impacted by these issues, as well as how the training process can partially overcome these additional challenges. While these works focus on the quantum optical platform, many of the aspects that we discussed in these works also apply to other quantum computing technologies.
The QONN is the quantum optical extension of neural networks, and is composed of multiple layers,
each composed of a linear unitary transformation and a set of nonlinear single-site transformations.
Input states in the network are photon states employed to encode qubits. More specifically, the dual-rail
encoding is used to associate each pair of modes to a qubit, where states |0⟩ and |1⟩ correspond to a
single photon in the first and second mode respectively. The QONN can be considered the quantum
optical version of the multi-layer perceptron (MLP), and was first introduced in a work by Steinbrecher
et al. [
CEUR Workshop
ISSN1613-0073
R(-π/2) B(θin,Φin) R(-π/2) R(φ)
R(-φ) R(-π/2) B(θ1out,Φ1out) R(-π/2) QONN
R(-φ) R(-π/2) B(θo2ut,Φ2out) R(-π/2) 1.0 0.8
In this work our objective was to train a simulated QONN to obtain a deterministic optimal quantum
cloner for the optical platform. We managed to successfully do so, and obtained an optical quantum
cloner whose performance is very close to that of an optimal universal quantum cloner. The optical
quantum cloner obtained was deterministic, which is very important, as current optical implementations
are inherently probabilistic [
This work thus showed the capabilities and flexibility of QONNs, which might prove important for
designing even more complex optical circuits, as well as highlighting some potential uses for QONNs.
3. Training a continuously coupled optical chip via machine learning
techniques
Continuously coupled optical chips [
Thus, in this work we make use of machine learning techniques to train the parameters of a continuously coupled chip to perform a desired unitary transformation. We simulate diferent sizes and structures of continuously coupled optical chips, and check how these techniques work in these various scenarios. We consider both flat and 3D designs, as well as a varying number of optical modes and the efect on training of having limited control on the quantum optical chip. We also evaluate the errors caused by several potential experimental limitations, such as those produced by a limited number of samples, and those caused by imperfections in the parametrization of the chip. We also tackle the issue of training the quantum optical chip with constraints similar as those that would be present in an actual physical experiment, such as the fact that backpropagation cannot be used [15], and thus alternative strategies need to be employed to obtain an estimation of the gradient. On top of that, we implement various optimizations during the training process that would reduce the number of measurements needed to physically implement this training process, thus leading to faster training times. We also train a classical machine learning model, to work in tandem with the quantum machine learning process, in cases in which only training the quantum chip directly does not provide the desired results.
This work thus showed the challenges that arise when attempting to train a quantum chip in a realistic scenario, as well as giving some insights on methods and optimizations that can be used to improve and accelerate the training process.
The authors have not employed any Generative AI tools. [12] Y. Yang, R. J. Chapman, B. Haylock, F. Lenzini, Y. N. Joglekar, M. Lobino, A. Peruzzo, Programmable high-dimensional hamiltonian in a photonic waveguide array, Nature Communications 15 (2024).
URL: http://dx.doi.org/10.1038/s41467-023-44185-z. doi:10.1038/s41467- 023- 44185- z. [13] M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, Experimental realization of any discrete unitary operator, Phys. Rev. Lett. 73 (1994) 58–61. URL: https://link.aps.org/doi/10.1103/PhysRevLett.73.58. doi:10.1103/PhysRevLett.73.58. [14] W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, I. A. Walmsley, Optimal design for universal multiport interferometers, Optica 3 (2016) 1460–1465. URL: https://opg.optica.org/ optica/abstract.cfm?URI=optica-3-12-1460. doi:10.1364/OPTICA.3.001460. [15] A. Abbas, R. King, H.-Y. Huang, W. J. Huggins, R. Movassagh, D. Gilboa, J. R. McClean, On quantum backpropagation, information reuse, and cheating measurement collapse, 2023. URL: https://arxiv.org/abs/2305.13362. arXiv:2305.13362.