Machine learning for optimal parameter prediction in quantum key distribution

Wenyuan Wang and Hoi-Kwong Lo

Phys. Rev. A 100, 062334 – Published 27 December 2019

Abstract

For a practical quantum key distribution (QKD) system, parameter optimization, the choice of intensities and the probabilities of sending them, is a crucial step in gaining optimal performance, especially when one realistically considers a finite communication time. With the increasing interest in the field to implement QKD over free space on moving platforms, such as drones, handheld systems, and even satellites, one needs to perform parameter optimization with low latency and with very limited computing power. Moreover, with the advent of the internet of things, a highly attractive direction of QKD could be a quantum network with multiple devices and numerous connections, which provides a huge computational challenge for the controller that optimizes parameters for a large-scale network. Traditionally, such an optimization relies on brute-force search or local search algorithms, which are computationally intensive, and will be slow on low-power platforms (which increases latency in the system) or infeasible for even moderately large networks. In this work we present a method that uses a neural network to directly predict the optimal parameters for QKD systems. We test our machine learning algorithm on hardware devices including a Raspberry Pi 3 single-board computer (similar devices are commonly used on drones) and a mobile phone, both of which have a power consumption of less than 5 W, and we find a speedup of up to two to four orders of magnitude when compared to standard local search algorithms. The predicted parameters are highly accurate and can preserve, e.g., over 95%–99% of the optimal secure key rate for a given protocol. Moreover, our approach is highly general and can be applied effectively to various kinds of common QKD protocols.

Received 6 June 2019

DOI:https://doi.org/10.1103/PhysRevA.100.062334

Physics Subject Headings (PhySH)

Machine learning Quantum communication Quantum cryptography Quantum networks

Quantum Information, Science & Technology

Authors & Affiliations

Wenyuan Wang ^* and Hoi-Kwong Lo^†

Centre for Quantum Information and Quantum Control, Department of Electrical & Computer Engineering and Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 3G4

^*wenyuan.wang@mail.utoronto.ca
^†hklo@comm.utoronto.ca

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 100, Iss. 6 — December 2019

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Shown on the left is a Raspberry Pi 3 single-board computer equipped with an Intel Movidius neural compute stick and on the right is a smartphone (iPhone XR) running parameter prediction for a QKD protocol with an on-device neural network. In the same app one can also choose to run a local search on the device (and compare its running time to that of neural networks).
Reuse & Permissions
Figure 2
Example of a neural network (in fact, here it is an illustration of the neural network used in our work). It has an input layer and an output layer of four and six neurons, respectively, and has two fully connected hidden layers with 400 and 200 neurons with a rectified linear unit (ReLU) function as activation. The cost function (not shown here) is a mean-square error.
Reuse & Permissions
Figure 3
Data flow of the training and testing of the neural network. The rounded-corner boxes represent programs and rectangular boxes represent data. The generator program generates many random sets of experimental parameters $\vec{e}$ and calculates the corresponding optimal parameters ${\vec{p}}_{opt}$ . These data are used to train the neural network. After the training is complete, the network can be used to predict optimal parameters based on new arbitrary sets of random experimental data and generate ${\vec{p}}_{pred}$ (for instance, to plot the results of Figs. 4 and 5, for each protocol a single random set of data is used as input). Finally, another validation program calculates the key rate based on the actual optimal parameters ${\vec{p}}_{opt}$ found by local search and the predicted ${\vec{p}}_{pred}$ , respectively, and compares their performances.
Reuse & Permissions
Figure 4
Comparison of expected key rate using NN-predicted parameters vs using optimal parameters found by a local search for various protocols, using experimental parameters from Table 3, at different distances between Alice (or Charles) and Bob. We compare the key rate generated with either set of parameters (dots with NN-predicted parameters and lines with local-search-generated parameters). We tested four protocols: (a) symmetric MDI-QKD (four-intensity protocol) [23], (b) asymmetric MDI-QKD (seven-intensity protocol) [26], (c) BB84 protocol [22], and (d) asymmetric TF-QKD protocol [27]. As can be seen, the key rate obtained using predicted parameters is very close to that obtained from using optimal parameters found with a local search.
Reuse & Permissions
Figure 5
Comparison of NN-predicted parameters vs optimal parameters found by local search for various protocols, using experimental parameters from Table 3, at different distances between Alice (or Charles) and Bob. We compare NN-predicted parameters (dots) versus optimal parameters found by a local search (lines) for four protocols: (a) symmetric MDI-QKD (four-intensity protocol), (b) asymmetric MDI-QKD (seven-intensity protocol), (c) BB84 protocol, and (d) asymmetric TF-QKD protocol. Similar to Fig. 4, as can be seen, the NN-predicted parameters are very close to optimal values found with a local search. Note that there is some noise present for the BB84 protocol. This is because the key rate versus parameter function shows some level of nonconvexity, and we combined the local search with a randomized approach (similar to a global search) that chooses results from multiple random starting points. Therefore, there is some level of noise for the probability parameters (which are insensitive to small perturbations), while the neural network is shown to learn the overall shape of the global maximum of the parameters and return a smooth function. Similar parameters apply for TF-QKD, which has small levels of nonconvexity due to linear solvers being inherently nonconvex, although due to the limitation in training time, we did not apply a global search for TF-QKD.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information