Francisco J. H. Heras

Johannes Bausch, Andrew W Senior, Francisco J H Heras et al.

Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our decoder outperforms state-of-the-art algorithmic decoders on real-world data from Google's Sycamore quantum processor for distance 3 and 5 surface codes. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk, leakage, and analog readout signals, and sustains its accuracy far beyond the 25 cycles it was trained on. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers.

Francisco J. R. Ruiz, Tuomas Laakkonen, Johannes Bausch et al.

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way.

Francisco J. H. Heras, Gonzalo G. de Polavieja

We explore the application of linear discriminant analysis (LDA) to the features obtained in different layers of pretrained deep convolutional neural networks (CNNs). The advantage of LDA compared to other techniques in dimensionality reduction is that it reduces dimensions while preserving the global structure of data, so distances in the low-dimensional structure found are meaningful. The LDA applied to the CNN features finds that the centroids of classes corresponding to the similar data lay closer than classes corresponding to different data. We applied the method to a modification of the MNIST dataset with ten additional classes, each new class with half of the images from one of the standard ten classes. The method finds the new classes close to the corresponding standard classes we took the data form. We also applied the method to a dataset of images of butterflies to find that related subspecies are found to be close. For both datasets, we find a performance similar to state-of-the-art methods.

Francisco Romero-Ferrero, Mattia G. Bergomi, Robert Hinz et al.

Our understanding of collective animal behavior is limited by our ability to track each of the individuals. We describe an algorithm and software, idtracker.ai, that extracts from video all trajectories with correct identities at a high accuracy for collectives of up to 100 individuals. It uses two deep networks, one detecting when animals touch or cross and another one for animal identification, trained adaptively to conditions and difficulty of the video.