Antonio Acín

Timothy Heightman, Edward Jiang, Antonio Acín

Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under the action of such Hamiltonians. This inherent complexity limits our ability to characterise quantum many-body systems, highlighting the need for innovative approaches to unlock their full potential. To address this challenge, we propose a novel method to solve the Hamiltonian Learning (HL) problem-inferring quantum dynamics from many-body state trajectories-using Neural Differential Equations combined with an Ansatz Hamiltonian. Our method is reliably convergent, experimentally friendly, and interpretable, making it a stable solution for HL on a set of Hamiltonians previously unlearnable in the literature. In addition to this, we propose a new quantitative benchmark based on power laws, which can objectively compare the reliability and generalisation capabilities of any two HL algorithms. Finally, we benchmark our method against state-of-the-art HL algorithms with a 1D spin-1/2 chain proof of concept.

Timothy Heightman, Roman Aseguinolaza Gallo, Edward Jiang et al.

Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to $N=6$ qubits with fewer than $5 \times 10^5$ shots.

Gabriel Senno, Antonio Acín

Quantum Bell nonlocality allows for the design of protocols that amplify the randomness of public and arbitrarily biased Santha-Vazirani sources, a classically impossible task. Information-theoretical security in these protocols is certified in a device-independent manner, i.e. solely from the observed nonlocal statistics and without any assumption about the inner-workings of the intervening devices. On the other hand, if one is willing to trust on a complete quantum-mechanical description of a protocol's devices, the elementary scheme in which a qubit is alternatively measured in a pair of mutually unbiased bases is, straightforwardly, a protocol for randomness amplification. In this work, we study the unexplored middle ground. We prove that full randomness amplification can be achieved without requiring entanglement or a complete characterization of the intervening quantum states and measurements. Based on the energy-bounded framework introduced in [Van Himbeeck et al., Quantum 1, 33 (2017)], our prepare-and-measure protocol is able to amplify the randomness of any public Santha-Vazirani source, requiring the smallest number of inputs and outcomes possible and being secure against quantum adversaries.

Alejandro Pozas-Kerstjens, Gorka Muñoz-Gil, Eloy Piñol et al.

We introduce a new family of energy-based probabilistic graphical models for efficient unsupervised learning. Its definition is motivated by the control of the spin-glass properties of the Ising model described by the weights of Boltzmann machines. We use it to learn the Bars and Stripes dataset of various sizes and the MNIST dataset, and show how they quickly achieve the performance offered by standard methods for unsupervised learning. Our results indicate that the standard initialization of Boltzmann machines with random weights equivalent to spin-glass models is an unnecessary bottleneck in the process of training. Furthermore, this new family allows for very easy access to low-energy configurations, which points to new, efficient training algorithms. The simplest variant of such algorithms approximates the negative phase of the log-likelihood gradient with no Markov chain Monte Carlo sampling costs at all, and with an accuracy sufficient to achieve good learning and generalization.

Elie Wolfe, Alejandro Pozas-Kerstjens, Matan Grinberg et al.

Causality is a seminal concept in science: Any research discipline, from sociology and medicine to physics and chemistry, aims at understanding the causes that could explain the correlations observed among some measured variables. While several methods exist to characterize classical causal models, no general construction is known for the quantum case. In this work, we present quantum inflation, a systematic technique to falsify if a given quantum causal model is compatible with some observed correlations. We demonstrate the power of the technique by reproducing known results and solving open problems for some paradigmatic examples of causal networks. Our results may find applications in many fields: from the characterization of correlations in quantum networks to the study of quantum effects in thermodynamic and biological processes.