arXiv subjects

Lorenzo Buffoni

Publications and source records attributed to Lorenzo Buffoni.

At least 37 records · Page 2Linked to original sources

arXiv2024

Competition of decoherence and quantum speed limits for quantum-gate fidelity in the Jaynes-Cummings model

Quantum computers are operated by external driving fields, such as lasers, microwaves or transmission lines, that execute logical operations on multi-qubit registers, leaving the system in a pure state. However, the drive and the logical system might become correlated in such a way that, after tracing out the degrees of freedom of the driving field, the output state will not be pure. Previous works have pointed out that the resulting error scales inversely with the energy of the drive, thus imposing a limit on the energy-efficiency of quantum computing. In this study, focusing on the Jaynes-Cummings model, we show how the same scaling can be seen as a consequence of two competing phenomena: the entanglement-induced error, which grows with time, and a minimal time for computation imposed by quantum speed limits. This evidence is made possible by quantifying, at any time, the computation error via the spectral radius associated to the density operator of the logical qubit. Moreover, we also prove that, in order to attain a given target state at a chosen fidelity, it is energetically more efficient to perform a single driven evolution of the logical qubits rather than to split the computation in sub-routines, each operated by a dedicated pulse.

quant-ph↗

arXiv2024

Generalized Landauer bound from absolute irreversibility

In this work, we introduce a generalization of the Landauer bound for erasure processes that stems from absolutely irreversible dynamics. Assuming that the erasure process is carried out in an absolutely irreversible way so that the probability of observing some trajectories is zero in the forward process but finite in the reverse process, we derive a generalized form of the bound for the average erasure work, which is valid also for imperfect erasure and asymmetric bits. The generalized bound obtained is tighter or, at worst, as tight as existing ones. Our theoretical predictions are supported by numerical experiments and the comparison with data from previous works.

cond-mat.stat-mech↗

arXiv2023

Complex Recurrent Spectral Network

This paper presents a novel approach to advancing artificial intelligence (AI) through the development of the Complex Recurrent Spectral Network ($\mathbb{C}$-RSN), an innovative variant of the Recurrent Spectral Network (RSN) model. The $\mathbb{C}$-RSN is designed to address a critical limitation in existing neural network models: their inability to emulate the complex processes of biological neural networks dynamically and accurately. By integrating key concepts from dynamical systems theory and leveraging principles from statistical mechanics, the $\mathbb{C}$-RSN model introduces localized non-linearity, complex fixed eigenvalues, and a distinct separation of memory and input processing functionalities. These features collectively enable the $\mathbb{C}$-RSN evolving towards a dynamic, oscillating final state that more closely mirrors biological cognition. Central to this work is the exploration of how the $\mathbb{C}$-RSN manages to capture the rhythmic, oscillatory dynamics intrinsic to biological systems, thanks to its complex eigenvalue structure and the innovative segregation of its linear and non-linear components. The model's ability to classify data through a time-dependent function, and the localization of information processing, is demonstrated with an empirical evaluation using the MNIST dataset. Remarkably, distinct items supplied as a sequential input yield patterns in time which bear the indirect imprint of the insertion order (and of the time of separation between contiguous insertions).

cs.LG↗

arXiv2023

How a student becomes a teacher: learning and forgetting through Spectral methods

In theoretical ML, the teacher-student paradigm is often employed as an effective metaphor for real-life tuition. The above scheme proves particularly relevant when the student network is overparameterized as compared to the teacher network. Under these operating conditions, it is tempting to speculate that the student ability to handle the given task could be eventually stored in a sub-portion of the whole network. This latter should be to some extent reminiscent of the frozen teacher structure, according to suitable metrics, while being approximately invariant across different architectures of the student candidate network. Unfortunately, state-of-the-art conventional learning techniques could not help in identifying the existence of such an invariant subnetwork, due to the inherent degree of non-convexity that characterizes the examined problem. In this work, we take a leap forward by proposing a radically different optimization scheme which builds on a spectral representation of the linear transfer of information between layers. The gradient is hence calculated with respect to both eigenvalues and eigenvectors with negligible increase in terms of computational and complexity load, as compared to standard training algorithms. Working in this framework, we could isolate a stable student substructure, that mirrors the true complexity of the teacher in terms of computing neurons, path distribution and topological attributes. When pruning unimportant nodes of the trained student, as follows a ranking that reflects the optimized eigenvalues, no degradation in the recorded performance is seen above a threshold that corresponds to the effective teacher size. The observed behavior can be pictured as a genuine second-order phase transition that bears universality traits.

cs.LG↗

arXiv2023

Universal defects statistics with strong long-range interactions

Quasi-static transformations, or slow quenches, of many-body quantum systems across quantum critical points create topological defects. The Kibble-Zurek mechanism regulates the appearance of defects in a local quantum system through a classical combinatorial process. However, long-range interactions disrupt the conventional Kibble-Zurek scaling and lead to a density of defects that is independent of the rate of the transformation. In this study, we analytically determine the complete full counting statistics of defects generated by slow annealing a strong long-range system across its quantum critical point. We demonstrate that the mechanism of defect generation in long-range systems is a purely quantum process with no classical equivalent. Furthermore, universality is not only observed in the defect density but also in all the moments of the distribution. Our findings can be tested on various experimental platforms, including Rydberg gases and trapped ions.

quant-ph↗

arXiv2023

Cooperative quantum information erasure

We demonstrate an information erasure protocol that resets $N$ qubits at once. The method displays exceptional performances in terms of energy cost (it operates nearly at Landauer energy cost $kT \ln 2$), time duration ($\sim μs$) and erasure success rate ($\sim 99,9\%$). The method departs from the standard algorithmic cooling paradigm by exploiting cooperative effects associated to the mechanism of spontaneous symmetry breaking which are amplified by quantum tunnelling phenomena. Such cooperative quantum erasure protocol is experimentally demonstrated on a commercial quantum annealer and could be readily applied in next generation hybrid gate-based/quantum-annealing quantum computers, for fast, effective, and energy efficient initialisation of quantum processing units.

quant-ph↗

arXiv2023

Convergence of the Integral Fluctuation Theorem estimator for nonequilibrium Markov systems

The Integral Fluctuation Theorem for entropy production (IFT) is among the few equalities that are known to be valid for physical systems arbitrarily driven far from equilibrium. Microscopically, it can be understood as an inherent symmetry for the fluctuating entropy production rate implying the second law of thermodynamics. Here, we examine an IFT statistical estimator based on regular sampling and discuss its limitations for nonequilibrium systems, when sampling rare events becomes pivotal. Furthermore, via a large deviation study, we discuss a method to carefully setup an experiment in the parameter region where the IFT estimator safely converges and also show how to improve the convergence region for Markov chains with finite correlation time. We corroborate our arguments with two illustrative examples.

cond-mat.stat-mech↗

arXiv2022

Third law of thermodynamics and the scaling of quantum computers

The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near to absolute zero. On the other hand, a fundamental assumption of quantum computing is to start each computation from a register of qubits initialized in a pure state, i.e., at zero temperature. These conflicting aspects, at the interface between quantum computing and thermodynamics, are often overlooked or, at best, addressed only at a single-qubit level. In this work, we argue how the existence of a small, but finite, effective temperature, which makes the initial state a mixed state, poses a real challenge to the fidelity constraints required for the scaling of quantum computers. Our theoretical results, carried out for a generic quantum circuit with $N$-qubit input states, are validated by test runs performed on a real quantum processor.

quant-ph↗

arXiv2022

Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge network

A tool that could suggest new personalized research directions and ideas by taking insights from the scientific literature could significantly accelerate the progress of science. A field that might benefit from such an approach is artificial intelligence (AI) research, where the number of scientific publications has been growing exponentially over the last years, making it challenging for human researchers to keep track of the progress. Here, we use AI techniques to predict the future research directions of AI itself. We develop a new graph-based benchmark based on real-world data -- the Science4Cast benchmark, which aims to predict the future state of an evolving semantic network of AI. For that, we use more than 100,000 research papers and build up a knowledge network with more than 64,000 concept nodes. We then present ten diverse methods to tackle this task, ranging from pure statistical to pure learning methods. Surprisingly, the most powerful methods use a carefully curated set of network features, rather than an end-to-end AI approach. It indicates a great potential that can be unleashed for purely ML approaches without human knowledge. Ultimately, better predictions of new future research directions will be a crucial component of more advanced research suggestion tools.

cs.AI↗

arXiv2022

Quantum density peak clustering

Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing analysis. In this work, we introduce a quantum version of the density peak clustering algorithm, built upon a quantum routine for minimum finding. We prove a quantum speedup for a decision version of density peak clustering depending on the structure of the dataset. Specifically, the speedup is dependent on the heights of the trees of the induced graph of nearest-highers, i.e., the graph of connections to the nearest elements with higher density. We discuss this condition, showing that our algorithm is particularly suitable for high-dimensional datasets. Finally, we benchmark our proposal with a toy problem on a real quantum device.

quant-ph↗

arXiv2022

Recurrent Spectral Network (RSN): shaping the basin of attraction of a discrete map to reach automated classification

A novel strategy to automated classification is introduced which exploits a fully trained dynamical system to steer items belonging to different categories toward distinct asymptotic attractors. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Non-linear terms act for a transient and allow to disentangle the data supplied as initial condition to the discrete dynamical system, shaping the boundaries of different attractors. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling. Our novel approach to classification, that we here term Recurrent Spectral Network (RSN), is successfully challenged against a simple test-bed model, created for illustrative purposes, as well as a standard dataset for image processing training.

cond-mat.dis-nn↗

arXiv2022

Noise fingerprints in quantum computers: Machine learning software tools

In this paper we present the high-level functionalities of a quantum-classical machine learning software, whose purpose is to learn the main features (the fingerprint) of quantum noise sources affecting a quantum device, as a quantum computer. Specifically, the software architecture is designed to classify successfully (more than 99% of accuracy) the noise fingerprints in different quantum devices with similar technical specifications, or distinct time-dependences of a noise fingerprint in single quantum machines.

quant-ph↗

arXiv2022

Energy fluctuation relations and repeated quantum measurements

In this review paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form $\langle e^{-βQ}\rangle = 1$, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies.

quant-ph↗

arXiv2022

Spontaneous fluctuation-symmetry breaking and the Landauer principle

We study the problem of the energetic cost of information erasure by looking at it through the lens of the Jarzynski equality. We observe that the Landauer bound, $\langle W \rangle \geq kT \ln 2$, on average dissipated work $\langle W \rangle$ associated to an erasure process, literally emerges from the underlying second law bound as formulated by Kelvin, $\langle W \rangle \geq 0$, as consequence of a spontaneous breaking of the Crooks-Tasaki fluctuation-symmetry, that accompanies logical irreversibility. We illustrate and corroborate this insight with numerical simulations of the process of information erasure performed on a 2D Ising ferromagnet.

cond-mat.stat-mech↗

arXiv2022

Spectral pruning of fully connected layers: ranking the nodes based on the eigenvalues

Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the eigenvalues can be used to rank the nodes' importance within the ensemble. Indeed, we will prove that sorting the nodes based on their associated eigenvalues, enables effective pre- and post-processing pruning strategies to yield massively compacted networks (in terms of the number of composing neurons) with virtually unchanged performance. The proposed methods are tested for different architectures, with just a single or multiple hidden layers, and against distinct classification tasks of general interest.

cond-mat.dis-nn↗

arXiv2022

Network-based link prediction of scientific concepts -- a Science4Cast competition entry

We report on a model built to predict links in a complex network of scientific concepts, in the context of the Science4Cast 2021 competition. We show that the network heavily favours linking nodes of high degree, indicating that new scientific connections are primarily made between popular concepts, which constitutes the main feature of our model. Besides this notion of popularity, we use a measure of similarity between nodes quantified by a normalized count of their common neighbours to improve the model. Finally, we show that the model can be further improved by considering a time-weighted adjacency matrix with both older and newer links having higher impact in the predictions, representing rooted concepts and state of the art research, respectively.

cs.SI↗

arXiv2021

Learning the noise fingerprint of quantum devices

Noise sources unavoidably affect any quantum technological device. Noise's main features are expected to strictly depend on the physical platform on which the quantum device is realized, in the form of a distinguishable fingerprint. Noise sources are also expected to evolve and change over time. Here, we first identify and then characterize experimentally the noise fingerprint of IBM cloud-available quantum computers, by resorting to machine learning techniques designed to classify noise distributions using time-ordered sequences of measured outcome probabilities.

quant-ph↗

arXiv2021

New Trends in Quantum Machine Learning

Here we will give a perspective on new possible interplays between Machine Learning and Quantum Physics, including also practical cases and applications. We will explore the ways in which machine learning could benefit from new quantum technologies and algorithms to find new ways to speed up their computations by breakthroughs in physical hardware, as well as to improve existing models or devise new learning schemes in the quantum domain. Moreover, there are lots of experiments in quantum physics that do generate incredible amounts of data and machine learning would be a great tool to analyze those and make predictions, or even control the experiment itself. On top of that, data visualization techniques and other schemes borrowed from machine learning can be of great use to theoreticians to have better intuition on the structure of complex manifolds or to make predictions on theoretical models. This new research field, named as Quantum Machine Learning, is very rapidly growing since it is expected to provide huge advantages over its classical counterpart and deeper investigations are timely needed since they can be already tested on the already commercially available quantum machines.

quant-ph↗