90 citations · 760 across the 38 of their papers we have counts for
40 papers
Rapid mixing for Gibbs samplers for quantum spin systems with all-to-all interactions
Nicola Bertoni, Giacomo De Palma
Understanding when quantum many-body systems rapidly converge to thermal equilibrium is a central problem in quantum statistical mechanics. While spatial locality provides powerful…
Lazy training of quantum physics informed neural networks
Anderson Melchor Hernandez, Giacomo De Palma
We study the gradient-flow training dynamics of quantum physics-informed neural networks (QPINNs) for the solution of second-order elliptic partial differential equations with Diri…
Quantum Shannon theory made robust: a tale of three protocols for almost i.i.d. sources
Filippo Girardi, Nilanjana Datta, Giacomo De Palma +1
The asymptotic rates of information-theoretic protocols - including error exponents, data-compression rates, and channel capacities - are traditionally derived under the idealised…
New approaches to almost i.i.d. information theory
Filippo Girardi, Giacomo De Palma, Ludovico Lami
Independent and identically distributed (i.i.d.) states are ubiquitous in quantum information theory. However, in a practical setting, the i.i.d. assumption is too stringent, and p…
Efficient classical computation of the neural tangent kernel of quantum neural networks
Anderson Melchor Hernandez, Davide Pastorello, Giacomo De Palma
We propose an efficient classical algorithm to estimate the Neural Tangent Kernel (NTK) associated with a broad class of quantum neural networks. These networks consist of arbitrar…
Entanglement Degradation in the Presence of Markovian Noise: a Statistical Analysis
Nunzia Cerrato, Giacomo De Palma, Vittorio Giovannetti
Adopting a statistical approach we study the degradation of entanglement of a quantum system under the action of an ensemble of randomly distributed Markovian noise. This enables u…
Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach
Giacomo De Palma, Davide Pastorello
We prove new concentration inequalities for quantum spin systems which apply to any local observable measured on any product state or on any state with exponentially decaying corre…
Trained quantum neural networks are Gaussian processes
Filippo Girardi, Giacomo De Palma
We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of infinite width, where the generated function is the expectation value…
Classical shadows meet quantum optimal mass transport
Giacomo De Palma, Tristan Klein, Davide Pastorello
Classical shadows constitute a protocol to estimate the expectation values of a collection of M observables acting on O(1) qubits of an unknown n-qubit state with a number of measu…
Quantum Optimal Transport: Quantum Channels and Qubits
Giacomo De Palma, Dario Trevisan
These notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erdös Center in September 2022. The focus of the exposi…
Improving the speed of variational quantum algorithms for quantum error correction
Fabio Zoratti, Giacomo De Palma, Bobak Kiani +4
We consider the problem of devising a suitable Quantum Error Correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic u…
The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
Giacomo De Palma, Dario Trevisan
We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice , which we call specific quantum distance. The proposa…
Optimal local work extraction from bipartite quantum systems in the presence of Hamiltonian couplings
Raffaele Salvia, Giacomo De Palma, Vittorio Giovannetti
We investigate the problem of finding the local analogue of the ergotropy, that is the maximum work that can be extracted from a system if we can only apply local unitary transform…
Limitations of variational quantum algorithms: a quantum optimal transport approach
Giacomo De Palma, Milad Marvian, Cambyse Rouzé +1
The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. Howe…
Quantum algorithms for group convolution, cross-correlation, and equivariant transformations
Grecia Castelazo, Quynh T. Nguyen, Giacomo De Palma +3
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inher…
Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
Giacomo De Palma, Lucas Hackl
We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable q…
Quantum concentration inequalities
Giacomo De Palma, Cambyse Rouzé
We establish transportation cost inequalities (TCI) with respect to the quantum Wasserstein distance by introducing quantum extensions of well-known classical methods: first, using…
The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
Giacomo De Palma, Dario Trevisan
We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear c…
Learning quantum data with the quantum Earth Mover's distance
Bobak Toussi Kiani, Giacomo De Palma, Milad Marvian +2
Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly us…
Quantum advantage for differential equation analysis
Bobak T. Kiani, Giacomo De Palma, Dirk Englund +3
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also…
The Quantum Wasserstein Distance of Order 1
Giacomo De Palma, Milad Marvian, Dario Trevisan +1
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of qudits. The proposal recovers the Hamming distance for the vectors of the canonical…
Adversarial Robustness Guarantees for Random Deep Neural Networks
Giacomo De Palma, Bobak T. Kiani, Seth Lloyd
The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close t…
Quantum optimal transport with quantum channels
Giacomo De Palma, Dario Trevisan
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a tran…
Uncertainty relations with quantum memory for the Wehrl entropy
Giacomo De Palma
We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum…