arXiv subjects

Paolo Santini

Publications and source records attributed to Paolo Santini.

40 records · Page 3Linked to original sources

arXiv2016

Soft McEliece: MDPC code-based McEliece cryptosystems with very compact keys through real-valued intentional errors

We propose to use real-valued errors instead of classical bit flipping intentional errors in the McEliece cryptosystem based on moderate-density parity-check (MDPC) codes. This allows to exploit the error correcting capability of these codes to the utmost, by using soft-decision iterative decoding algorithms instead of hard-decision bit flipping decoders. However, soft reliability values resulting from the use of real-valued noise can also be exploited by attackers. We devise new attack procedures aimed at this, and compute the relevant work factors and security levels. We show that, for a fixed security level, these new systems achieve the shortest public key sizes ever reached, with a reduction up to 25% with respect to previous proposals.

cs.IT↗

arXiv2015

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely-promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model; for these, we numerically simulate the scheme by including the main sources of decoherence. In addition, we show how to circumvent the potentially harmful effects of inhomogeneous broadening of the spin systems.

quant-ph↗

arXiv2011

Understanding complex dynamics by means of an associated Riemann surface

We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the orbits can be derived, which is shown to depend on the initial data and the continued fraction expansion of a simple ratio of the coupling constants of the problem. For rational values of this ratio and generic values of the initial data, all orbits are periodic and the system is isochronous. For irrational values of the ratio, there exist periodic and quasi-periodic orbits for different initial data. Moreover, the dependence of the period on the initial data shows a rich behavior and initial data can always be found such the period is arbitrarily high.

nlin.CD↗

arXiv1999

Heteroskedastic Levy Flights

Truncated Lévy flights are random walks in which the arbitrarily large steps of a Lévy flight are eliminated. Since this makes the variance finite, the central limit theorem applies, and as time increases the probability distribution of the increments becomes Gaussian. Here, truncated Lévy flights with correlated fluctuations of the variance (heteroskedasticity) are considered. What makes these processes interesting is the fact that the crossover to the Gaussian regime may occur for times considerably larger than for uncorrelated (or no) variance fluctuations. These processes may find direct application in the modeling of some economic time series.

cond-mat.stat-mech↗