arXiv subjects

Francesco Petruccione

Publications and source records attributed to Francesco Petruccione.

At least 109 records · Page 6Linked to original sources

arXiv2014

Simulating a perceptron on a quantum computer

Perceptrons are the basic computational unit of artificial neural networks, as they model the activation mechanism of an output neuron due to incoming signals from its neighbours. As linear classifiers, they play an important role in the foundations of machine learning. In the context of the emerging field of quantum machine learning, several attempts have been made to develop a corresponding unit using quantum information theory. Based on the quantum phase estimation algorithm, this paper introduces a quantum perceptron model imitating the step-activation function of a classical perceptron. This scheme requires resources in $\mathcal{O}(n)$ (where $n$ is the size of the input) and promises efficient applications for more complex structures such as trainable quantum neural networks.

quant-ph↗

arXiv2014

Non-equilibrium thermodynamics approach to open quantum systems

Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local in time master equation that provides a direct connection of dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated with the application to the damped harmonic oscillator and the damped driven two-level system resulting in analytical expressions for the non-Markovian and non-equilibrium entropy and inverse temperature.

quant-ph↗

arXiv2014

Quantum walks on graphs representing the firing patterns of a quantum neural network

Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts neurons with a qubit in order to use the advantages of quantum computing in neural networks. A quantum walk on the firing states of such a QNN is supposed to simulate central properties of the dynamics of classical neural networks, such as associative memory. It is shown that a biased discrete Hadamard walk derived from the updating process of a biological neuron does not lead to a unitary walk. However, a Stochastic Quantum Walk between the global firing states of a QNN can be constructed and it is shown that it contains the feature of associative memory. The quantum contribution to the walk accounts for a modest speed-up in some regimes.

quant-ph↗

arXiv2014

Higher-dimensional orbital angular momentum based quantum key distribution with mutually unbiased bases

We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d+1) mutually unbiased measurements in a classical prepare and measure scheme and on a pair of entangled photons for dimensions ranging from d = 2 to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon up to a dimension of d = 4.

quant-ph↗

arXiv2013

On Filtering Schemes in the Quantum-Classical Liouville Approach to Non-adiabatic Dynamics

We study a number of filtering schemes for the reduction of the statistical error in non-adiabatic calculations by means of the quantum-classical Liouville equation. In particular, we focus on a scheme based on setting a threshold value on the sampling weights, so that when the threshold is overcome the value of the weight is reset, and on another approach which prunes the ensemble of the allowed non-adiabatic transitions according to a generalised sampling probability. Both methods have advantages and drawbacks, however their combination drastically improves the performance of an algorithm known as the Sequential Short Time Step Propagation [D. MacKernan et al., J. Phys: Condens. Matter {\bf 14} 9069 (2002)], which is derived from a simple first order expansion of the quantum-classical propagator. Such an algorithm together with the combined filtering procedures produce results that compare very well with those obtained by means of numerically "exact" quantum calculations for the spin-boson model, even for intermediate and strong coupling regimes.

quant-ph↗

arXiv2013

Open system approach to the internal dynamics of a model multilevel molecule

A model multilevel molecule described by two sets of rotational internal energy levels of different parity and degenerate ground states, coupled by a constant interaction, is considered, by assuming that the random collisions in a gas of identical molecules, provoke transitions between adjacent energy levels of the same parity. The prescriptions of the continuous time quantum random walk are applied to the single molecule, interpreted as an open quantum system, and the master equation driving its internal dynamics is built for a general distribution of the waiting times between two consecutive collisions. The coherence terms and the populations of the energy levels relax to the asymptotics with inverse power laws for relevant classes of non-Poissonian distributions of the collision times. The stable asymptotic equilibrium configuration is independent of the distribution. The long time dynamics may be hindered by increasing the tail of the distribution density. This effect may be interpreted as the appearance of the quantum Zeno effect over long time scales.

quant-ph↗

arXiv2012

Unsharp continuous measurement of a Bose-Einstein condensate: full quantum state estimation and the transition to classicality

We study a Bose-Einstein condensate (BEC) in a double-well potential subject to an unsharp continuous measurement of the atom number in one of the two wells. We investigate the back action of the measurement on the quantum dynamics and the viability to monitor the ensuing time evolution. For vanishing inter-atomic interactions, mainly the expectation values of the measured local observable can be inferred from the measurement record. Conversely, in the presence of moderate inter-atomic interactions, the entire many-body state --modified by the measurement-- is monitored with unit fidelity and, at the same time, the measurement effects a transition from quantum to mean-field (classical) behavior of the BEC. We show that this perfect state estimation is possible because the inter-atomic interactions enhance the information gained via the measurement.

quant-ph↗

arXiv2012

Singularity strength based characterization of financial networks

Financial markets are well known examples of multi-fractal complex systems that have garnered much interest in their characterization through complex network theory. The recent studies have used correlation based distance metrics for defining and analyzing financial networks. In this work the singularity strength is employed to define a distance metric and the existence of hierarchical structure in the Johannesburg Stock Exchange is investigated. The multi-fractal nature of the financial market, which is otherwise hidden in the correlation coefficient based prescriptions, is analyzed through the use of the singularity strength based method. The presence of a super cluster is exhibited in the network which accounts for half of the network size and is homogeneous in the sectoral composition of the South African market.

q-fin.ST↗

arXiv2011

Anomalous decay of an atom in structured band gap reservoirs

We analyze the spontaneous emission of a two-level atom interacting with a special class of structured reservoirs of field modes with band gap edge coinciding with the atomic transition frequency. The exact time evolution of the population of the excited level is evaluated analytically through series of Fox-$H$ functions. Over estimated long time scales, inverse power law relaxations emerge, with powers decreasing continuously to 2 according to the choice of the special reservoir. No trapping of the population of the excited level emerges. The same results are recovered in presence of $N-1$ atoms, each one in the ground state, described by the Dicke model. The power of the inverse power law decay results to be independent of $N$. A critical number $N_α^{(\star)}$ is evaluated, such that, for $N \gg N_α^{(\star)}$, the inverse power law decay vanishes.

quant-ph↗

arXiv2011

A reservoir for inverse power law decoherence of a qubit

The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a continuous distribution of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power law relaxation, of power 3/2, over an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is strongly suppressed. The special reservoir exhibits an upper band edge frequency coinciding with the qubit transition frequency. Known theoretical models of photonic band gap media suitable for the realization of the designed reservoir are proposed.

quant-ph↗

arXiv2010

Designing reservoirs for 1/t decoherence of a qubit

Anomalous decoherence in the Jaynes-Cummings model emerges for a certain class of bosonic reservoirs, described by spectral densities with a band edge frequency coinciding with the qubit transition frequency. The special reservoirs are piecewise similar to those usually adopted in Quantum Optics, i.e., sub-ohmic at low frequencies and inverse power laws at high frequencies. The exact dynamics of the qubit is described analytically through Fox $H$-functions. Over estimated long time scales, decoherence results in inverse power laws with powers decreasing continuously to unity, according to the particular choice of the special reservoir. The engineering reservoir approach is a new way of strongly delaying the decoherence process with possible applications to Quantum Technologies, due to the simple form of the designed reservoirs.

quant-ph↗

arXiv2010

Stochastic Simulation of Nonadiabatic Dynamics at Long Time

Using a generalized energy-conserving transition probability, it is shown how nonadiabatic calculations, within the Wigner-Heisenberg representation of quantum mechanics, can be reliably extended to far longer times than those allowed by a primitive sampling scheme. Tackling the spin-boson model as a paradigmatic example, substantial numerical evidence is provided that effective integration of the dynamics can be achieved for a wide range of temperatures and friction.

quant-ph↗

arXiv2010

Sampling of quantum dynamics at long time

The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the parameters of the calculation) over previous schemes is achieved. Novel perspectives for theoretical calculations in coherent many-body systems are opened.

quant-ph↗

arXiv2010

Security and entanglement in differential-phase-shift quantum key distribution

The differential-phase-shift quantum key distribution protocol is formalised as a prepare-and-measure scheme and translated into an equivalent entanglement-based protocol. A necessary condition for security is that Bob's measurement can detect the entanglement of the distributed state in the entanglement-based translation, which implies that his measurement is described by non-commuting POVM elements. This condition is shown to be met.

quant-ph↗

arXiv2009

Diffusion Approximation of Stochastic Master Equations with Jumps

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models as approximation. A necessary condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov process which are based upon the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.

math-ph↗

arXiv2009

Markovian and Post-Markovian dynamics of nonequilibrium thermal entanglement

The dynamics of two spins coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system in the Markovian and Post-Markovian case with exponential memory kernel is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed.

quant-ph↗

arXiv2009

Dynamics of nonequilibrium thermal entanglement

The dynamics of a simple spin chain (2 spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed. It is shown that the system converges to a steady-state. If the energy levels of the two spins are different, the steady-state concurrence assumes its maximum at unequal bath temperatures. It is found that a difference in local energy levels can make the steady-state entanglement more stable against high temperatures.

quant-ph↗

arXiv2009

Stochastic Wave-Function Unravelling of the Generalized Lindblad Master Equation

Recently a generalized master equation was derived that extends the Lindblad theory to highly non-Markovian quantum processes (H.-P. Breuer, Phys. Rev. A \textbf{75}, 022103 (2007)). We perform a stochastic unravelling of this master equation by considering $n$ random state vectors that satisfy the corresponding stochastic differential equation for a piecewise deterministic process. As an application we consider a two-state system randomly coupled to an environment consisting of two energy bands with finite number of levels. Our numerical results are compared to results obtained from the time-convolutionless (TCL) projection operator method using correlated projection superoperators and the exact solution of the Schrödinger equation for this system.

quant-ph↗