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Ruggero Vaia

Publications and source records attributed to Ruggero Vaia.

At least 19 recordsLinked to original sources
arXiv2024

Full-magnetic implementation of a classical Toffoli gate

The Toffoli gate is the essential ingredient for reversible computing, an energy efficient classical computational paradigm that evades the energy dissipation resulting from Landauer's principle. In this paper we analyze different setups to realize a magnetic implementation of the Toffoli gate using three interacting classical spins, each one embodying one of the three bits needed for the Toffoli gate. In our scheme, different control-spins configurations produce an effective field capable of conditionally flipping the target spin. We study what are the experimental requirements for the realization of our scheme, focusing on the degree of local control, the ability to dynamically switch the spin-spin interactions, and the required single-spin anisotropies to make the classical spin stable, showing that these are compatible with current technology.

quant-ph↗
arXiv2021

Single-qubit remote manipulation by magnetic solitons

Magnetic solitons can constitute a means for manipulating qubits from a distance. This would overcome the necessity of directly applying selective magnetic fields, which is unfeasible in the case of a matrix of qubits embedded in a solid-state quantum device. If the latter contained one-dimensional Heisenberg spin chains coupled to each qubit, one can originate a soliton in a selected chain by applying a time-dependent field at one end of it, far from the qubits. The generation of realistic solitons has been simulated. When a suitable soliton passes by, the coupled qubit undergoes nontrivial operations, even in the presence of moderate thermal noise.

quant-ph↗
arXiv2020

Dispersionless pulse transport in mass-spring chains: All possible perfect Newton's cradles

A pulse traveling on a uniform nondissipative chain of $N$ masses connected by springs is soon destructured by dispersion. Here it is shown that a proper modulation of the masses and the elastic constants makes it possible to obtain a periodic dynamics and a perfect transmission of any kind of pulse between the chain ends, since the initial configuration evolves to its mirror image in the half period. This makes the chain to behave as a Newton's cradle. By a known algorithm based on orthogonal polynomials one can numerically solve the general inverse problem leading from the spectrum to the dynamical matrix and then to the corresponding mass-spring sequence, so yielding all possible ``perfect cradles''. As quantum linear systems obey the same dynamics of their classical counterparts, these results also apply to the quantum case: for instance, a wavefunction localized at one end would evolve to its mirror image at the opposite chain end.

physics.class-ph↗
arXiv2019

Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains

A real persymmetric Jacobi matrix of order $n$ whose eigenvalues are $2k^2$ $(k=0, ..., n-1)$ is presented, with entries given as explicit functions of $n$. Besides the possible use for testing forward and inverse numerical algorithms, such a matrix is especially relevant for its connection with the dynamics of a mass-spring chain, which is a multi-purpose prototype model. Indeed, the mode frequencies being the square roots of the eigenvalues of the interaction matrix, one can shape the chain in such a way that its dynamics be perfectly periodic and dispersionless.

math-ph↗
arXiv2019

Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities

We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semi-analytical approximation of transition probabilities and Arrow-Debreu densities for arbitrary diffusions. We illustrate the accuracy of the method by presenting results for the Black-Karasinski and the GARCH linear models, for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility, and for multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of derivatives pricing applications.

q-fin.CP↗
arXiv2018

Almost-dispersionless pulse transport in long quasiuniform spring-mass chains: A new kind of Newton's cradle

Almost-dispersionless pulse transfer between the extremal masses of a uniform harmonic spring-mass chain of arbitrary length can be induced by suitably modifying two masses and their spring's elastic constant at both extrema of the chain. It is shown that a deviation (or a pulse) imposed to the first mass gives rise to a wave packet that, after a time of the order of the chain length, almost perfectly reproduces the same deviation (pulse) at the opposite end, with an amplitude loss that is as small as 1.3 % in the infinite-length limit; such a dynamics can continue back and forth again for several times before dispersion cleared the effect. The underlying coherence mechanism is that the initial condition excites a bunch of normal modes with almost equal frequency spacing. This constitutes a possible mechanism for efficient energy transfer, e.g., in nanofabricated structures.

physics.class-ph↗
arXiv2017

Quantum correlations between distant qubits conveyed by large-$S$ spin chains

We consider two distant spin-$\frac{1}{2}$ particles (or qubits) and a number of interacting objects, all with the same value $S\gg1$ of their respective spin, distributed on a one-dimensional lattice (or large-$S$ spin chain). The quantum states of the chain are constructed by linearly combining tensor products of single-spin coherent states, whose evolution is determined accordingly, i.e., via classical-like equations of motions. We show that the quantum superposition of the above product states resulting from a local interaction between the first qubit and one spin of the chain evolves so that the second qubit, after having itself interacted with another spin of the chain, can be entangled with the first qubit. Obtaining such outcome does not imply imposing constraints on the length of the chain or the distance between the qubits, which demonstrates the possibility of generating quantum correlations at a distance by means of a macroscopic system, as far as local interactions with just a few of its components are feasible.

quant-ph↗
arXiv2016

Quantum effects in nanosystems: good reasons to use phase-space Weyl symbols

Bogoliubov transformations have been successfully applied in several Condensed Matter contexts, e.g., in the theory of superconductors, superfluids, and antiferromagnets. These applications are based on bulk models where translation symmetry can be assumed, so that few degrees of freedom in Fourier space can be `diagonalized' separately, and in this way it is easy to find the approximate ground state and its excitations. As translation symmetry cannot be invoked when it comes about nanoscopic systems, the corresponding multidimensional Bogoliubov transformations are more complicated. For bosonic systems it is much simpler to proceed using phase-space variables, i.e., coordinates and momenta. Interactions can be accounted for by the self-consistent harmonic approximation, which is naturally developed using phase-space Weyl symbols. The spin-flop transition in a short antiferromagnetic chain is illustrated as an example. This approach, rarely used in the past, is expected to be generally useful to estimate quantum effects, e.g., on phase diagrams of ordered vs disordered phases.

quant-ph↗
arXiv2015

Getting through to a qubit by magnetic solitons

We propose a method for acting on the spin state of a spin-1/2 localized particle, or `qubit', by means of a magnetic signal effectively generated by the nearby transit of a magnetic soliton, there conveyed through a transmission line. We first introduce the specific magnetic soliton of which we will make use, and briefly review the properties that make it apt to represent a signal. We then show that a Heisenberg spin chain can serve as transmission line, and propose a method for injecting a soliton into the chain by acting just on one of its ends. We finally demonstrate that the resulting magnetic pulse can indeed cause, just passing by the spin-1/2 localized particle embodying the qubit, a permanent change in its spin state, thus realizing the possibility of getting through to a single, localized qubit, and manipulate its state. A thorough analysis of how the overall dynamical system operates depending on the setting of its parameters demonstrates that fine tuning is not necessary as it exists an extended region in the parameters space that corresponds to an effective functioning. Moreover, we show that possible noise on the transmission line does not invalidate the scheme.

cond-mat.mtrl-sci↗
arXiv2014

Re-entrant spin-flop transition in nanomagnets

Antiferromagnetic chains with an odd number of spins are known to undergo a transition from an antiparallel to a spin-flop configuration when subjected to an increasing magnetic field. We show that in the presence of an anisotropy favoring alignment perpendicular to the field, the spin-flop state appears for both weak and strong field, the antiparallel state appearing for intermediate fields. Both transitions are second order, the configuration varying continuously with the field intensity. Such re-entrant transition is robust with respect to quantum fluctuations and it might be observed in different types of nanomagnets.

cond-mat.mes-hall↗
arXiv2014

Newton's cradle analogue with Bose-Einstein condensates

We propose a possible experimental realization of a quantum analogue of Newton's cradle using a configuration which starts from a Bose-Einstein condensate. The system consists of atoms with two internal states trapped in a one dimensional tube with a longitudinal optical lattice and maintained in a strong Tonks-Girardeau regime at maximal filling. In each site the wave function is a superposition of the two atomic states and a disturbance of the wave function propagates along the chain in analogy with the propagation of momentum in the classical Newton's cradle. The quantum travelling signal is generally deteriorated by dispersion, which is large for a uniform chain and is known to be zero for a suitably engineered chain, but the latter is hardly realizable in practice. Starting from these opposite situations we show how the coherent behaviour can be enhanced with minimal experimental effort.

quant-ph↗
arXiv2012

Diagonalization of quasi-uniform tridiagonal matrices

The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where one-dimensional interactions prevail. These include magnetic chains, 1D arrays of Josephson junctions or of quantum dots, boson and fermion hopping models, random walks, and so on. In such systems the bulk interactions are uniform, and differences may occur around the boundaries of the arrays. Since in the uniform case the spectrum consists of a band, we exploit the bulk uniformity of quasi-uniform tridiagonal matrices in order to express the spectral problem in terms of a variation of the distribution of eigenvalues in the band and of the corresponding eigenvectors. In the limit of large matrices this naturally leads to a deformation of the density of states which can be expressed analytically; a few out-of-band eigenvalues can show up and have to be accounted for separately. The general procedure is illustrated with some examples.

math-ph↗
arXiv2012

Reentrant enhancement of quantum fluctuations for symmetric environmental coupling

The `system-plus-reservoir' (SPR) model is the most common and effective approach to study quantum dissipative effects. Indeed, it makes quantization possible by considering the whole energy-conserving system, while the reservoir's degrees of freedom, assumed to be harmonic, can be `traced out' by the path-integral technique, leading to a formulation that only includes the system of interest. In the standard SPR model the environment is only coupled with the system's coordinate and turns out to quench its quantum fluctuations. However, there are physical systems coupled with an environment whose `coordinates' and `momenta' can be completely interchangeable (e.g., magnets), so an SPR coupling must symmetrically affect both canonical variables. In this paper such a general environmental coupling is studied in the case of a harmonic oscillator. It is found that quantum fluctuations are generally enhanced by environmental coupling, with an unexpected nonmonotonic behavior. This leads one to speculate about the possibility that spin-lattice coupling could drive the 2D Heisenberg antiferromagnet to reach its quantum-critical point.

cond-mat.stat-mech↗
arXiv2011

Long quantum channels for high-quality entanglement transfer

High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are coupled to the chain by an exchange interaction $j_0$ comparable with the intrachain exchange. Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value $j_0^{opt}(N)$, where $N$ is the channel length. We show that $j_0^{opt}(N)$ scales as $N^{-1/6}$ for large $N$ and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, the average quantum-state transmission fidelity exceeds 90% for any chain length. We emphasize that, taking the reverse point of view, should $j_0$ be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.

quant-ph↗
arXiv2010

Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum wires

It is shown that effective quantum-state and entanglement transfer can be obtained by inducing a coherent dynamics in quantum wires with homogeneous intrawire interactions. This goal is accomplished by tuning the coupling between the wire endpoints and the two qubits there attached, to an optimal value. A general procedure to determine such value is devised, and scaling laws between the optimal coupling and the length of the wire are found. The procedure is implemented in the case of a wire consisting of a spin-1/2 XY chain: results for the time dependence of the quantities which characterize quantum-state and entanglement transfer are found of extremely good quality and almost independent of the wire length. The present approach does not require `ad hoc' engineering of the intrawire interactions nor a specific initial pulse shaping, and can be applied to a vast class of quantum channels.

quant-ph↗
arXiv2008

Vortex-enhanced alternating order around impurities in antiferromagnets

It has been recently pointed out that the presence of a nonmagnetic impurity in a Heisenberg antiferromagnet generates an alternating order of the surrounding spins which is independent of temperature in a wide range. Quantum Monte Carlo simulations in the two-dimensional $S=1/2$ case confirmed this picture, but showed a counterintuitive enhancement of the alternating order around the Kosterlitz-Thouless transition. We propose here an explanation in terms of the effect of vortex excitations.

cond-mat.str-el↗
arXiv2007

Extracting signatures of quantum criticality in the finite-temperature behavior of many-body systems

We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum S=1/2 Ising chain is exactly solvable and extensively studied, results for the classical limit (infinite S) of such model are lacking, and we supply them here. They are obtained numerically, via the Transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase-diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to thermal ones.

cond-mat.stat-mech↗