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Quantum walk continui nel tempo per le tecnologie quantistiche: stima quantistica e modellizzazione di fenomeni di trasporto
No full textI quantum walk sono la controparte quantistica dei random walk classici e descrivono il moto di un walker quantistico confinato su posizioni discrete. La natura quantistica del walker conferisce loro caratteristiche peculiari, totalmente diverse da quelle classiche. Nel quantum walk continuo nel tempo (CTQW) lo stato del walker soddisfa l’equazione di Schrödinger ed evolve secondo l’Hamiltoniana data, tipicamente, dalla matrice Laplaciana. Quest’ultima è la rappresentazione matematica di un grafo, i cui vertici sono le posizioni permesse e gli archi i cammini consentiti. In realtà, qualsiasi Hamiltoniana che rispetta la topologia del grafo definisce un CTQW. I CTQW sono studiati in diverse aree di ricerca, dalla modellizzazione di fenomeni fisici alla comunicazione quantistica, dalla computazione quantistica universale allo sviluppo di algoritmi quantistici. Sperimentalmente, possono essere implementati su diverse piattaforme, quali computer quantistici NMR, atomi di Rydberg ultrafreddi in reticoli ottici, chip fotonici, catene di spin e qubit superconduttori. Questa tesi è uno studio teorico sui CTQW focalizzato sulla loro dinamica, libera o in presenza di perturbazioni esterne, e sul loro potenziale utilizzo come sonde in problemi di stima quantistica. Una sonda quantistica è un sistema fisico preparato in uno stato quantistico sensibile alle fluttuazioni di uno o più parametri. L’informazione di Fisher quantistica (QFI) è la quantità centrale della metrologia quantistica, in quanto stabilisce il limite ultimo alla precisione ottenibile nella stima di un parametro di interesse. Una QFI divergente corrisponde alla stimabilità ottimale. Abbiamo studiato CTQW generati dalla matrice Laplaciana e perturbati dal suo quadrato, in quanto questo termine introduce hopping a secondi vicini. Dopo aver analizzato l’evoluzione di un walker su grafi paradigmatici per connettività e simmetria, abbiamo determinato le preparazioni del walker e i grafi che massimizzano la QFI per la stima del parametro perturbativo. Inoltre, abbiamo analizzato i CTQW sulle tassellature regolari del piano Euclideo, mostrando che la propagazione non è universalmente balistica. Assumendo poi un walker dotato di carica, abbiamo inserito un campo magnetico uniforme perpendicolare e confrontato due definizioni dell’Hamiltoniana del CTQW: (i) l’introduzione dei fattori di fase di Peierls e (ii) la discretizzazione spaziale dell’Hamiltoniana originale nel continuo. Quindi, abbiamo utilizzato una particella carica (senza spin) su un reticolo quadrato finito come sonda per rilevare un campo magnetico localmente statico e perpendicolare, avanzando l’idea di magnetometria quantistica reticolare. Il nostro schema deriva dai CTQW, ma non ne sfrutta le proprietà dinamiche, basandosi su misure di stato fondamentale. Il sistema è di interesse come magnetometro quantistico, poiché fornisce una QFI non trascurabile e con picchi rilevanti per numerose configurazioni. Utilizzando il concetto di QFI e la teoria dei grafi, abbiamo valutato il ruolo della topologia sulle prestazioni termometriche di un dato sistema. Modellizzando il termometro come un insieme di vertici per il CTQW di un’eccitazione all’equilibrio termico, abbiamo trovato che una bassa connettività è una risorsa per realizzare termometri precisi a basse temperature, mentre sistemi altamente connessi sono adatti per temperature più elevate. Grafi con diversa topologia presentano anche proprietà diverse di trasporto. Per correlarle, abbiamo modellizzato i processi di trasporto come CTQW coerenti di un’eccitazione ed abbiamo calcolato analiticamente l’efficienza di trasporto per diversi stati iniziali e grafi. I nostri risultati suggeriscono che in generale la connettività non è un buon indice per l’efficienza di trasporto.Quantum walks are the quantum counterpart of classical random walks and describe the motion of a quantum walker when confined to discrete spatial locations. The quantum nature of the walker gives them peculiar features, totally different from the classical ones. In the continuous-time quantum walk (CTQW) the state of the walker obeys the Schrödinger equation and evolves under a Hamiltonian typically given by the Laplacian matrix. The latter is the mathematical representation of a graph, whose vertices are the allowed positions, and the edges the allowed paths. Actually, any Hamiltonian which respects the topology of the graph defines a CTQW, thus making CTQWs extremely versatile. CTQWs are investigated in several research areas, ranging from modeling of physical phenomena to quantum communication, from universal quantum computation to the development of quantum algorithms. Experimentally, they can be implemented on different platforms, e.g., NMR quantum computers, optical lattices of ultracold Rydberg atoms, photonic chips, spin chains, and superconducting qubits. This thesis is a theoretical study on CTQWs, with a focus on their dynamics, free or in the presence of external perturbations, and on their potential use as probes in quantum estimation problems. A quantum probe is a physical system prepared in a quantum state sensitive to fluctuations affecting one or more parameters of interest. The quantum Fisher information (QFI) is the central quantity in quantum metrology, as it establishes the ultimate bound on the achievable precision in estimating a parameter of interest. Diverging QFI corresponds to optimal estimability. We studied CTQWs generated by the Laplacian matrix and perturbed by its square, as this term introduces next-nearest-neighbor hopping. After investigating the evolution of a walker on paradigmatic graphs for connectivity and symmetry, we determined the walker preparations and the graphs that maximize the QFI for estimating the perturbation parameter. Moreover, we investigated CTQWs on the regular tessellations of the Euclidean plane, showing that the spread is not universally ballistic. Then, assuming a charged walker, we inserted a perpendicular uniform magnetic field and compared two approaches to define the CTQW Hamiltonian: (i) Introducing the Peierls phase-factors and (ii) spatially discretizing the original Hamiltonian in the continuum. Based on this, we used a charged (spinless) particle on a finite square lattice as a probe to detect a locally static transverse magnetic field, putting forward the idea of lattice quantum magnetometry. Our scheme finds its root in CTQWs, but it does not exploit their dynamical properties, being based on ground-state measurements. The system turned out to be of interest as a quantum magnetometer, providing non-negligible QFI with relevant peaks in a large range of configurations. Employing the concept of QFI and graph theory, we assessed the role of topology on the thermometric performance of a given system. Upon modeling the thermometer as a set of vertices for the CTQW of an excitation at thermal equilibrium, we found that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Graphs with different topology also exhibit different transport properties. To correlate them, we modeled transport processes as coherent CTQWs of an excitation and we analytically assessed the transport efficiency for different initial states and graphs. Our results suggest that, in general, connectivity is a poor indicator for transport efficiency
Synchronization-induced violation of thermodynamic uncertainty relations
Full text linkFluctuations affect the functionality of nanodevices. Thermodynamic uncertainty relations (TURs), derived within the framework of stochastic thermodynamics, show that a minimal amount of dissipation is required to obtain a given relative energy current dispersion, that is, current precision has a thermodynamic cost. It is therefore of great interest to explore the possibility that TURs are violated, particularly for quantum systems, leading to accurate currents at lower cost. Here, we show that two quantum harmonic oscillators are synchronized by coupling to a common thermal environment, at strong dissipation and low temperature. In this regime, periodically modulated couplings to a second thermal reservoir, breaking time-reversal symmetry and taking advantage of non-Markovianity of this latter reservoir, lead to strong violation of TURs for local work currents, while maintaining finite output power. Our results pave the way for the use of synchronization in the thermodynamics of precision
Dissipation-induced collective advantage of a quantum thermal machine
Full text linkDo quantum correlations lead to better performance with respect to several
different systems working independently? For quantum thermal machines, the
question is whether a working medium (WM) made of constituents exhibits
better performance than independent engines working in parallel. Here, by
inspecting a microscopic model with the WM composed by two non-interacting
quantum harmonic oscillators, we show that the presence of a common environment
can mediate non-trivial correlations in the WM leading to better quantum heat
engine performance -- maximum power and efficiency -- with respect to an
independent configuration. Furthermore, this advantage is striking for strong
dissipation, a regime in which two independent engines cannot deliver any
useful power. Our results show that dissipation can be exploited as a useful
resource for quantum thermal engines, and are corroborated by optimization
techniques here extended to non-Markovian quantum heat engines.Comment: Accepted Manuscript: Main text (13 pages, 8 figures) + Supplementary
Material (9 pages, 3 figures). This article may be downloaded for personal
use only. Any other use requires prior permission of the author and AIP
Publishing. This article appeared in AVS Quantum Science 6, 025001 (2024) and
may be found at https://doi.org/10.1116/5.019034
Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers
Full text linkQuantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the (Formula presented.) -cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only (Formula presented.) two-qubit gates compared to the (Formula presented.) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers
Efficiency and thermodynamic uncertainty relations of a dynamical quantum heat engine
Full text linkIn the quest for high-performance quantum thermal machines, looking for an optimal thermodynamic efficiency is only part of the issue. Indeed, at the level of quantum devices, fluctuations become extremely relevant and need to be taken into account. In this paper we study the thermodynamic uncertainty relations for a quantum thermal machine with a quantum harmonic oscillator as a working medium, connected to two thermal baths, one of which is dynamically coupled. We show that parameters can be found such that the machine operates both as a quantum engine or refrigerator, with both sizeable efficiency and small fluctuations.16 pages, 5 color figures. This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1140/epjs/s11734-023-00949-
Universality of the fully connected vertex in Laplacian continuous-time quantum walk problems
Full text linkA fully connected vertex in a simple graph of order is a vertex
connected to all the other vertices. Upon denoting by the Laplacian
matrix of the graph, we prove that the continuous-time quantum walk (CTQW) --
with Hamiltonian -- of a walker initially localized at does not depend on the graph . We also prove that for any
Grover-like CTQW -- with Hamiltonian -- the probability amplitude at the fully connected
marked vertices does not depend on . The result does not hold for CTQW
with Hamiltonian (adjacency matrix). We apply our results to
spatial search and quantum transport for single and multiple fully connected
marked vertices, proving that CTQWs on any graph inherit the properties
already known for the complete graph of the same order, including the
optimality of the spatial search. Our results provide a unified framework for
several partial results already reported in literature for fully connected
vertices, such as the equivalence of CTQW and of spatial search for the central
vertex of the star and wheel graph, and any vertex of the complete graph.Comment: 22 pages, 2 figures, accepted versio
Cyclic solid-state quantum battery: thermodynamic characterization and quantum hardware simulation
Full text linkWe introduce a cyclic quantum battery QB model, based on an interacting bipartite system, weakly coupled to a thermal bath. The working cycle of the battery consists of four strokes: system thermalization, disconnection of subsystems, ergotropy extraction, and reconnection. The thermal bath acts as a charger in the thermalization stroke, while ergotropy extraction is possible because the ensuing thermal state is no longer passive after the disconnection stroke. Focusing on the case of two interacting qubits, we show that phase coherence, in the presence of non-trivial correlations between the qubits, can be exploited to reach working regimes with efficiency higher than 50% while providing finite ergotropy. Our protocol is illustrated through a simple and feasible circuit model of a cyclic superconducting QB. Furthermore, we simulate the considered cycle on superconducting IBM quantum machines. The good agreement between the theoretical and simulated results strongly suggests that our scheme for cyclic QBs can be successfully realized in superconducting quantum hardware
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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