arXiv subjects

Giuseppe E. Santoro

Publications and source records attributed to Giuseppe E. Santoro.

At least 37 records · Page 2Linked to original sources

arXiv2020

Reinforcement Learning assisted Quantum Optimization

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quan-tum approximate optimization algorithm (QAOA). QAOA requires a variational minimization for states constructed by applying a sequence of unitary operators, depending on parameters living ina highly dimensional space. We reformulate such a minimum search as a learning task, where a RL agent chooses the control parameters for the unitaries, given partial information on the system. We show that our RL scheme finds a policy converging to the optimal adiabatic solution for QAOA found by Mbeng et al. arXiv:1906.08948 for the translationally invariant quantum Ising chain. In presence of disorder, we show that our RL scheme allows the training part to be performed on small samples, and transferred successfully on larger systems.

quant-ph↗

arXiv2020

Dissipation assisted Thouless pumping in the Rice-Mele model

We investigate the effect of dissipation from a thermal environment on topological pumping in the periodically-driven Rice-Mele model. We report that dissipation can improve the robustness of pumping quantisation in a regime of finite driving frequencies. Specifically, in this regime, a low-temperature dissipative dynamics can lead to a pumped charge that is much closer to the Thouless quantised value, compared to a coherent evolution. We understand this effect in the Floquet framework: dissipation increases the population of a Floquet band which shows a topological winding, where pumping is essentially quantised. This finding is a step towards understanding a potentially very useful resource to exploit in experiments, where dissipation effects are unavoidable. We consider small couplings with the environment and we use a Bloch-Redfield quantum master equation approach for our numerics: Comparing these results with an exact MPS numerical treatment we find that the quantum master equation works very well also at low temperature, a quite remarkable fact.

cond-mat.quant-gas↗

arXiv2019

Superfluid to Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation

We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition towards the Mott-insulating phase. By means of a combination of the Time-Dependent Variational Principle and a Tree-Tensor Network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the amplitude of such oscillations is connected to the residual energy, characterizing the creation of defects while crossing the quantum critical point, while their frequency matches the spectral gap in the Mott insulating phase. Our predictions can be verified in future atomtronics experiments with neutral atoms in ring shaped traps. We believe that the proposed setup provides an interesting but simple platform to study the non-equilibrium quantum dynamics of persistent currents experimentally.

quant-ph↗

arXiv2019

Optimal quantum control with digitized Quantum Annealing

We show how a digitized version of Quantum Annealing can be made optimal, realizing the best possible solution allowed by quantum mechanics in the shortest time, without any prior knowledge on the location and properties of the spectral gap. Our findings elucidate the intimate relation between digitized-QA, optimal Quantum Control, and recently proposed hybrid quantum-classical variational algorithms for quantum-state preparation and optimization. We illustrate this on the simple benchmark problem of an unfrustrated antiferromagnetic Ising chain in a transverse field.

quant-ph↗

arXiv2019

Optimal working point in digitized quantum annealing

We present a study of the digitized Quantum Annealing protocol proposed by R. Barends et al., Nature 534, 222 (2016). Our analysis, performed on the benchmark case of a transverse Ising chain problem, shows that the algorithm has a well defined optimal working point for the annealing time $τ^{\mathrm{opt}}_\mathrm{P}$ --- scaling as $τ^{\mathrm{opt}}_\mathrm{P}\sim \mathrm{P}$, where $\mathrm{P}$ is the number of digital Trotter steps --- beyond which, the residual energy error shoots-up towards the value characteristic of the maximally disordered state. We present an analytical analysis for the translationally invariant transverse Ising chain case, but our numerical evidence suggests that this scenario is more general, surviving, for instance, the presence of disorder.

cond-mat.stat-mech↗

arXiv2019

Localization, topology and quantized transport in disordered Floquet systems

We investigate the transition induced by disorder in a periodically-driven one-dimensional model displaying quantized topological transport. We show that, while instantaneous eigenstates are necessarily Anderson localized, the periodic driving plays a fundamental role in delocalizing Floquet states over the whole system, henceforth allowing for a steady state nearly-quantized current. Remarkably, this is linked to a localization/delocalization transition in the Floquet states of a one dimensional driven Anderson insulator, which occurs for periodic driving corresponding to a nontrivial loop in the parameter space. As a consequence, the Floquet spectrum becomes continuous in the delocalized phase, in contrast with a pure-point instantaneous spectrum.

cond-mat.dis-nn↗

arXiv2018

On the quantization of the Hall conductivity in the Harper-Hofstadter model

We study the robustness of the quantization of the Hall conductivity in the Harper-Hofstadter model towards the details of the protocol with which a longitudinal uniform driving force $F_x(t)$ is turned on. In the vector potential gauge, through Peierls substitution, this involves the switching-on of complex time-dependent hopping amplitudes $\mathrm{e}^{-\frac{i}{\hbar}\mathcal{A}_x(t)}$ in the $\hat{\mathbf{x}}$-direction such that $\partial_t \mathcal{A}_x(t)=F_x(t)$. The switching-on can be sudden, $F_x(t)=θ(t) F$, where $F$ is the steady driving force, or more generally smooth $F_x(t)=f(t/t_{0}) F$, where $f(t/t_{0})$ is such that $f(0)=0$ and $f(1)=1$. We investigate how the time-averaged (steady-state) particle current density $j_y$ in the $\hat{\mathbf{y}}$-direction deviates from the quantized value $j_y \, h/F = n$ due to the finite value of $F$ and the details of the switching-on protocol. Exploiting the time-periodicity of the Hamiltonian $\hat{H}(t)$, we use Floquet techniques to study this problem. In this picture the (Kubo) linear response $F\to 0$ regime corresponds to the adiabatic limit for $\hat{H}(t)$. In the case of a sudden quench $j_y \, h/F$ shows $F^2$ corrections to the perfectly quantized limit. When the switching-on is smooth, the result depends on the switch-on time $t_{0}$: for a fixed $t_{0}$ we observe a crossover force $F^*$ between a quadratic regime for $F F^*$. The crossover $F^*$ decreases as $t_{0}$ increases, eventually recovering the topological robustness. These effects are in principle amenable to experimental tests in optical lattice cold atomic systems with synthetic gauge fields.

cond-mat.quant-gas↗

arXiv2018

On the dynamics of Simulated Quantum Annealing in random Ising chains

Simulated Quantum Annealing (SQA), that is emulating a Quantum Annealing (QA) dynamics on a classical computer by a Quantum Monte Carlo whose parameters are changed during the simulation, is a well established computational strategy to cope with the exponentially large Hilbert space. It has enjoyed some early successes but has also raised more recent criticisms. Here we investigate, on the paradigmatic case of a one-dimensional transverse field Ising chain, two issues related to SQA in its Path-Integral implementation: the question of Monte Carlo vs physical (Schrödinger) dynamics and the issue of the imaginary-time continuum limit to eliminate the Trotter error. We show that, while a proper time-continuum limit is able to restitute the correct Kibble-Zurek scaling of the residual energy $\varepsilon_\mathrm{res}(τ)\sim τ^{-1/2}$ for the ordered case --- $τ$ being the total annealing time ---, the presence of disorder leads to a characteristic sampling crisis for a large number of Trotter time-slices, in the low-temperature ordered phase. Such sampling problem, in turn, leads to SQA results which are apparently unrelated to the coherent Schrödinger QA even at intermediate $τ$.

quant-ph↗

arXiv2018

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

We revisit the issue of thermally assisted quantum annealing by a detailed study of the dissipative Landau-Zener problem in presence of a Caldeira-Leggett bath of harmonic oscillators, using both a weak-coupling quantum master equation and a quasi-adiabatic path-integral approach. Building on the known zero-temperature exact results (Wubs et al., PRL 97, 200404 (2006)), we show that a finite temperature bath can have a beneficial effect on the ground-state probability only if it couples also to a spin-direction that is transverse with respect to the driving field, while no improvement is obtained for the more commonly studied purely longitudinal coupling. In particular, we also highlight that, for a transverse coupling, raising the bath temperature further improves the ground-state probability in the fast-driving regime. We discuss the relevance of these findings for the current quantum-annealing flux qubit chips.

cond-mat.mes-hall↗

arXiv2018

On the optimal working point in dissipative quantum annealing

We study the effect of a thermal environment on the quantum annealing dynamics of a transverse-field Ising chain. The environment is modelled as a single Ohmic bath of quantum harmonic oscillators weakly interacting with the total transverse magnetization of the chain in a translationally invariant manner. We show that the density of defects generated at the end of the annealing process displays a minimum as a function of the annealing time, the so-called optimal working point, only in rather special regions of the bath temperature and coupling strength plane. We discuss the relevance of our results for current and future experimental implementations with quantum annealing hardware.

quant-ph↗

arXiv2018

Non-adiabatic breaking of topological pumping

We study Thouless pumping out of the adiabatic limit. Our findings show that despite its topological nature, this phenomenon is not {generically} robust to non-adiabatic effects. Indeed we find that the Floquet diagonal ensemble value of the pumped charge shows a deviation from the topologically quantized limit which is quadratic in the driving frequency {for a sudden switch-on of the driving}. This is reflected also in the charge pumped in a single period, which shows a non-analytic behaviour on top of an overall quadratic decrease. Exponentially small corrections are recovered only with a careful tailoring of the driving protocol. We also discuss thermal effects and the experimental feasibility of observing such a deviation.

cond-mat.quant-gas↗

arXiv2018

Analytic understanding and control of dynamical friction

Recent model simulations discovered unexpected non-monotonic features in the wear-free dry phononic friction as a function of the sliding speed. Here we demonstrate that a rather straight- forward application of linear-response theory, appropriate in a regime of weak slider-substrate in- teraction, predicts frictional one-phonon singularities which imply a non-trivial dependence of the dynamical friction force on the slider speed and/or coupling to the substrate. The explicit formula which we derive reproduces very accurately the classical atomistic simulations when available. By modifying the slider-substrate interaction the analytical understanding obtained provides a practical means to tailor and control the speed dependence of friction with substantial freedom.

cond-mat.mes-hall↗

arXiv2017

Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model

We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between non-adiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (average value of the Hamiltonian) as a measure of the deviation from reaching the target final ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find a robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the non-adiabatic effects and the dissipative processes. We compare these results with matrix-product-operator simulations of an Ising system and show that the phenomenology we found applies also for this more realistic case.

quant-ph↗

arXiv2017

Floquet resonances close to the adiabatic limit and the effect of dissipation

We study the approach to the adiabatic limit in periodically driven systems. Specifically focusing on a spin-1/2 in a magnetic field we find that, when the parameters of the Hamiltonian lead to a quasi-degeneracy in the Floquet spectrum, the evolution is not adiabatic even if the frequency of the field is much smaller than the spectral gap of the Hamiltonian. We argue that this is a general phenomenon of periodically driven systems. Although an explanation based on a perturbation theory in $ω_0$ cannot be given, because of the singularity of the zero frequency limit, we are able to describe this phenomenon by means of a mapping to an extended Hilbert space, in terms of resonances of an effective two-band Wannier-Stark ladder. Remarkably, the phenomenon survives in the presence of dissipation towards an environment and can be therefore easily experimentally observed.

quant-ph↗

arXiv2017

Friction Anomalies at First-Order Transition Spinodals: 1T-TaS$_2$

Revealing phase transitions of solids through mechanical anomalies in the friction of nanotips sliding on their surfaces is an unconventional and instructive tool for continuous transitions, unexplored for first-order ones. Owing to slow nucleation, first-order structural transformations generally do not occur at the precise crossing of free energies, but hysteretically, near the spinodal temperatures where, below and above the thermodynamic transition temperature, one or the other metastable free energy branches terminates. The spinodal transformation, a collective one-shot event with no heat capacity anomaly, is easy to trigger by a weak external perturbations. Here we propose that even the gossamer mechanical action of an AFM tip may locally act as a surface trigger, narrowly preempting the spontaneous spinodal transformation, and making it observable as a nanofrictional anomaly. Confirming this expectation, the CCDW-NCCDW first-order transition of the important layer compound 1T-TaS$_2$ is shown to provide a demonstration of this effect.

cond-mat.mes-hall↗

arXiv2017

Quantum Lubricity

The quantum motion of nuclei, generally ignored in sliding friction, can become important for an atom, ion, or light molecule sliding in an optical lattice. The density-matrix-calculated evolution of a quantum Prandtl-Tomlinson model, describing the frictional dragging by an external force of a quantum particle, shows that classical predictions can be very wrong. The strongest quantum effect occurs not for weak, but for strong periodic potentials, where barriers are high but energy levels in each well are discrete, and resonant tunnelling to excited states in the nearest well can preempt classical stick-slip with great efficiency. The resulting permeation of otherwise impassable barriers is predicted to cause quantum lubricity

cond-mat.mes-hall↗

arXiv2017

Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet

We compare the performance of quantum annealing (QA, through Schrödinger dynamics) and simulated annealing (SA, through a classical master equation) on the $p$-spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second-order ($p=2$, the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition ($p \ge 3$, i.e., with multi-spin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards $0$ when the total annealing time $τ$ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schrödinger and master equations in combination with a non-equilibrium Landau-Zener analysis. We also analyse the imaginary-time QA dynamics of the model, finding a $1/τ^2$ behaviour for all finite values of $p$, as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit $p({\rm odd})=\infty$ is also discussed.

quant-ph↗

arXiv2016

Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators

Inducing topological transitions by a time-periodic perturbation offers a route to controlling the properties of materials. Here we show that the adiabatic preparation of a non-trivial state involves a selective population of edge-states, due to exponentially-small gaps preventing adiabaticity. We illustrate this by studying graphene-like ribbons with hopping's phases of slowly increasing amplitude, as for, e.g., a circularly polarized laser slowly turned-on. The induced currents have large periodic oscillations, but flow solely at the edges upon time-averaging, and can be controlled by focusing the laser on either edge. The bulk undergoes a non-equilibrium topological transition, as signaled by the local Chern marker introduced by Bianco & Resta in equilibrium. The failure of the adiabatic picture in presence of intraband resonances is discussed.

quant-ph↗