arXiv subjects

Alessandro Santini

Publications and source records attributed to Alessandro Santini.

29 records · Page 2Linked to original sources

arXiv2023

Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware

On a quantum superconducting processor we observe partial and infinite-temperature thermalization induced by a sequence of repeated quantum projective measurements, interspersed by a unitary (Hamiltonian) evolution. Specifically, on a qubit and two-qubit systems, we test the state convergence of a monitored quantum system in the limit of a large number of quantum measurements, depending on the non-commutativity of the Hamiltonian and the measurement observable. When the Hamiltonian and observable do not commute, the convergence is uniform towards the infinite-temperature state. Conversely, whenever the two operators have one or more eigenvectors in common in their spectral decomposition, the state of the monitored system converges differently in the subspaces spanned by the measurement observable eigenstates. As a result, we show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis, with a finite effective temperature in each measurement subspace. Finally, we quantify the effects of the quantum hardware noise on the data by modelling them by means of depolarizing quantum channels.

quant-ph↗

arXiv2023

Continuously Monitored Quantum Systems beyond Lindblad Dynamics

The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.

quant-ph↗

arXiv2023

Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models

In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian, and is revealed via the Kirkwood-Dirac quasiprobability (KDQ) approach to two-times correlators. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work, in the form of negative and complex values that no classical theory can reveal. By applying these concepts on the one-dimensional transverse-field Ising model, we relate non-classical behaviours of the KDQ statistics of work in correspondence of the critical points of the model. Finally, we also prove the enhancement of the extracted work in non-classical regimes where the non-commutativity takes a role.

quant-ph↗

arXiv2022

Spreading of a local excitation in a Quantum Hierarchical Model

We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. We provide analytical predictions for its time evolution, solving the single-particle dynamics on a hierarchical network. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times. Furthermore, a universal scaling among space and time is found related to the algebraic decay of the interactions as $r^{-1-σ}$. We compare our predictions to numerics, employing tensor network techniques, for large magnetic fields, discussing the robustness of the mechanism in the full many-body dynamics.

quant-ph↗

arXiv2022

Clean two-dimensional Floquet time-crystal

We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. Employing careful scaling analysis, we show the feasibility of a two-dimensional discrete time-crystal (DTC) pre-thermal phase. Despite an unbounded energy pumped into the system, in the high-frequency limit, a well-defined effective Hamiltonian controls a finite-temperature intermediate regime, wherein local time averages are described by thermal averages. As a consequence, the long-lived stability of the DTC relies on the existence of a long-range ordeblack phase at finite temperature. Interestingly, even for large deviations from the perfect spin flip, we observe a non-perturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.

cond-mat.stat-mech↗

arXiv2022

Quantum thermodynamic methods to purify a qubit on a quantum processing unit

We report on a quantum thermodynamic method to purify a qubit on a quantum processing unit (QPU) equipped with (nearly) identical qubits. Our starting point is a three qubit design that emulates the well known two qubit swap engine. Similar to standard fridges, the method would allow to cool down a qubit at the expense of heating two other qubits. A minimal modification thereof leads to a more practical three qubit design that allows for enhanced refrigeration tasks, such as increasing the purity of one qubit at the expense of decreasing the purity of the other two. The method is based on the application of properly designed quantum circuits, and can therefore be run on any gate model quantum computer. We implement it on a publicly available superconducting qubit based QPU, and observe a purification capability down to 200 mK. We identify gate noise as the main obstacle towards practical application for quantum computing.

quant-ph↗

arXiv2022

Experimental violations of Leggett-Garg's inequalities on a quantum computer

Leggett-Garg's inequalities predict sharp bounds for some classical correlation functions that address the quantum or classical nature of real-time evolutions. We experimentally observe the violations of these bounds on single- and multi-qubit systems, in different settings, exploiting the IBM Quantum platform. In the multi-qubit case we introduce the Leggett-Garg-Bell's inequalities as an alternative to the previous ones. Measuring these correlation functions, we find quantum error mitigation to be essential to spot inequalities violations. Accessing only two qubit readouts, we assess Leggett-Garg-Bell's inequalities to emerge as the most efficient quantum coherence witnesses to be used for investigating quantum hardware, as the complexity of their calculation does not scale with the number of constituents of the system. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.

quant-ph↗

arXiv2021

Violent relaxation in the Hamiltonian mean field model: II. Non-equilibrium phase diagrams

A classical long-range-interacting $N$-particle system relaxes to thermal equilibrium on time scales growing with $N$; in the limit $N\to \infty$ such a relaxation time diverges. However, a completely non-collisional relaxation process, known as violent relaxation, takes place on a much shorter time scale independent of $N$ and brings the system towards a non-thermal quasi-stationary state. A finite system will eventually reach thermal equilibrium, while an infinite system will remain trapped in the quasi-stationary state forever. For times smaller than the relaxation time the distribution function of the system obeys the collisionless Boltzmann equation, also known as the Vlasov equation. The Vlasov dynamics is invariant under time reversal so that it does not "naturally" describe a relaxational dynamics. However, as time grows the dynamics affects smaller and smaller scales in phase space, so that observables not depending upon small-scale details appear as relaxed after a short time. Herewith we present an approximation scheme able to describe violent relaxation in a one-dimensional toy-model, the Hamiltonian Mean Field (HMF). The approach described here generalizes the one proposed in G. Giachetti and L. Casetti, J. Stat. Mech.: Theory Exp. 2019, 043201 (2019), that was limited to "cold" initial conditions, to generic initial conditions, allowing us to to predict non-equilibrium phase diagrams that turn out to be in good agreement with those obtained from the numerical integration of the Vlasov equation.

cond-mat.stat-mech↗

arXiv2021

Experimental verification of fluctuation relations with a quantum computer

Inspired by the idea that quantum computers can be useful in advancing basic science, we use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics, that were not (or were very little) corroborated so far. In order to do so, we first put forward a novel method to implement the so called two point measurement scheme, which is at the basis of the study of non-equilibrium energetic exchanges in quantum systems. Like the well-established interferometric method, our method uses an ancillary system, but at variance with it, it provides direct access to the energy exchange statistics, rather than its Fourier transform, thus being extremely more effective. We first experimentally validate our ancilla-assisted two point measurement scheme, and then apply it to i) experimentally verify that fluctuation theorems are robust against projective measurements, a theoretical prediction which was not validated so far, ii) experimentally verify the so called heat engine fluctuation relation, by implementing a SWAP quantum heat engine. iii) experimentally verify that the heat engine fluctuation relation continues to hold in presence of intermediate measurements, by implementing the design at the basis of the so called quantum-measurement-cooling concept. For both engines, we report the measured average heat and work exchanged and single out their operation mode. Our experiments constitute the experimental basis for the understanding of the non-equilibrium energetics of quantum computation and for the implementation of energy management devices on quantum processors.

quant-ph↗

arXiv2020

Coarse-grained collisionless dynamics with long-range interactions

We present an effective evolution equation for a coarse-grained distribution function of a long-range-interacting system preserving the symplectic structure of the non-collisional Boltzmann, or Vlasov, equation. We first derive a general form of such an equation based on symmetry considerations only. Then, we explicitly derive the equation for one-dimensional systems, finding that it has the form predicted on general grounds. Finally, we use such an equation to predict the dependence of the damping times on the coarse-graining scale and numerically check it for some one-dimensional models, including the Hamiltonian Mean Field (HMF) model, a scalar field with quartic interaction, a 1-d self-gravitating system, and the Self-Gravitating Ring (SGR).

cond-mat.stat-mech↗

arXiv2018

Learning universality and scaling from simple deposition models

We use deposition models of kinetic roughening of a growing surface to introduce the concepts of universality and scaling and to analyze the qualitative and quantitative role of different parameters. In particular, we focus on two classes of models where the deposition is accompanied by a local relaxation process within a distance $δ$. The models are in the Edwards-Wilkinson universality class, but the role of $δ$ is nontrivial.

cond-mat.stat-mech↗