arXiv subjects

Paolo Muratore-Ginanneschi

Publications and source records attributed to Paolo Muratore-Ginanneschi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantum Trajectory Approach to Error Mitigation

Quantum Error Mitigation (EM) is a collection of strategies to reduce errors on noisy intermediate scale quantum (NISQ) devices on which proper quantum error correction is not feasible. One of such strategies aimed at mitigating noise effects of a known environment is to realise the inverse map of the noise using a set of completely positive maps weighted by a quasi-probability distribution, i.e. a probability distribution with positive and negative values. This quasi-probability distribution is realised using classical post-processing after final measurements of the desired observables have been made. Here we make a connection with quasi-probability EM and recent results from quantum trajectory theory for open quantum systems. We show that the inverse of noise maps can be realised by performing classical post-processing on the quantum trajectories generated by an additional reservoir with a quasi-probability measure called the influence martingale. We demonstrate our result on a model relevant for current NISQ devices. Finally, we show the quantum trajectories required for error correction can themselves be simulated by coupling an ancillary qubit to the system. In this way, we can avoid the introduction of the engineered reservoir.

quant-ph↗

arXiv2022

Unraveling-paired dynamical maps can recover the input of quantum channels

We explore algebraic and dynamical consequences of unraveling general time-local master equations. We show that the "influence martingale", the paramount ingredient of a recently discovered unraveling framework, pairs any time-local master equation with a one parameter family of Lindblad-Gorini-Kossakowski-Sudarshan master equations. At any instant of time, the variance of the influence martingale provides an upper bound on the Hilbert-Schmidt distance between solutions of paired master equations. Finding the lowest upper bound on the variance of the influence martingale yields an explicit criterion of "optimal pairing". The criterion independently retrieves the measure of isotropic noise necessary for the structural physical approximation of the flow the time-local master equation with a completely positive flow. The optimal pairing also allows us to invoke a general result on linear maps on operators (the "commutant representation") to embed the flow of a general master equation in the off-diagonal corner of a completely positive map which in turn solves a time-local master equation that we explicitly determine. We use the embedding to reverse a completely positive evolution, a quantum channel, to its initial condition thereby providing a protocol to preserve quantum memory against decoherence. We thus arrive at a model of continuous time error correction by a quantum channel.

quant-ph↗

arXiv2022

Interference of Quantum Trajectories

We extend quantum trajectory theory to encompass the evolution of a large class of open quantum systems interacting with an environment at {arbitrary coupling strength}. Specifically, we prove that general time-local quantum master equations admit an unraveling described by ordinary jump-stochastic differential equations. The sufficient condition is to weigh the state vector Monte Carlo averages by a probability pseudo-measure which we call the "influence martingale". The influence martingale satisfies a $ 1d $ stochastic differential equation enslaved to the ones governing the quantum trajectories. Our interpretation is that the influence martingale models interference effects between distinct realizations of quantum trajectories at strong system-environment coupling. Our result proves the existence of a Markovian quantum trajectory picture in the Hilbert space of the system for completely bounded divisible dynamical maps. Furthermore, our result provides a new avenue to numerically integrate systems with large numbers of degrees of freedom by naturally extending the existing theory.

quant-ph↗

arXiv2021

E. Schrödinger's 1931 paper "On the Reversal of the Laws of Nature" ["Über die Umkehrung der Naturgesetze",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]

We present an English translation of Erwin Schrödinger's paper on "On the Reversal of the Laws of Nature". In this paper Schrödinger analyses the idea of time reversal of a diffusion process. Schrödinger's paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schrödinger also inspired the development of probabilistic interpretations of quantum mechanics by Fényes, Nelson and others as well as the notion of "Euclidean Quantum Mechanics" as probabilistic analogue of quantization. In the second part of the paper Schrödinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schrödinger's intuitions for contemporary developments in statistical nano-physics.

physics.hist-ph↗

arXiv2020

An exactly solvable model of calorimetric measurements

Calorimetric measurements are experimentally realizable methods to assess thermodynamics relations in quantum devices. With this motivation in mind, we consider a resonant level coupled to a Fermion reservoir. We consider a transient process, in which the interaction between the level and the reservoir is initially switched on and then switched off again. We find the time dependence of the energy of the reservoir, of the energy of the level and of the interaction energy between them at weak, intermediate, strong and ultra-strong coupling. We also determine the statistical distributions of these energies.

cond-mat.stat-mech↗

arXiv2020

R. Fürth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", \textit{Zeitschrift für Physik,} \textbf{81} 143-162]

We present a translation of the 1933 paper by R. Fürth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. This paper opened in some sense the way to the stochastic methods of quantization developed almost 30 years later by Edward Nelson and others.

physics.hist-ph↗

arXiv2018

Hybrid master equation for calorimetric measurements

Ongoing experimental activity aims at calorimetric measurements of thermodynamic indicators of quantum integrated systems. We study a model of a driven qubit in contact with a finite-size thermal electron reservoir. The temperature of the reservoir changes due to energy exchanges with the qubit and an infinite-size phonon bath. Under the assumption of weak coupling and weak driving, we model the evolution of the qubit-electron-temperature as a hybrid master equation for the density matrix of the qubit at different temperatures of the calorimeter. We compare the temperature evolution with an earlier treatment of the qubit-electron model, where the dynamics were modelled by a Floquet master equation under the assumption of drive intensity much larger than the qubit-electron coupling squared. We numerically and analytically inquire the predictions of the two mathematical models of dynamics in the weak-drive parametric region. We numerically determine the parametric regions where the two models of dynamics give distinct temperature predictions and those where their predictions match.

quant-ph↗

arXiv2018

A model for calorimetric measurements in an open quantum system

We investigate the experimental setup proposed in [New J. Phys., 15, 115006 (2013)] for calorimetric measurements of thermodynamic indicators in an open quantum system. As theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker--Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.

quant-ph↗

arXiv2017

Eddy diffusivity of quasi-neutrally-buoyant inertial particles

We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid which is also constant. Our approach differs from the usual over-damped expansion inasmuch we do not assume a separation of time scales between thermalization and small-scale convection effects. For general incompressible flows, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach enables to shed light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.

physics.flu-dyn↗

arXiv2017

An application of Pontryagin's principle to Brownian particle engineered equilibration

We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the equations governing the optimal control steering \emph{in finite time} the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well known models of optimal mass transport by a compressible velocity field.

cond-mat.mes-hall↗

arXiv2016

Eddy diffusivities of inertial particles in random Gaussian flows

We investigate the large-scale transport of inertial particles. We derive explicit analytic expressions for the eddy diffusivities for generic Stokes times. These latter expressions are exact for any shear flow while they correspond to the leading contribution either in the deviation from the shear flow geometry or in the Péclet number of general random Gaussian velocity fields. Our explicit expressions allow us to investigate the role of inertia for such a class of flows and to make exact links with the analogous transport problem for tracer particles.

physics.flu-dyn↗

arXiv2016

Fluctuation Relation for Qubit-Calorimetry

Motivated by proposed thermometry measurement on an open quantum system, we present a simple model of an externally driven qubit interacting with a finite sized, fermion environment acting as calorimeter. The derived dynamics is governed by a stochastic Schrödinger equation coupled to the temperature change of the calorimeter. We prove a fluctuation relation and deduce from it a notion of entropy production. Finally, we discuss the first and second law associated to the dynamics.

quant-ph↗

arXiv2016

Energy fluctuations of finite free-electron Fermi gas

We discuss the energy distribution of free-electron Fermi-gas, a problem with a textbook solution of Gaussian energy fluctuations in the limit of a large system. We find that for a small system, characterized solely by its heat capacity $C$, the distribution can be solved analytically, and it is both skewed and it vanishes at low energies, exhibiting a sharp drop to zero at the energy corresponding to the filled Fermi sea. The results are relevant from the experimental point of view, since the predicted non-Gaussian effects become pronounced when $C/k_B \lesssim 10^3$ ($k_B$ is the Boltzmann constant), a regime that can be easily achieved for instance in mesoscopic metallic conductors at sub-kelvin temperatures.

cond-mat.mes-hall↗

arXiv2015

On the efficiency of heat engines at the micro-scale and below

We investigate the thermodynamic efficiency of sub-micro-scale heat engines operating under the conditions described by over-damped stochastic thermodynamics. We prove that at maximum power the efficiency obeys for constant isotropic mobility the universal law $η=2\,η_{C}/(4-η_{C})$ where $η_{C}$ is the efficiency of an ideal Carnot cycle. The corresponding power optimizing protocol is specified by the solution of an optimal mass transport problem. Such solution can be determined explicitly using well known Monge--Ampère--Kantorovich reconstruction algorithms. Furthermore, we show that the same law describes the efficiency of heat engines operating at maximum work over short time periods. Finally, we illustrate the straightforward extension of these results to cases when the mobility is anisotropic and temperature dependent.

cond-mat.stat-mech↗

arXiv2014

On how nanomechanical systems can minimize dissipation

Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. In this letter we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such cost becomes negligible, the optimal control strategy can be constructed by transparent geometrical methods and recovers the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well-known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised

cond-mat.stat-mech↗

arXiv2014

On extremals of the entropy production by "Langevin-Kramers" dynamics

We refer as "Langevin-Kramers" dynamics to a class of stochastic differential systems exhibiting a degenerate "metriplectic" structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated to random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in an heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin-Kramers models differs from the now well-understood case of Langevin-Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge-Ampère-Kantorovich optimal mass transport equations.

cond-mat.stat-mech↗

arXiv2012

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.

cond-mat.stat-mech↗

arXiv2012

On the use of stochastic differential geometry for non-equilibrium thermodynamics modeling and control

We discuss the relevance of geometric concepts in the theory of stochastic differential equations for applications to the theory of non-equilibrium thermodynamics of small systems. In particular, we show how the Eells-Elworthy-Malliavin covariant construction of the Wiener process on a Riemann manifold provides a physically transparent formulation of optimal control problems of finite-time thermodynamic transitions. Based on this formulation, we turn to an evaluative discussion of recent results on optimal thermodynamic control and their interpretation.

cond-mat.stat-mech↗