arXiv subjects

Fernando de Melo

Publications and source records attributed to Fernando de Melo.

At least 19 recordsLinked to original sources

arXiv2026

Boltzmann counting in Hilbert space

We introduce a geometric entropy for quantum preparations, defined as the logarithm of the Hilbert-space volume of pure states compatible with a given set of constraints. This construction extends Boltzmann's counting perspective to the quantum setting, where compatible states need not be orthogonal and the relevant notion of "number of states" is naturally replaced by a volume in state space. We analyze three classes of constraints: restriction to a subspace, fixed expectation values, and coarse-grained subsystem descriptions. For representative examples, including subspace projection, spin expectation values, partial trace, and an imperfect detector map, we obtain explicit scaling laws and closed-form expressions for the associated volumes. The resulting framework provides a geometric measure of quantum ignorance at the level of the preparation and complements entropy notions based on density matrices and coarse graining.

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arXiv2026

When Isolated Quantum Systems Appear Classical

The emergence of classical behavior and the origin of thermal equilibrium are two central problems in the foundations of physics. In the standard accounts, both phenomena are typically explained through interactions with an external environment: decoherence suppresses quantum interference, while coupling to a thermal bath drives relaxation toward equilibrium. Over the last decades, however, it has become clear that equilibration and thermalization can arise even in fully isolated quantum systems, in the operational sense that the expectation values of relevant observables remain close to equilibrium values for most of the time. Here, we ask whether the same intrinsic equilibration mechanism can also account for the emergence of classical behavior. Using rigorous bounds on equilibration in closed systems, we derive sufficient conditions under which a time-evolved pure state becomes, for most times, operationally indistinguishable from a classical mixture associated with a chosen physical property. We identify two complementary routes to such operational classicality: either the chosen property almost commutes with the system Hamiltonian or the observables used to probe the system lose access to the remaining coherence after equilibration. Our results show that classical behavior need not be confined to the energy basis and may emerge even when substantial coherence remains present in the equilibrium state. This establishes a direct connection between two foundational questions: the origin of thermalization in isolated quantum systems and the quantum-to-classical transition

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arXiv2026

Comparing Classical Simulation and Sample-Based Learning of Quantum Systems

We investigate the relationship between two distinct classical approaches to quantum systems: direct simulation from a classical description and sample-based learning from measurement data. While both tasks ultimately aim to reproduce Born-rule statistics, complexity-theoretic results suggest that simulability and learnability need not coincide in general. Here we study this relationship empirically using a fixed deep energy-based generative model trained on measurement samples from controlled families of quantum states. We independently tune two quantum resources associated with classical simulation cost: entanglement, through the bond dimension of random matrix product states, and non-stabilizerness, through the number of T gates in Clifford-dominated circuits. Learning difficulty is characterized using two probes of neural-network complexity: the largest Hessian eigenvalue at convergence and Random Subspace Optimization. For both quantum resources, increasing simulation hardness systematically correlates with sharper loss landscapes and degraded reconstruction performance under constrained capacity. Our results indicate that, within the regimes studied here, classical learnability tracks known simulation complexity measures, suggesting that neural-network training dynamics can provide an empirical probe of quantum computational hardness.

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arXiv2024

A finite-resources description of a measurement process and its implications for the "Wigner's Friend" scenario

Quantum mechanics started out as a theory to describe the smallest scales of energy in Nature. After a hundred years of development it is now routinely employed to describe, among others, quantum computers with thousands of qubits. This tremendous progress turns the debate of foundational questions into a technological imperative. In what follows we introduce a model of a quantum measurement process that consistently includes the impact of having access only to finite resources when describing a macroscopic system, like a measurement apparatus. Leveraging modern tools from equilibration of closed systems and typicality, we show how the measurement collapse can be seen as an effective description of a closed dynamics, of which we do not know all its details. Our model is then exploited to address the ``Wigner Friend Scenario'', and we observe that an agreement is reached when both Wigner and his friend acknowledge their finite resources perspective and describe the measurement process accordingly.

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arXiv2024

Canonical typicality under general quantum channels

With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the often natural correspondence between the particles that compose the system and the relevant degrees-of-freedom might not be observed. In the present work we employ quantum channels to define generalized subsystems, which should capture the pertinent degrees-of-freedom, and obtain their associated canonical state. Moreover, we show that generalized subsystems also display the phenomena of canonical typicality, i.e., the generalized subsystem description generated from almost any microscopic pure state of the whole system will behave similarly as the corresponding canonical state. In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem.

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arXiv2023

Majorization-based benchmark of the complexity of quantum processors

Here we investigate the use of the majorization-based indicator introduced in [R. O. Vallejos, F. de Melo, and G. G. Carlo, Phys. Rev. A 104, 012602 (2021)] as a way to benchmark the complexity within reach of quantum processors. By considering specific architectures and native gate sets of currently available technologies, we numerically simulate and characterize the operation of various quantum processors. We characterize their complexity for different native gate sets, qubit connectivity and increasing number of gates. We identify and assess quantum complexity by comparing the performance of each device against benchmark lines provided by randomized Clifford circuits and Haar-random pure states. In this way, we are able to specify, for each specific processor, the number of native quantum gates which are necessary, on average, for achieving those levels of complexity. Lastly, we study the performance of the majorization-based characterization in the presence of distinct types of noise. We find that the majorization-based benchmark holds as long as the circuits' output states have, on average, high purity ($\gtrsim 0.9$). In such cases, the indicator showed no significant differences from the noiseless case.

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arXiv2022

Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics

The characterization of physical systems relies on the observable properties which are measured, and how such measurements are performed. Here we analyze two ways of assigning a description to a quantum system assuming that we only have access to coarse-grained properties. More specifically, we compare the Maximum Entropy Principle method, with the Bayesian-inspired recently proposed Average Assignment Map method [P. S. Correia et al, Phys. Rev. A 103, 052210 (2021)]. Despite the fact that the assigned descriptions by both methods respect the measured constraints, and that they share the same conceptual foundations, the descriptions differ in scenarios that go beyond the traditional system-environment structure. The Average Assignment Map is thus shown to be a more sensible choice for the ever more prevalent scenario of complex quantum systems. We discuss the physics behind such a difference, and further exploit it in a quantum thermodynamics process.

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arXiv2022

Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics

We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.

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arXiv2021

Macro-to-micro quantum mapping and the emergence of nonlinearity

As a universal theory of physics, quantum mechanics must assign states to every level of description of a system -- from a full microscopic description, all the way up to an effective macroscopic characterization -- and also to describe the interconnections among them. Assuming that we only have a coarse-grained access to a physical system, here we show how to assign to it a microscopic description that abides by all macroscopic constraints. In order to do that, we employ general coarse-graining maps, allowing our approach to be used even when the split between system and environment is not obvious. As a by-product, we show how effective nonlinear dynamics can emerge from the linear quantum evolution, and we readily apply it to a state discrimination task.

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arXiv2021

The principle of majorization: application to random quantum circuits

We test the principle of majorization [J. I. Latorre and M. A. Martin-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates going to infinity) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated to asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and non-universal classes of random quantum circuits, and they also detect the complexity of some non-universal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as a indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators (OTOCs).

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arXiv2020

Entropic Uncertainty Relations and the Quantum-to-Classical transition

Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities, even if their associated observables do not commute. We also establish how the precision of measurements must increase in order to keep quantum properties, a desirable feature for large quantum computers.

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arXiv2020

Coarse Graining of Partitioned Cellular Automata

Partitioned cellular automata are known to be an useful tool to simulate linear and nonlinear problems in physics, specially because they allow for a straightforward way to define conserved quantities and reversible dynamics. Here we show how to construct a local coarse graining description of partitioned cellular automata. By making use of this tool we investigate the effective dynamics in this model of computation. All examples explored are in the scenario of lattice gases, so that the information lost after the coarse graining is related to the number of particles. It becomes apparent how difficult it is to remain with a deterministic dynamics after coarse graining. Several examples are shown where an effective stochastic dynamics is obtained after a deterministic dynamics is coarse grained. These results suggest why random processes are so common in nature.

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arXiv2019

Spin-entanglement wave in a coarse-grained optical lattice

In the present work we explore a suitable coarse graining channel as a tool to describe the effective entanglement spreading in a coarse-grained spin-chain with different degrees of resolution. Comparing it with the experimental realizations performed with ultracold atoms, our results suggest that even if we are not able to fully resolve the system, entanglement can still be detected for some coarse graining levels. Furthermore, we show that it is possible to have some information about the "microscopic" entanglement, even if we have access only to the system's coarse-grained description. We show that the amount of entanglement decays exponentially with the lack of system resolution. The lack of experimental resolution might thus lead to an effective classical description.

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arXiv2019

Multiparticle quantum walk with a gas-like interaction

We analyze the dynamics of multiparticle discrete-time quantum walk on the two-dimensional lattice, with an interaction inspired on a classical model for gas collision, called HPP model. In this classical model, the direction of motion changes only when the particles collide head-on, preserving momentum and energy. In our quantum model, the dynamics is driven by the usual quantum-walk evolution operator if the particles are on different nodes, and is driven by the HPP rules if the particles are in the same node, linearly extended for superpositions. Using this new form of evolution operator, we numerically analyze three physical quantities for the two-walker case: The probability distribution of the position of one walker, the standard deviation of the position of one walker, and the entanglement between the walkers as a function of the number of steps. The numerical analysis implies that the entanglement between the walkers as a function of the number of steps initially increases and quickly tends to a constant value, which depends on the initial condition. We compare the results obtained using the HPP interaction with the equivalent ones using the phase interaction, which is based on an evolution operator that inverts the sign of the coin operator if the walkers are in the same position.

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arXiv2018

Quantum Walks via Quantum Cellular Automata

Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with the same amount of resources (in terms of effective Hilbert space dimension), various models of quantum walks. All the algorithms developed within quantum walk models are thus directly inherited by the quantum cellular automata. The latter, however, has its structure based on local interactions between qubits, and as such it can be more suitable for present (and future) experimental implementations.

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arXiv2017

Emerging dynamics arising from coarse-grained quantum systems

The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would be highly impractical. To not get lost in unnecessary details, effective descriptions are mandatory. Here we analyze the dynamics that may emerge from a full quantum description when one does not have access to all the degrees of freedom of a system. More concretely, we describe the properties of the dynamics that arise from quantum mechanics if one has access only to a coarse-grained description of the system. We obtain that the effective maps are not necessarily of Kraus form, due to correlations between accessible and nonaccessible degrees of freedom, and that the distance between two effective states may increase under the action of the effective map. We expect our framework to be useful for addressing questions such as the thermalization of closed quantum systems, as well as the description of measurements in quantum mechanics.

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arXiv2017

Reliability of digitized quantum annealing and the decay of entanglement

We performed a banged-digital-analog simulation of a quantum annealing protocol in a two-qubit Nuclear Magnetic Resonance (NMR) quantum computer. Our experimental simulation employed up to 235 Trotter steps, with more than 2000 gates (pulses), and we obtained a protocol success above 80%. Given the exquisite control of the NMR quantum computer, we performed the simulation with different noise levels. We thus analyzed the reliability of the quantum annealing process, and related it to the level of entanglement produced during the protocol. Although the presence of entanglement is not a sufficient signature for a better-than-classical simulation, the level of entanglement achieved relates to the fidelity of the protocol.

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arXiv2014

Quantum Information Processing by Weaving Quantum Talbot Carpets

Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled operations between two quDits. A new form of universal quantum information processing can then be implemented with linear optics and ancilla photons. Though we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.

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