arXiv subjects

Reginaldo de Jesus Napolitano

Publications and source records attributed to Reginaldo de Jesus Napolitano.

16 recordsLinked to original sources

arXiv2026

Minimal-Energy Optimal Control of Tunable Two-Qubit Gates in Superconducting Platforms Using Continuous Dynamical Decoupling

We present a unified scheme for generating high-fidelity entangling gates in superconducting platforms by continuous dynamical decoupling (CDD) combined with variational minimal-energy optimal control. During the CDD stage, we suppress residual couplings, calibration drifting, and quasistatic noise, resulting in a stable effective Hamiltonian that preserves the designed ZZ interaction intended for producing tunable couplers. In this stable $\mathrm{SU}(4)$ manifold, we calculate smooth low-energy single-quibt control functions using a variational geodesic optimization process that directly minimizes gate infidelity. We illustrate the methodology by applying it to CZ, CX, and generic engangling gates, achieving virtually unit fidelity and robustness under restricted single-qubit action, with experimentally realistic control fields. These results establish CDD-enhanced variational geometric optimal control as a practical and noise-resilient scheme for designing superconducting entangling gates.

quant-ph↗

arXiv2025

Monte Carlo approach for finding optimally controlled quantum gates with differential geometry

A unitary evolution in time may be treated as a curve in the manifold of the special unitary group. The length of such a curve can be related to the energetic cost of the associated computation, meaning a geodesic curve identifies an energetically optimal path. In this work, we employ sub-Riemannian geometry on the manifold of the unitary group to obtain optimally designed Hamiltonians for generating single-qubit gates in an environment with the presence of dephasing noise as well as a two-qubit gate under a time-constant crosstalk interaction. The resulting geodesic equation involves knowing the initial conditions of the parameters that cannot be obtained analytically. We then introduce a random sampling method combined with a minimization function and a cost function to find initial conditions that lead to optimal control fields. We also compare the optimized control fields obtained from the solutions of the geodesic equation with those extracted from the well-known Krotov method. Both approaches provide high fidelity values for the desired quantum gate implementation, but the geodesic method has the advantage of minimizing the required energy to execute the same task. These findings bring new insights for the design of more efficient fields in the arsenal of optimal control theory.

quant-ph↗

arXiv2024

Optimized continuous dynamical decoupling via differential geometry and machine learning

We introduce a strategy to develop optimally designed fields for continuous dynamical decoupling. Using our methodology, we obtain the optimal continuous field configuration to maximize the fidelity of a general one-qubit quantum gate. To achieve this, considering dephasing-noise perturbations, we employ an auxiliary qubit instead of the boson bath to implement a purification scheme, which results in unitary dynamics. Employing the sub-Riemannian geometry framework for the two-qubit unitary group, we derive and numerically solve the geodesic equations, obtaining the optimal time-dependent control Hamiltonian. Also, due to the extended time required to find solutions to the geodesic equations, we train a neural network on a subset of geodesic solutions, enabling us to promptly generate the time-dependent control Hamiltonian for any desired gate, which is crucial in circuit optimization.

quant-ph↗

arXiv2024

Rydberg atom-based microwave electrometry using polarization spectroscopy

In this study, we investigated Rydberg atom-based microwave electrometry using polarization spectroscopy in a room-temperature vapor cell. By measuring Autler-Townes splitting in the electromagnetically induced transparency (EIT) spectrum, we determined that the minimum measurable microwave electric field is approximately five times lower than conventional EIT techniques. The results are well reproduced by a full optical Bloch equation model, which takes into account all the hyperfine levels involved. Subsequently, the EIT setup was used to characterize a custom microwave cylindrical lens, which increases the field at the focus by a factor of three, decreasing the minimum measurable microwave electric field by the same amount. Our results indicate that the combination of polarization spectroscopy and a microwave lens may enhance microwave electrometry.

physics.atom-ph↗

arXiv2024

Time-dependent Rabi frequencies to protect quantum operations on an atomic qutrit by continuous dynamical decoupling

We investigate the form required for the time-dependent Rabi frequencies involved in a procedure capable to protect the action of quantum gates on an atomic qutrit by means of external fields continuously decoupling the system from the environmental noise. Several simulations are considered to protect the action of quantum-gate models, including randomly chosen ones. We argue that the requirements for the Rabi frequencies could be nowadays experimentally met. We also investigate the transition from one gate operation to another, including protecting a qutrit memory state. We finally apply our methodology to protect from noise the application of an algorithm capable of distinguishing the parity of permutations of three elements.

quant-ph↗

arXiv2021

Protecting qudit operations from noise by continuous dynamical decoupling

We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of $d$-level systems (qudits), allowing one to protect the action of an arbitrary multi-qudit gate from general noise. We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit. This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of $^{87}\mathrm{Rb}$ and laser beams whose intensities and phases are modulated according to our prescription. We show that this model allows one to generate continuously all the possible SU(3) group operations which are, in general, needed to apply the GCDD procedure. We finally show that our method can be extended to the case of an ensemble of qudits, identical or not.

quant-ph↗

arXiv2021

Visualizing Kraus operators for dephasing noise during application of the $\sqrt{\mathrm{\mathrm{SWAP}}}$ quantum gate

We consider the case of a $\sqrt{\mathrm{SWAP}}$ quantum gate and its optimized entangling action, via continuous dynamical decoupling, in the presence of dephasing noise. We illustrate the procedure in the specific case where only the two-qubit operation is controlled and no single-qubit operations are included in the description. To compare the optimized dynamics in the presence of noise with the ideal case, we use the standard fidelity measure. Then we discuss the importance of using optimized gates in the quantum operational-probabilistic theory. Because of their importance for the explicit construction of the completely positive maps representing the operations, we derive optimized Kraus operators in this specific case, focusing on the entanglement operation. We then show how to visualize the time evolution of each Kraus operator as a curve in a three-dimensional Euclidean space. Finally, we connect this formalism with the operational framework of quantum mechanics by describing a possible set of measurements that could be performed to obtain the Kraus operators.

quant-ph↗

arXiv2020

Phase-retrieval from Bohm's equations

We present an analytic method, based on the Bohmian equations for quantum mechanics, for approaching the phase-retrieval problem in the following formulation: By knowing the probability density $\left\vert ψ\left(\overrightarrow{r},t\right)\right\vert ^{2}$ and the energy potential $V\left(\overrightarrow{r},t\right)$ of a system, how can one determine the complex state $ψ\left(\overrightarrow{r},t\right)$? We illustrate our method with three classic examples involving Gaussian states, suggesting applications to quantum state and Hamiltonian engineering.

quant-ph↗

arXiv2018

Weak values in collision theory

Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin, yielding surprising results after post-selection. That description often ignores the kinetic energy of the particle and its movement in three dimensions. Here, we include these elements and re-obtain the weak values within the context of collision theory by two different approaches, and prove that the results are compatible with each other and with the results from the traditional approach. To provide a more complete description of the Stern-Gerlach apparatus, we use weak vectors, a generalization of the weak values.

quant-ph↗

arXiv2016

Elliptical orbits in the phase-space quantization

The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses.

quant-ph↗

arXiv2016

Error correction in short time steps during the application of quantum gates

We propose a method for applying the quantum error-correction method for errors that occur during quantum gates. Using a perturbation treatment of the noise that allows us to separate it from the ideal evolution of the quantum gate, we demonstrate that in certain cases it is necessary to divide the quantum gate in short time steps intercalated by correction procedures. A prescription of how these gates can be constructed is provided, as well as a proof that, even for the cases when the division of the quantum gate in short time steps is not necessary, this method may be advantageous for reducing the total duration of the computation.

quant-ph↗

arXiv2014

Efficient finite-time measurements under thermal regimes

Contrary to conventional quantum mechanics, which treats measurement as instantaneous, here we explore a model for finite-time measurement. The main two-level system interacts with the measurement apparatus in a Markovian way described by the Lindblad equation, and with an environment, which does not include the measuring apparatus. To analyse the environmental effects on the final density operator, we use the Redfield approach, allowing us to consider a non-Markovian noise. In the present hybrid theory, to trace out the environmental degrees of freedom, we use a previously-developed analytic method based on superoperator algebra and Nakajima-Zwanzig superoperators. Here, we analyse two types of system-environment interaction, phase and amplitude damping, which allows us to conclude that, in general, a finite-time quantum measurement performed during a certain period is more efficient than an instantaneous measurement performed at the end of it, because the rate of change of the populations is attenuated by the system-measurement apparatus interaction.

quant-ph↗

arXiv2013

How much time does a measurement take?

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.

quant-ph↗

arXiv2012

A simple derivation of the Lindblad equation

We present a derivation of the Lindblad equation - an important tool for the treatment of non-unitary evolutions - that is accessible to undergraduate students in physics or mathematics with a basic background on quantum mechanics. We consider a specific case, corresponding to a very simple situation, where a primary system interacts with a bath of harmonic oscillators at zero temperature, with an interaction Hamiltonian that resembles the Jaynes-Cummings format. We start with the Born-Markov equation and, tracing out the bath degrees of freedom, we obtain an equation in the Lindblad form. The specific situation is very instructive, for it makes it easy to realize that the Lindblads represent the effect on the main system caused by the interaction with the bath, and that the Markov approximation is a fundamental condition for the emergence of the Lindbladian operator. The formal derivation of the Lindblad equation for a more general case requires the use of quantum dynamical semi-groups and broader considerations regarding the environment and temperature than we have considered in the particular case treated here.

quant-ph↗

arXiv2011

The master equation for the reduced open-system dynamics, including a Lindbladian description of finite-duration measurement

We consider the problem of the measurement of a system occurring during a finite time interval, while environmentally-induced noise decreases the system-state coherence. We assume a Markovian measuring device and, therefore, use a Lindbladian description for the measurement dynamics. For studying the case of noise produced by a non-Markovian environment, whose definition does not include the measuring apparatus, we use the Redfield approach to the interaction between system and environment. In the present hybrid theory, to trace out the environmental degrees of freedom, we introduce an analytic method based on superoperator algebra and Nakajima-Zwanzig projectors. The resulting master equation, describing the reduced system dynamics, is illustrated in the case of a qubit under phase noise during a finite-time measurement.

quant-ph↗

arXiv2011

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

quant-ph↗