arXiv subjects

Adrian Ortega

Publications and source records attributed to Adrian Ortega.

14 recordsLinked to original sources

arXiv2024

Towards a benchmark for quantum computers based on an iterated post-selective protocol

Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.

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arXiv2024

Spectra and transport of probability and energy densities in a $\mathcal{PT}$-symmetric square well with a delta-function potential

We study the spectrum, eigenstates and transport properties of a simple $\mathcal{P}\mathcal{T}$-symmetric model consisting in a finite, complex, square well potential with a delta potential at the origin. We show that as the strength of the delta potential increases, the system exhibits exceptional points accompanied by an accumulation of density associated with the break in the $\mathcal{P}\mathcal{T}$-symmetry. We also obtain the density and energy density fluxes and analyze their transport properties. We find that in the $\mathcal{P}\mathcal{T}-$ symmetric phase transport is efficient, in the sense that all the density that flows into the system at the source, flows out at the sink, which is sufficient to derive a generalized unitary relation for the transmission and reflection coefficients.

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arXiv2023

On the energy density in quantum mechanics

There are several definitions of energy density in quantum mechanics. These yield expressions that differ locally, but all satisfy a continuity equation and integrate to the value of the expected energy of the system under consideration. Thus, the question of whether there are physical grounds to choose one definition over another arises naturally. In this work, we propose a way to probe a system by varying the size of a well containing a quantum particle. We show that the mean work done by moving the wall is closely related to one of the definitions for energy density. Specifically, the appropriate energy density, evaluated at the wall corresponds to the force exerted by the particle locally, against which the work is done. We show that this identification extends to two and three dimensional systems.

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arXiv2023

Testing quantum computers with the protocol of quantum state matching

The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy, intermediate-scale quantum (NISC) computers is therefore of high importance. Here, we suggest the application of the so-called quantum state matching protocol for testing purposes. This protocol was originally proposed to determine if an unknown quantum state falls in a prescribed neighborhood of a reference state. We decompose the unitary specific to the protocol and construct the quantum circuit implementing one step of the dynamics for different characteristic parameters of the scheme and present test results for two different IBM quantum computers. By comparing the experimentally obtained relative frequencies of success to the ideal success probability with a maximum statistical tolerance, we discriminate statistical errors from device specific ones. For the characterization of noise, we also use the fact that while the output of the ideal protocol is insensitive to the internal phase of the input state, the actual implementation may lead to deviations. For systematically varied inputs we find that the device with the smaller quantum volume performs better on our tests than the one with larger quantum volume, while for random inputs they show a more similar performance.

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arXiv2023

Orders of chaoticity of unitaries

We introduce the concept of K-th order chaoticity of unitaries, and analyze it for the case of two-level quantum systems. This property is relevant in a certain quantum random number generation scheme. We show that no unitaries exist with an arbitrary order of chaoticity.

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arXiv2021

Spectra, eigenstates and transport properties of a $\mathcal{PT}$-symmetric ring

We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric tight-binding ring with an onsite energy $a$ at the gain and loss sites. We show that if $a\neq 0$, the system generically exhibits an unbroken $\mathcal{PT}$-symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points, there are "diabolical points", and inverse exceptional points at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary "backflow" of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.

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arXiv2021

$\mathcal{PT}$-symmetry in compact phase space for a linear Hamiltonian

We study the time evolution of a PT-symmetric, non-Hermitian quantum system for which the associated phase space is compact. We focus on the simplest non-trivial example of such a Hamiltonian, which is linear in the angular momentum operators. In order to describe the evolution of the system, we use a particular disentangling decomposition of the evolution operator, which remains numerically accurate even in the vicinity of the Exceptional Point. We then analyze how the non-Hermitian part of the Hamiltonian affects the time evolution of two archetypical quantum states, coherent and Dicke states. For that purpose we calculate the Husimi distribution or Q function and study its evolution in phase space. For coherent states, the characteristics of the evolution equation of the Husimi function agree with the trajectories of the corresponding angular momentum expectation values. This allows to consider these curves as the trajectories of a classical system. For other types of quantum states, e.g. Dicke states, the equivalence of characteristics and trajectories of expectation values is lost.

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arXiv2021

Quantum transport in a combined kicked rotor and quantum walk system

We present a theoretical and numerical study of the competition between two opposite interference effects, namely interference-induced ballistic transport on one hand, and strong (Anderson) localization on the other. While the former effect allows for resistance free transport, the latter brings the transport to a complete halt. As a model system, we consider the quantum kicked rotor, where strong localization is observed in the discrete momentum coordinate. In this model, we introduce the ballistic transport in the form of a Hadamard quantum walk in that momentum coordinate. The two transport mechanisms are combined by alternating the corresponding Floquet operators. Extending the corresponding calculation for the kicked rotor, we estimate the classical diffusion coefficient for thecombined dynamics. Another argument, based on the introduction of an effective Heisenberg time should then allow to estimate the localization time and the localization length. While this is known to work reasonably well in the kicked rotor case, we find that it fails in our case. While the combined dynamics still shows localization, it takes place at much larger times and shows much larger localization lengths than predicted. Finally, we combine the kicked rotor with other types of quantum walks, namely diffusive and localizing quantum walks. In the diffusive case, the localizing dynamics of the kicked rotor is completely canceled and we get pure diffusion. In the case of the localizing quantum walk, the combined system remains localized, but with a larger localization length.

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arXiv2020

Spectral and transport properties of a $\mathcal{PT}$-symmetric tight-binding chain with gain and loss

We derive a continuity equation to study transport properties in a $\mathcal{PT}$-symmetric tight-binding chain with gain and loss in symmetric configurations. This allows us to identify the density fluxes in the system, and to define a transport coefficient to characterize the efficiency of transport of each state. These quantities are studied explicitly using analytical expressions for the eigenvalues and eigenvectors of the system. We find that in states with broken $\mathcal{PT}$-symmetry, transport is inefficient, in the sense that either inflow exceeds outflow and density accumulates within the system, or outflow exceeds inflow, and the system becomes depleted. We also report the appearance of two subsets of interesting eigenstates whose eigenvalues are independent on the strength of the coupling to gain and loss. We call these opaque and transparent states. Opaque states are decoupled from the contacts and there is no transport; transparent states exhibit always efficient transport. Interestingly, the appearance of such eigenstates is connected with the divisors of the length of the system plus one and the position of the contacts. Thus the number of opaque and transparent states varies very irregularly.

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arXiv2019

Two-particle quantum correlations in stochastically-coupled networks

Quantum walks in dynamically-disordered networks have become an invaluable tool for understanding the physics of open quantum systems. In this work, we introduce a novel approach to describe the dynamics of indistinguishable particles in noisy quantum networks. By making use of stochastic calculus, we derive a master equation for the propagation of two non-interacting correlated particles in tight-binding networks affected by off-diagonal dynamical disorder. We show that the presence of noise in the couplings of a quantum network creates a pure-dephasing-like process that destroys all coherences in the single-particle Hilbert subspace. Remarkably, we find that when two or more correlated particles propagate in the network, coherences accounting for particle indistinguishability are robust against the impact of noise, thus showing that it is possible, in principle, to find specific conditions for which many indistinguishable particles can traverse dynamically-disordered systems without losing their ability to interfere. These results shed light on the role of particle indistinguishability in the preservation of quantum coherence in dynamically-disordered quantum networks.

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arXiv2018

Robustness of optimal transport in disordered interacting many-body networks

The robustness of quantum transport under various perturbations is analyzed in disordered interacting many-body systems, which are constructed from the embedded Gaussian random matrix ensembles (EGEs). The transport efficiency can be enhanced drastically, if centrosymmetry (csEGE) is imposed. When the csEGE is perturbed with an ordinary EGE, the transport efficiency in the optimal cases is reduced significantly, while in the suboptimal cases the changes are less pronounced. Qualitatively the same behavior is observed, when parity and centrosymmetry are broken by block perturbations. Analyzing the influence of the environment coupling, optimal transport is observed at a certain coupling strength, while too weak and too strong coupling reduce the transport. Taking into account the effects of decoherence, in the EGE the transport efficiency approaches its maximum at a finite nonzero decoherence strength (environment-assisted transport). In the csEGE the efficiency decays monotonically with the decoherence but is always larger than in the EGE.

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arXiv2016

Efficient quantum transport in disordered interacting many-body networks

The coherent transport of $n$ fermions in disordered networks of $l$ single-particle states connected by $k$-body interactions is studied. These networks are modeled by embedded Gaussian random matrix ensemble (EGE). The conductance bandwidth as well as the ensemble-averaged total current attain their maximal values if the system is highly filled $n \sim l-1$ and $k\sim n/2$. For the cases $k=1$ and $k=n$ the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever centrosymmetric ensemble (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and thus, causes backscattering-free transmission resonances which enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak for $n=l-1$, close to the highest observed currents.

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arXiv2015

Quantum efficiencies in finite disordered networks connected by many-body interactions

The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the $k$-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or absence of time-reversal symmetry and centrosymmetry/centrohermiticity are addressed. For bosons and fermions, the best efficiencies of the realizations of the ensemble are dramatically enhanced when centrosymmetry (centrohermiticity) is imposed. For few bosons distributed in two single-particle levels this permits perfect state transfer for almost all realizations when one-particle interactions are considered. For fermionic systems the enhancement is found to be maximal for cases when all but one single particle levels are occupied.

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arXiv2012

Mode resolved travel time statistics for elastic rays in three-dimensional billiards

We consider the ray limit of propagating ultrasound waves in three-dimensional bodies made from an homogeneous, isotropic, elastic material. Using a Monte Carlo approach, we simulate the propagation and proliferation of elastic rays using realistic angle dependent reflection coefficients, taking into account mode conversion and ray-splitting. For a few simple geometries, we analyse the long time equilibrium distribution focussing on the energy ratio between compressional and shear waves. Finally, we study the travel time statistics, i.e. the distribution of the amount of time a given trajectory spends as a compressional wave, as compared to the total travel time. These results are intimately related to recent elastodynamics experiments on Coda wave interferometry by Lobkis and Weaver [Phys. Rev. E 78, 066212 (2008)].

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