arXiv subjects

Herschel A. Rabitz

Publications and source records attributed to Herschel A. Rabitz.

At least 19 recordsLinked to original sources

arXiv2025

Stability and quasi-Periodicity of Many-Body Localized Dynamics

The connection between entanglement dynamics and non-equilibrium statistics in isolated many-body quantum systems has been established both theoretically and experimentally. Many-Body Localization (MBL), a phenomenon where interacting particles in disordered (i.e., random) chains fail to thermalize, exemplifies this connection. However, the systematic proof of critical phenomena such as MBL remains challenging due to the lack of robust methods for analyzing many-body entanglement dynamics. In this paper, we identify MBL through quasi-periodic dynamics in the entanglement evolution of subsystems in a disordered Heisenberg chain. This new form of characterizing MBL, through stable quasi-periodic dynamics of entanglement -- where stable means they persist in the thermodynamic limit -- concretely distinguishes between two competing scenarios: fully localized behavior of subsystems or slowly, exponentially slow in disorder, thermalizing subsystems -- a heated controversy in the literature. Utilizing perturbation theory, we derive the entanglement dynamics of single spins through an infinite perturbative series, while also modeling rare Griffiths regions (locally thermal inclusions). Our results prove that in regimes of sufficiently strong disorder, the entanglement evolution of individual subsystems remains quasi-periodic in the thermodynamic limit, thereby providing concrete evidence for the stability of MBL dynamics in disordered Heisenberg chains. This behavior contrasts with the widely reported logarithmic growth of subsystem entanglement in the MBL phase. We show that the logarithmic growth observed in prior studies arises from statistical ensemble averaging, which is prohibited due to the intrinsic non-ergodic dynamics characteristic of MBL systems, rooted in their quasi-periodic features.

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arXiv2025

Emergence of Light Cones in Long-range Interacting Spin Chains Is Due to Destructive Interference

Despite extensive research on long-range interacting quantum systems, the physical mechanism responsible for the emergence of light cones remains unidentified. This work presents a novel perspective on the origins of locality and emergent light cones in quantum systems with long-range interactions. We identify a mechanism in such spin chains where effective entanglement light cones emerge due to destructive interference among quantum effects that entangle spins. Although long-range entangling effects reach beyond the identified light cone, due to destructive interference, entanglement remains exponentially suppressed in that region, ultimately leading to the formation of the light cone. We demonstrate that this interference not only drives but is also necessary for the emergence of light cones. Furthermore, our analysis reveals that reducing the interaction range weakens this interference, surprisingly increasing the speed of entanglement transport, an effect that opens new experimental opportunities for investigation.

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arXiv2024

Measuring Entanglement by Exploiting its Anti-symmetric Nature

Despite significant progress in experimental quantum sciences, measuring entanglement entropy remains challenging. Through a geometric perspective, we reveal the intrinsic anti-symmetric nature of entanglement. We prove that most entanglement measures, such as von Neumann and Renyi entropies, can be expressed in terms of exterior products, which are fundamentally anti-symmetric. Leveraging this, we propose utilizing the anti-symmetric nature of fermions to measure entanglement entropy efficiently, offering a resource-efficient approach to probing bipartite entanglement.

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arXiv2024

Decoherence-Free Subspaces Cannot Prevent the Collapse of Wave Functions

Efficacious quantum information processing relies on extended coherence and precise control. Investigating the limitations surrounding quantum processors is vital for their advancement. In their operation, one challenge is inadvertent wave function collapse. Decoherence-free subspaces, theoretically capable of mitigating specific non unitary dynamics, present a promising avenue. However, our study unveils their inability to safeguard against spontaneous wave function collapse. Thus, the spontaneous-collapse rate becomes a critical limiting factor for quantum systems' physical coherence, restricting the options for maintaining coherence to active error correction.

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arXiv2023

Quantum tracking control of the orientation of symmetric top molecules

The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables. In this article, we generalize the ideas in Phys. Rev. A 98, 043429 (2018) to the task of orienting symmetric top molecules in 3D. To this end, we derive equations for the control fields capable of directly tracking the expected value of the 3D dipole orientation vector along a desired path in time. We show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric top tracking control problems.

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arXiv2022

Sequential optical response suppression for chemical mixture characterization

The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce an approach based on quantum tracking control that allows for determining the relative concentrations of constituents in a quantum mixture, using a single pulse which enhances the distinguishability of components of the mixture and has a length that scales linearly with the number of mixture constituents. To illustrate the method, we consider two very distinct model systems: mixtures of diatomic molecules in the gas phase, as well as solid-state materials composed of a mixture of components. A set of numerical analyses are presented, showing strong performance in both settings.

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arXiv2021

Progress toward favorable landscapes in quantum combinatorial optimization

The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on algorithms for solving the combinatorial optimization problem MaxCut, and study how the structure of the classical optimization landscape relates to the quantum circuit used to evaluate the MaxCut objective function. In order to analytically characterize the impact of quantum features on the critical points of the landscape, we consider a family of quantum circuit ansätze composed of mutually commuting elements. We identify multiqubit operations as a key resource and show that overparameterization allows for obtaining favorable landscapes. Namely, we prove that an ansatz from this family containing exponentially many variational parameters yields a landscape free of local optima for generic graphs. However, we further prove that these ansätze do not offer superpolynomial advantages over purely classical MaxCut algorithms. We then present a series of numerical experiments illustrating that noncommutativity and entanglement are important features for improving algorithm performance.

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arXiv2021

Digital quantum simulation of molecular dynamics and control

Optimally-shaped electromagnetic fields have the capacity to coherently control the dynamics of quantum systems and thus offer a promising means for controlling molecular transformations relevant to chemical, biological, and materials applications. Currently, advances in this area are hindered by the prohibitive cost of the quantum dynamics simulations needed to explore the principles and possibilities of molecular control. However, the emergence of nascent quantum-computing devices suggests that efficient simulations of quantum dynamics may be on the horizon. In this article, we study how quantum computers could be employed to design optimally-shaped fields to control molecular systems. We introduce a hybrid algorithm that utilizes a quantum computer for simulating the field-induced quantum dynamics of a molecular system in polynomial time, in combination with a classical optimization approach for updating the field. Qubit encoding methods relevant for molecular control problems are described, and procedures for simulating the quantum dynamics and obtaining the simulation results are discussed. Numerical illustrations are then presented that explicitly treat paradigmatic vibrational and rotational control problems, and also consider how optimally-shaped fields could be used to elucidate the mechanisms of energy transfer in light-harvesting complexes. Resource estimates, as well as a numerical assessment of the impact of hardware noise and the prospects of near-term hardware implementations, are provided for the latter task.

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arXiv2021

From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms

The last decade has witnessed remarkable progress in the development of quantum technologies. Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes. Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities. In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory. To set the stage, we identify VQAs and quantum optimal control as formulations of variational optimization at the circuit level and pulse level, respectively, where these represent just two levels in a broader hierarchy of abstractions that we consider. In this unified picture, we suggest several ways that the different levels of abstraction may be connected, in order to facilitate the application of quantum optimal control theory to VQA challenges associated with ansatz selection, optimization landscapes, noise, and robustness. A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and conclude with a look to the future.

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arXiv2020

Asymptotic proximal point methods: finding the global minima with linear convergence for a class of multiple minima problems

We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of nonconvex proximal points so that it can find the global minimizer without being trapped in saddle points, local minima, or even discontinuities. Our main result shows that the method enjoys the global linear convergence for such a class of functions. Furthermore, the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is also bounded, so it has a complexity bound $\mathcal{O}(\log\frac{1}ε)$ for finding a point such that the gap between this point and the global minimizer is less than $ε>0$. Numerical experiments and comparisons in various dimensions from $2$ to $500$ demonstrate the benefits of the method.

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arXiv2018

Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit

The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic Ehrenfest theorems by assuming that the coordinates and momenta do not commute. Forbidding creation of antiparticles and requiring the commutativity of the coordinates and momenta lead to classical Spohn's equation [Ann. Phys. {\bf 282}, 420 (2000)]. Moreover, Spohn's equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.

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arXiv2017

Analytic Solutions to Coherent Control of the Dirac Equation

A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.

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arXiv2016

Dirac open quantum system dynamics: formulations and simulations

We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing.

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arXiv2016

Efficient computations of quantum canonical Gibbs state in phase space

The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.

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arXiv2016

Wigner-Lindblad equations for quantum friction

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

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arXiv2015

Efficient method to generate time evolution of the Wigner function for open quantum systems

The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging however; a variety of methods have been devised but suffer from being cumbersome and resource intensive. Here we present an efficient fast-Fourier method for evolving the Wigner function, that has a complexity of $O(N\log N)$ where $N$ is the size of the array storing the Wigner function. The efficiency, stability, and simplicity of this method allows us to simulate open system dynamics previously thought to be prohibitively expensive. As a demonstration we simulate the dynamics of both one-particle and two-particle systems under various environmental interactions. For a single particle we also compare the resulting evolution with that of the classical Fokker-Planck and Koopman-von Neumann equations, and show that the environmental interactions induce the quantum-to-classical transition as expected. In the case of two interacting particles we show that an environment interacting with one of the particles leads to the loss of coherence of the other.

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arXiv2013

Wigner phase space distribution as a wave function

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.

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arXiv2013

Sampling-based learning control of inhomogeneous quantum ensembles

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present a systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $Λ$ type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find the control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented showing the success of the SLC method.

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