Functional observability and subspace reconstruction in nonlinear systems

in Physical Review Research (2022), 4

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time- ordered data, with applications in many disciplines such as physics, biology, finance, and engineering ... [more ▼]

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time- ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are often low dimensional or even univariate, thus requiring embedding methods to reconstruct the original system’s state space. The observability of a system establishes fundamental conditions under which such reconstruction is possible. However, complete observability is too restrictive in applications where reconstructing the entire state space is not necessary and only a specific subspace is relevant. Here, we establish the theoretic condition to reconstruct a nonlinear functional of state variables from measurement processes, generalizing the concept of functional observability to nonlinear systems. When the functional observability condition holds, we show how to construct a map from the embedding space to the desired functional of state variables, characterizing the quality of such reconstruction. The theoretical results are then illustrated numerically using chaotic systems with contrasting observability properties. By exploring the presence of functionally unobservable regions in embedded attractors, we also apply our theory for the early warning of seizure-like events in simulated and empirical data. The studies demonstrate that the proposed functional observability condition can be assessed a priori to guide time-series analysis and experimental design for the dynamical characterization of complex systems. [less ▲]

Lipid islands on liquid crystal shells

in Physical Review Research (2022), 4

By inducing phase separation in lipid monolayers on liquid crystal (LC) shells—thin hollow spheres of LC with water inside and outside—we reveal a rich set of coupled two- and three-dimensional (2D and 3D ... [more ▼]

By inducing phase separation in lipid monolayers on liquid crystal (LC) shells—thin hollow spheres of LC with water inside and outside—we reveal a rich set of coupled two- and three-dimensional (2D and 3D) self- organization phenomena enabled by the dual closely spaced internal and external spherical LC-water interfaces. Spindle-shaped 2D islands of condensed lipid monolayer first form at the primary interface where lipids are deposited, later also at the initially unexposed secondary interface, because lipids transfer through the LC. The LCs’ elastic response to the 3D deformation caused by islands moves them from thin to thick regions on the shell and creates an attraction between opposite-side islands, topologically separated by the LCs, until they stack in a sandwich-like manner. We propose that the phase separation may be used for studying liposome adsorption on soft hydrophobic substrates, and to create unconventional colloidal particles with programmed interactions. [less ▲]

Digitized-counterdiabatic quantum approximate optimization algorithm

in Physical Review Research (2022)

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼]

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since the QAOA is an Ansatz-dependent algorithm, there is always a need to design Ansätze for better optimization. To this end, we propose a digitized version of the QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better Ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-CD QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms the standard QAOA in all cases we study. [less ▲]

Benchmarking quantum annealing dynamics: The spin-vector Langevin model

in Physical Review Research (2022)

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the ... [more ▼]

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the annealing dynamics in real-time.We introduce the spin-vector Langevin (SVL) model as an alternative benchmark in which the time evolution is described by Langevin dynamics. The SVL model is shown to provide a more stringent test than the SVMC model for the identification of quantum signatures in the performance of quantum annealing devices, as we illustrate by describing the Kibble-Zurek scaling associated with the dynamics of symmetry breaking in the transverse field Ising model, recently probed using D-Wave machines. Specifically, we show that D-Wave data are reproduced by the SVL model. [less ▲]

Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain

in Physical Review Research (2021)

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction ... [more ▼]

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲]

Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism

in Physical Review Research (2021)

We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically ... [more ▼]

We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink-number distribution to assess adiabaticity and its breakdown.We consider linear, nonlinear, and exponential cooling schedules, among which the last provides the most efficient shortcuts to cooling in a given quench time. The nonthermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state. [less ▲]

Digitized-counterdiabatic quantum approximate optimization algorithm

in Physical Review Research (2021)

The quantum approximate optimization algorithm (QAOA) has proved to be an e ective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼]

The quantum approximate optimization algorithm (QAOA) has proved to be an e ective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitizedcounterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study. [less ▲]

Correlation satellites in optical and loss spectra

in Physical Review Research (2020), 2

Coupling of excitations leads to intriguing effects on the spectra of materials. We propose a cumulant formulation for neutral electronic excitations which opens the way to describe effects such as double ... [more ▼]

Coupling of excitations leads to intriguing effects on the spectra of materials. We propose a cumulant formulation for neutral electronic excitations which opens the way to describe effects such as double plasmon satellites or exciton-exciton coupling. Our approach starts from the GW+Bethe-Salpeter approximation to many-body perturbation theory which is based on a quasiparticle picture, and it adds coupling of excitations through a consistent inclusion of dynamically screened interactions. This requires one to consider scattering contributions that are usually neglected. The result is formulated in a way that highlights essential physics, that can be implemented as a postprocessing tool in first-principles codes, and that suggests which kind of materials and measurements should exhibit strong effects. This is illustrated using a model. [less ▲]

Discrimination of thermal baths by single-qubit probes

in Physical Review Research (2020)

Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics. We extend these studies to a more ... [more ▼]

Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that nonequilibrium states are not universally optimal and detail the conditions in which it becomes advantageous to wait for complete thermalization of the probe. These concepts are illustrated in a linear-optical simulation. [less ▲]