arXiv subjects

Xikun Li

Publications and source records attributed to Xikun Li.

13 recordsLinked to original sources

arXiv2025

Swinging small quantum systems out of available values of control parameters

When a quantum system is prepared in its many-body ground state, it can be adiabatically driven to another ground state by changing its control parameter. However, relying on adiabaticity is experimentally unjustified. Moreover, the target value of the control parameter may occur outside the experimentally accessible range. The indicated target state, however, can still be reached within a clever protocol of temporal changes of the control parameter provided its decomposition into some basis is known. It turns out that such a protocol can be obtained in the framework of the optimal control theory. In this paper, we show how to apply such an optimization scheme to small quantum systems treating interaction strength as the control parameter. We believe that the proposed approach can be creatively extended to various complex quantum systems.

quant-ph↗

arXiv2025

Optimal control for preparing fractional quantum Hall states in optical lattices

Preparing fractional quantum Hall (FQH) states represents a key challenge for quantum simulators. While small Laughlin-type states have been realized by manipulating two atoms or two photons, scaling up these settings to larger ensembles stands as an impractical task using existing methods and protocols. In this work, we propose to use optimal-control methods to substantially accelerate the preparation of small Laughlin-type states, and demonstrate that the resulting protocols are also well suited to realize larger FQH states under realistic preparation times. Our schemes are specifically built on the recent optical-lattice experiment [Leonard et al., Nature (2023)], and consist in optimizing very few control parameters: the tunneling amplitudes and linear gradients along the two directions of the lattice. We demonstrate the robustness of our optimal-control schemes against control errors and disorder, and discuss their advantages over existing preparation methods. Our work paves the way to the efficient realization of strongly-correlated topological states in quantum-engineered systems.

cond-mat.quant-gas↗

arXiv2024

Dynamics of quasiholes and quasiparticles at the edges of small lattices

We study quench dynamics of bosonic fractional quantum Hall systems in small lattices with cylindrical boundary conditions and low particle density. The states studied have quasiholes or quasiparticles relative to the bosonic Laughlin state at half filling. Pinning potentials are placed at edge sites (or sites close to the edges) and are then turned off. Because the edges of fractional quantum Hall systems host chiral edge modes, we expect chiral dynamics, with motion in one direction for positive potentials pinning quasiholes, and motion in the other direction for negative potentials pinning quasiparticles. We numerically show that chiral motion of the density distribution is observed and robust for the case with positive potentials (quasiholes), but that there is no noticeable chiral motion for negative potentials (quasiparticles). The comparison of the numerical ground states with model lattice Laughlin wavefunctions suggests that both positive and negative potentials do create and pin anyons that are not necessarily well-separated on small lattices. Initializing the dynamics with the model state also shows the lack of chiral dynamics of quasiparticles. Our results suggest that, in small lattices with low particle density, quasiparticles are strongly adversely affected in dynamical processes, whereas quasiholes are dynamically robust.

cond-mat.mes-hall↗

arXiv2023

Estimation of optimal control for two-level and three-level quantum systems with bounded amplitude

A systematic scheme is proposed to numerically estimate the quantum speed limit and temporal shape of optimal control in two-level and three-level quantum systems with bounded amplitude. For the two-level system, two quantum state transitions are studied as illustration. Comparisons between numerical and analytical results are made, and deviations are significantly small. For the three-level system, two critical time points are determined with high accuracy, and optimal controls are obtained for different durations. The shape of optimized control field is simple and does not switch frequently, thus are easy to implement in experiment. In addition, we compare our method with the chopped random basis (CRAB), and the performance of our method is much better than that of CRAB. Our scheme is of importance in estimating the quantum speed limit and optimal control for cases in which analytical solution is absent.

quant-ph↗

arXiv2023

Optimal control of quantum state preparation and entanglement creation in two-qubit quantum system with bounded amplitude

We consider the optimal control problem in a two-qubit system with bounded amplitude. Two cases are studied: quantum state preparation and entanglement creation. Cost functions, fidelity and concurrence, are optimized over bang-off controls for different values of the total duration, respectively. For quantum state preparation problem, three critical time points are determined with high precision, and optimal controls are obtained for different durations. A better estimation of the quantum speed limit is obtained, so is the time-optimal control. For entanglement creation problem, two critical time points are determined, one of them is the minimal time to achieve maximal entanglement (unit concurrence) starting from the product state. In addition, the optimal control to reach the unit concurrence is found.

quant-ph↗

arXiv2022

Laughlin topology on fractal lattices without area law entanglement

Laughlin states have recently been constructed on fractal lattices, and the charge and braiding statistics of the quasiholes were used to confirm that these states have Laughlin type topology. Here, we investigate density, correlation, and entanglement properties of the states on a fractal lattice derived from a Sierpinski triangle with the purpose of identifying similarities and differences compared to two-dimensional systems and with the purpose of investigating whether various probes of topology work for fractal lattices. Similarly to two-dimensional systems, we find that the connected particle-particle correlation function decays roughly exponentially with the distance between the lattice sites measured in the two-dimensional plane, but the values also depend on the local environment. Contrary to two-dimensional systems, we find that the entanglement entropy does not follow the area law if one defines the area to be the number of nearest neighbor bonds that cross the edge of the selected subsystem. Considering bipartitions with two bonds crossing the edge, we find a close to logarithmic scaling of the entanglement entropy with the number of sites in the subsystem. This also means that the topological entanglement entropy cannot be extracted using the Kitaev-Preskill or the Levin-Wen methods. Studying the entanglement spectrum for different bipartitions, we find that the number of states below the entanglement gap is robust and the same as for Laughlin states on two-dimensional lattices.

cond-mat.str-el↗

arXiv2021

Squeezing anyons for braiding on small lattices

Adiabatically exchanging anyons gives rise to topologically protected operations on the quantum state of the system, but the desired result is only achieved if the anyons are well separated, which requires a sufficiently large area. Being able to reduce the area needed for the exchange, however, would have several advantages, such as enabling a larger number of operations per area and allowing anyon exchange to be studied in smaller systems that are easier to handle. Here, we use optimization techniques to squeeze the charge distribution of Abelian anyons in lattice fractional quantum Hall models, and we show that the squeezed anyons can be exchanged within a smaller area with a close to ideal outcome. We first use a toy model consisting of a modified Laughlin trial state to show that one can shape the anyons without altering the exchange statistics under certain conditions. We then squeeze and braid anyons in the Kapit-Mueller model and an interacting Hofstadter model by adding suitable potentials. We consider a fixed system size, for which the charge distributions of the normal anyons overlap, and we find that the outcome of the exchange process is closer to the ideal value for the squeezed anyons. The time needed for the exchange is also important, and for a particular example we find that the duration needed for the process to be close to the adiabatic limit is about five times longer for the squeezed anyons when the path length is the same. Finally we show that the exchange outcome is robust with respect to small modifications of the potential away from the optimized value.

cond-mat.str-el↗

arXiv2018

Global optimization for quantum dynamics of few-fermion systems

Quantum state preparation is vital to quantum computation and quantum information processing tasks. In adiabatic state preparation, the target state is theoretically obtained with nearly perfect fidelity if the control parameter is tuned slowly enough. As this, however, leads to slow dynamics, it is often desirable to be able to do processes faster. In this work, we employ two global optimization methods to estimate the quantum speed limit for few-fermion systems confined in a one-dimensional harmonic trap. Such systems can be produced experimentally in a well controlled manner. We determine the optimized control fields and achieve a reduction in the ramping time of more than a factor of four compared to linear ramping. We also investigate how robust the fidelity is to small variations of the control fields away from the optimized shapes.

cond-mat.quant-gas↗

arXiv2018

Effective three-body interactions for bosons in a double-well confinement

When describing the low-energy physics of bosons in a double-well potential with a high barrier between the wells and sufficiently weak atom-atom interactions, one can to a good approximation ignore the high energy states and thereby obtain an effective two-mode model. Here, we show that the regime in which the two-mode model is valid can be extended by adding an on-site three-body interaction term and a three-body interaction-induced tunneling term to the two-mode Hamiltonian. These terms effectively account for virtual transitions to the higher energy states. We determine appropriate strengths of the three-body terms by an optimization of the minimal value of the wave function overlap within a certain time window. Considering different initial states with three or four atoms, we find that the resulting model accurately captures the dynamics of the system for parameters where the two-mode model without the three-body terms is poor. We also investigate the dependence of the strengths of the three-body terms on the barrier height and the atom-atom interaction strength. The optimal three-body interaction strengths depend on the initial state of the system.

cond-mat.quant-gas↗

arXiv2016

Optimal error intervals for properties of the quantum state

Quantum state estimation aims at determining the quantum state from observed data. Estimating the full state can require considerable efforts, but one is often only interested in a few properties of the state, such as the fidelity with a target state, or the degree of correlation for a specified bipartite structure. Rather than first estimating the state, one can, and should, estimate those quantities of interest directly from the data. We propose the use of optimal error intervals as a meaningful way of stating the accuracy of the estimated property values. Optimal error intervals are analogs of the optimal error regions for state estimation [New J. Phys. 15, 123026 (2013)]. They are optimal in two ways: They have the largest likelihood for the observed data and the pre-chosen size, and are the smallest for the pre-chosen probability of containing the true value. As in the state situation, such optimal error intervals admit a simple description in terms of the marginal likelihood for the data for the properties of interest. Here, we present the concept and construction of optimal error intervals, report on an iterative algorithm for reliable computation of the marginal likelihood (a quantity difficult to calculate reliably), explain how plausible intervals --- a notion of evidence provided by the data --- are related to our optimal error intervals, and illustrate our methods with single-qubit and two-qubit examples.

quant-ph↗

arXiv2013

Optimal error regions for quantum state estimation

Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we introduce the maximum-likelihood region---the region of largest likelihood among all regions of the same size. Here, the size of a region is its prior probability. Another concept is the smallest credible region---the smallest region with pre-chosen posterior probability. For both optimization problems, the optimal region has constant likelihood on its boundary. We discuss criteria for assigning prior probabilities to regions, and illustrate the concepts and methods with several examples.

quant-ph↗

arXiv2012

Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States

We propose a practical entanglement classification scheme for general multipartite pure states in arbitrary dimensions under local unitary equivalence by exploiting the high order singular value decomposition technique and local symmetries of the states. By virtue of this scheme, the method of determining the local unitary equivalence of $n$-qubit states proposed by Kraus is extended to the case for arbitrary dimensional multipartite states.

quant-ph↗

arXiv2010

The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System

We present in the work two intriguing results in the entanglement classification of pure and true tripartite entangled state of $2\times M\times N$ under stochastic local operation and classical communication. (i) the internal symmetric properties of the nonlocal parameters in the continuous entangled class; (ii) the analytic expression for the total numbers of the true and pure entangled class $2\times M \times N$ states. These properties help people to know more of the nature of the $2\times M\times N$ entangled system.

quant-ph↗