arXiv subjects

Xi-Dan Hu

Publications and source records attributed to Xi-Dan Hu.

6 recordsLinked to original sources

arXiv2025

Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators

Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator scrambling via Holevo information of operators, by taking its capacity to distinguish operator information locally. We show that the operator size is closely related to a special kind of Holevo information of operators. Moreover, we propose a feasible protocol for measuring Holevo information of operators on digital quantum simulators based on random states. \textcolor{black}{For the mixed-field Ising model,} our numerical simulations show that the integrable system can be told apart from the chaotic system by measuring the spatial-temporal patterns of Holevo information. Furthermore, we find that error mitigation is required to restore the time-oscillation behavior of Holevo information for the integrable system, a crucial feature distinct from the chaotic one. Our work provides a new perspective to understand the information scrambling and quantum chaos from aspects of Holevo information of operators.

quant-ph↗

arXiv2024

Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points

Dual-unitary quantum circuits can provide analytic spatiotemporal correlation functions of local operators from transfer matrices, enriching our understanding of quantum dynamics with exact solutions. Nevertheless, a full understanding is still lacking as the case of a non-diagonalizable transfer matrix with exceptional points has less been investigated. In this paper, we give an inverse approach for constructing dual-unitary quantum circuits with exceptional points in the transfer matrices, by establishing relations between transfer matrices and local unitary gates. As a consequence of the coalesce of eigenvectors, the correlation functions exhibit a polynomial modified exponential decay, which is significantly different from pure exponential decay, especially at early stages. Moreover, we point out that the Hamiltonian evolution of a kicked XXZ spin chain can be approximately mapped to a dual-unitary circuit with exceptional points by Trotter decomposition. Finally, we investigate the dynamics approaching and at exceptional points, showing that behaviors of correlation functions are distinct by Laplace transformation.

quant-ph↗

arXiv2023

Dynamical properties of quasiparticles in a tunable Kekulé graphene superlattice

We investigate the dynamical properties of quasiparticles in graphene superlattices with three typical Kekulé distortions (i.e., Kekulé-O, Kekulé-Y and Kekulé-M). On the one hand, we numerically show the visualized evolution process of Kekulé quasiparticles; while on the other hand, we analytically obtain the centroid trajectory of the quasiparticles, and both of them agree well with each other. The results reveal that the relativistic Zitterbewegung (ZB) phenomenon occurs in the Kekulé systems. Furthermore, through analyzing the frequency of ZB, we unveil the one-to-one relationship between ZB and Kekulé textures, i.e., the ZB frequenies of Kekulé-O, Kekulé-Y and Kekulé-M quasiparticles feature single, double and six frequencies, respectively. Finally, we propose a scheme to distinguish among different Kekulé textures from the dynamical perspective. The predictions in this paper are expected to be experimentally verified in the near future, so as to facilitate further research of Kekulé structures in solid materials or artificial systems.

cond-mat.mes-hall↗

arXiv2022

Quantum algorithm for evaluating operator size with Bell measurements

Operator size growth describes the scrambling of operators in quantum dynamics and stands out as an essential physical concept for characterizing quantum chaos. Important as it is, a scheme for direct measuring operator size on a quantum computer is still absent. Here, we propose a quantum algorithm for direct measuring the operator size and its distribution based on Bell measurement. The algorithm is verified with spin chains and meanwhile, the effects of Trotterization error and quantum noise are analyzed. It is revealed that saturation of operator size growth can be due to quantum chaos itself or be a consequence of quantum noises, which make a distinction between quantum integrable and chaotic systems difficulty on noisy quantum processors. Nevertheless, it is found that the error mitigation will effectively reduce the influence of noise, so as to restore the distinguishability of quantum chaotic systems. Our work provides a feasible protocol for investigating quantum chaos on noisy quantum computers by measuring operator size growth.

quant-ph↗

arXiv2022

Emergent phase transition in Cluster Ising model with dissipation

We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. String order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases and phase transitions induced by non-Hermiticity, we calculate the variation mode of spin correlation function as well as string parameter, which characterize the emergent phases and critical points with different patterns of decay and critical exponents. With the help of string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity -- the cluster phase, the gapless phase, the paramagnetic (PM) phase and the antiferromagnetic (AF) phase. A phase diagram is then presented to graphically illustrate, based on two "KT-like" phase transitions and an Ising phase transition, respectively, the generation of three critical lines as non-Hermitian strength increases. Our theoretical work is expected to be realized in the experiment of ultra-cold atoms, pushing for progress in exploring novel phases and phase transitions.

cond-mat.stat-mech↗

arXiv2022

Dynamics in an exact solvable quantum magnet: benchmark for quantum computer

Quantum magnets are never short of novel and fascinating dynamics, yet its simulation by classical computers requires exponentially-scaled computation resources, which renders the research on large-scale many-body dynamics fiendishly difficult. In this letter, we explore the dynamic behavior of 2D large-scale ferromagnetic J1-J2 Heisenberg model both theoretically and experimentally. First, the analytical solution of magnon dynamics is obtained to show an obvious ballistic propagation of magnon, which is typical for quantum walk. Then, we verify the dynamic behavior of the system through numerical approach of exact diagonalization and tensor network method. We also calculate out-of-time ordered correlators and butterfly velocities among different lattice points, finding that they can well depict the competition between different couplings. Finally, a quantum walk experiment is designed and conducted on the basis of IBM programmable quantum processors, and the experimental results are in consistence with our theoretical predictions. Since the analytical results can be used, in principle, to predict the behavior of large-scale quantum many-body systems and even those infinitely large, this work will help facilitate further research on quantum walk and quantum many-body dynamics in large-scale lattice systems, guide future design of quantum computers, as well as popularize quantum computers until they are known and available to every household in the world.

quant-ph↗