arXiv subjects

Liangsheng Li

Publications and source records attributed to Liangsheng Li.

18 recordsLinked to original sources

arXiv2026

Towards Robust Optimal Measurements Against Noise in Quantum Metrology

Quantum parameter estimation utilizes quantum mechanical effects to attain higher measurement precision than classical schemes. In practical implementations, however, noise is inevitably present during the measurement process, causing a decrease in precision. Quantifying the impact of noise on different measurements is of considerable significance. Here, we experimentally investigate robust optimal measurements based on the theory of Fisher information measurement noise susceptibility (FI MENOS), which quantifies how susceptible a measurement is to noise. By constructing a polarizing Mach-Zehnder interferometer, we implement phase estimation under controlled noise. Our results indicate that different measurements exhibit distinct sensitivities to noise. To assess the influence of diverse noise types on precision, we further construct an experimental setup capable of introducing various forms of noise. The experimental results affirm that FI MENOS represents the worst-case scenario for estimation precision, enabling us to evaluate the noise immunity of optimal measurements. Our work provides a deeper insight into quantum metrology with noise, marking a notable advancement in quantifying the robustness of quantum estimation schemes against measurement noise effects.

quant-ph↗

arXiv2026

Quantum criticality and factorization in a constrained Rydberg spin chain

We investigate the zero-temperature phase diagram of a one-dimensional constrained quantum spin chain realized in coherently driven Rydberg-atom arrays with competing local Rabi driving and dipole-dipole exchange interactions. Projecting onto the blockade-constrained Hilbert space yields an effective model in which local and nonlocal quantum fluctuations compete on equal footing. Combining exact diagonalization, the density-matrix renormalization group, and variational uniform matrix-product-state calculations, we establish a complete phase diagram comprising a Luttinger liquid, an antiferromagnetic ordered phase, and a polarized paramagnet. We identify two distinct mechanisms for the destruction of antiferromagnetic order: a conventional Ising transition at strong driving and a continuous quantum melting into the Luttinger liquid at weak driving, characterized using entanglement-based diagnostics and finite-entanglement scaling. In addition, we uncover an exact ground-state factorization line embedded within the ordered phase, providing an analytically tractable zero-entanglement reference point for experiments with programmable Rydberg quantum simulators.

cond-mat.str-el↗

arXiv2025

Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime

Non-Hermitian quantum metrology, an emerging field at the intersection of quantum estimation and non-Hermitian physics, holds promise for revolutionizing precision measurement. Here, we present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime, with a special focus on achieving Heisenberg scaling. We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians, enabling the analysis of estimation precision in these systems. Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of $1/t$, where $t$ represents time. Moreover, we derive optimal measurement conditions based on the proposed QFI expression, demonstrating the attainment of the quantum Cram\'{e}r-Rao bound. By constructing non-unitary evolutions governed by two non-Hermitian Hamiltonians, one with parity-time symmetry and the other without specific symmetries, we experimentally validate our theoretical analysis. The experimental results affirm the realization of Heisenberg scaling in estimation precision, marking a substantial milestone in non-Hermitian quantum metrology.

quant-ph↗

arXiv2025

Continuously varying critical exponents in an exactly solvable long-range cluster XY mode

We investigate a generalized antiferromagnetic cluster XY model in a transverse magnetic field, where long-range interactions decay algebraically with distance. This model can be exactly solvable within a free fermion framework. By analyzing the gap, we explicitly derive the critical exponents $ν$ and $z$, finding that the relationship $νz = 1$ still holds. However, the values of $ν$ and $z$ depend on the decaying exponent $α$, in contrast to those for the quantum long-range antiferromagnetic Ising chain. To optimize scaling behavior, we verify these critical exponents using correlation functions and fidelity susceptibility, achieving excellent data collapse across various system sizes by adjusting fitting parameters. Finally, we compute the entanglement entropy at the critical point to determine the central charge $c$, and find it also varies with $α$. This study provides insights into the unique effect of long-range cluster interactions on the critical properties of quantum spin systems.

cond-mat.str-el↗

arXiv2024

Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies

We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological $θ$ angle of $π$. Introducing rhombic SIA shifts this angle from $π$, resulting in $y$- and $x$-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological $θ$ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators.

cond-mat.str-el↗

arXiv2024

Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

quant-ph↗

arXiv2024

Machine-learning-inspired quantum control in many-body dynamics

Achieving precise preparation of quantum many-body states is crucial for the practical implementation of quantum computation and quantum simulation. However, the inherent challenges posed by unavoidable excitations at critical points during quench processes necessitate careful design of control fields. In this work, we introduce a promising and versatile dynamic control neural network tailored to optimize control fields. We address the problem of suppressing defect density and enhancing cat-state fidelity during the passage across the critical point in the quantum Ising model. Our method facilitates seamless transitions between different objective functions by adjusting the {optimization strategy}. In comparison to gradient-based power-law quench methods, our approach demonstrates significant advantages for both small system sizes and long-term evolutions. We provide a detailed analysis of the specific forms of control fields and summarize common features for experimental implementation. Furthermore, numerical simulations demonstrate the robustness of our proposal against random noise and spin number fluctuations. The optimized defect density and cat-state fidelity exhibit a transition at a critical ratio of the quench duration to the system size, coinciding with the quantum speed limit for quantum evolution.

quant-ph↗

arXiv2024

Optimizing single-photon quantum radar detection through partially postselected filtering

In this study, we explore an approach aimed at enhancing the transmission or reflection coefficients of absorbing materials through the utilization of joint measurements of entangled photon states. On the one hand, through the implementation of photon catalysis in the reflected channel, we can effectively modify the state of the transmission channel, leading to a notable improvement in the transmission ratio. Similarly, this approach holds potential for significantly amplifying the reflection ratio of absorbing materials, which is useful for detecting cooperative targets. On the other hand, employing statistical counting methods based on the technique of heralding on zero photons, we evaluate the influence of our reflection enhancement protocol for detecting noncooperative targets, which is validated through Monte Carlo simulations of a quantum radar setup affected by Gaussian white noise. Our results demonstrate a remarkable enhancement in the signal-to-noise ratio of imaging, albeit with an increase in mean-square error. These findings highlight the potential practical applications of our approach in the implementation of quantum radar.

quant-ph↗

arXiv2023

Quantum error pre-compensation for quantum noisy channels

Most previous efforts of quantum error correction focused on either extending classical error correction schemes to the quantum regime by performing a perfect correction on a subset of errors, or seeking a recovery operation to maximize the fidelity between a input state and its corresponding output state of a noisy channel. There are few results concerning quantum error pre-compensation. Here we design an error pre-compensated input state for an arbitrary quantum noisy channel and a given target output state. By following a procedure, the required input state, if it exists, can be analytically obtained in single-partite systems. Furthermore, we also present semidefinite programs to numerically obtain the error pre-compensated input states with maximal fidelities between the target state and the output state. The numerical results coincide with the analytical results.

quant-ph↗

arXiv2022

Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model

We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-André-Harper model with p-wave pairing, which have rarely been exploited as most investigations focus on the localization transition from the critical phase to the localized phase. We find that the spectrum averaged entanglement entropy and the generalized fidelity susceptibility act as eminent universal order parameters of the corresponding critical point without gap closing. We introduce a Widom scaling ansatz for these criticality probes to develop a unified theory of critical exponents and scaling functions. We thus extract the correlation-length critical exponent $ν$ and the dynamical exponent $z$ through the finite-size scaling given the system sizes increase in the Fibonacci sequence. The retrieved values of $ν\simeq 1.000$ and $z \simeq 3.610$ indicate that the transition from the extended phase to the critical phase belongs to a different universality class from the localization transition. Our approach sets the stage for exploring the unconventional quantum criticality and the associated universal information of quasiperiodic systems in state-of-the-art quantum simulation experiments.

cond-mat.dis-nn↗

arXiv2022

Quantum Many-Body Scars in Spin-1 Kitaev Chains

To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $\vert\mathbb{Z}_k\rangle$ ($k=2,3$) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $ϕ$, where the Kitaev term is $K\equiv\sin(ϕ)$ and competes with the Heisenberg $J\equiv\cos(ϕ)$ term. One finds a rich ground state phase diagram as a function of the angle $ϕ$. Depending on the ratio $K/J\equiv\tan(ϕ)$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey $\mathbb{Z}_2$-symmetry, while it becomes unstable against Heisenberg-type perturbations.\\ \textit{Accepted for publication in Physical Review Research}

cond-mat.str-el↗

arXiv2022

Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model

We investigate the quantum criticality and universality in Aubry-André-Harper (AAH) model with $p$-wave superconducting pairing $Δ$ in terms of the generalized fidelity susceptibility (GFS). We show that the higher-order GFS is more efficient in spotlighting the critical points than lower-order ones, and thus the enhanced sensitivity is propitious for extracting the associated universal information from the finite-size scaling in quasiperiodic systems. The GFS obeys power-law scaling for localization transitions and thus scaling properties of the GFS provide compelling values of critical exponents. Specifically, we demonstrate that the fixed modulation phase $ϕ=π$ alleviates the odd-even effect of scaling functions across the Aubry-André transition with $Δ=0$, while the scaling functions for odd and even numbers of system sizes with a finite $Δ$ cannot coincide irrespective of the value of $ϕ$. A thorough numerical analysis with odd number of system sizes reveals the correlation-length exponent $ν\simeq 1.000$ and the dynamical exponent $z$ $\simeq$ 1.388 for transitions from the critical phase to the localized phase,suggesting the unusual universality class of localization transitions in the AAH model with a finite $p$-wave superconducting pairing lies in a different universality class from the Aubry-André transition. The results may be testified in near term state-of-the-art experimental settings.

cond-mat.dis-nn↗

arXiv2019

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of ground state wave function. The key point of the method is to introduce a variational parameter $λ$, which can be determined by minimizing the energy functional. Using this method, we calculate physical observables with high accuracy in comparison with the numerical exact one. Our method evidently improves the results from the widely used general rotating-wave approximation (GRWA) in both qualitative and quantitative ways.

quant-ph↗

arXiv2019

Variational generalized rotating-wave approximation in the two-qubit quantum Rabi model

We present an analytical method for the two-qubit quantum Rabi model. While still operating in the frame of the generalized rotating-wave approximation (GRWA), our method further embraces the idea of introducing variational parameters. The optimal value of the variational parameter is determined by minimizing the energy function of the ground state. Comparing with numerical exact results, we show that our method evidently improves the accuracy of the conventional GRWA in calculating fundamental physical quantities, such as energy spectra, mean photon number, and dynamics. Interestingly, the accuracy of our method allows us to reproduce the asymptotic behavior of mean photon number in large frequency ratio for the ground state and investigate the quasi-periodical structure of the time evolution, which are incapable of being predicted by the GRWA. The applicable parameter ranges cover the ultrastrong coupling regime, which will be helpful to recent experiments.

quant-ph↗

arXiv2019

Bottom stresses of static packing of granular chains

We experimentally measure the static stress at the bottom of a granular chains column with a precise and reproducible method. The relation, between the filling mass and the apparent mass converted from the bottom stress, is investigated on various chain lengths. Our measurements reconfirm that the scaling behavior of the stress saturation curves is in accord with the theoretical expectation of the Janssen model. Additionally, the saturation mass is displayed as a nonmonotonic function of the chain length, where a distinguishing transition of the saturation mass is found at the persistence length of the granular chain. We repeat the measurement with another measuring methodology and a silo with different size, respectively, the position of the peak maintains robust. In order to understand the transition of the saturation mass, the friction coefficient and the volume fraction of granular chains are also measured, from which Janssen parameter can be calculated. Finally, we preliminarily measure the bottom stress for two distinct packing structures of long chains, find the effect of the entanglements on the bottom stress, and argue that the entanglements might be responsible for the transition of the saturation mass.

cond-mat.soft↗

arXiv2017

Size Scaling of Velocity Field in Granular Flows through Apertures

For vertical velocity field $v_{\rm z} (r,z;R)$ of granular flow through an aperture of radius $R$, we propose a size scaling form $v_{\rm z}(r,z;R)=v_{\rm z} (0,0;R)f (r/R_{\rm r}, z/R_{\rm z})$ in the region above the aperture. The length scales $R_{\rm r}=R- 0.5 d$ and $R_{\rm z}=R+k_2 d$, where $k_2$ is a parameter to be determined and $d$ is the diameter of granule. The effective acceleration, which is derived from $v_{\rm z}$, follows also a size scaling form $a_{\rm eff} = v_{\rm z}^2(0,0;R)R_{\rm z}^{-1} θ(r/R_{\rm r}, z/R_{\rm z})$. For granular flow under gravity $g$, there is a boundary condition $a_{\rm eff} (0,0;R)=-g$ which gives rise to $v_{\rm z} (0,0;R)= \sqrt{ λg R_{\rm z}}$ with $λ=-1/θ(0,0)$. Using the size scaling form of vertical velocity field and its boundary condition, we can obtain the flow rate $W =C_2 ρ\sqrt{g } R_{\rm r}^{D-1} R_{\rm z}^{1/2} $, which agrees with the Beverloo law when $R \gg d$. The vertical velocity fields $v_z (r,z;R)$ in three-dimensional (3D) and two-dimensional (2D) hoppers have been simulated using the discrete element method (DEM) and GPU program. Simulation data confirm the size scaling form of $v_{\rm z} (r,z;R)$ and the $R$-dependence of $v_{\rm z} (0,0;R)$.

cond-mat.soft↗

arXiv2012

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability $p$. At $p=0.5$, the GAP becomes the random growth model and leads to the minority product rule at $p=1$. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with $0.5 \le p \le 1$ are always continuous and their critical exponents depend on $p$. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter $p$ in addition.

cond-mat.stat-mech↗

arXiv2012

Continuous percolation phase transitions of random networks under a generalized Achlioptas process

Using the finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with minimum product of two connecting cluster sizes is taken with a probability $p$ from two randomly chosen edges. This model becomes the Erd\H os-Rényi network at $p=0.5$ and the random network under the Achlioptas process at $p=1$. Using both the fixed point of $s_2/s_1$ and the straight line of $\ln s_1$, where $s_1$ and $s_2$ are the reduced sizes of the largest and the second largest cluster, we demonstrate that the phase transitions of this model are continuous for $0.5 \le p \le 1$. From the slopes of $\ln s_1$ and $\ln (s_2/s_1)'$ at the critical point we get the critical exponents $β$ and $ν$, which depend on $p$. Therefore the universality class of this model should be characterized by $p$ also.

cond-mat.stat-mech↗