arXiv subjects

Lijun Meng

Publications and source records attributed to Lijun Meng.

11 recordsLinked to original sources

arXiv2026

Universal Quantum Gate Compilation in $SU(2)_k$ Anyon Models via Multiple-Braiding

We investigate the capability of multiple-braiding in $SU(2)_k$ anyon models to realize universal quantum computation. The multiple elementary braiding matrices (MEBMs) are derived from the $q$-deformed representation theory of $SU(2)$. Through a general analysis of the MEBMs, we find that multiple-braiding loses its universality only when the braiding multiplicity $m$ causes the MEBMs to collapse to a scalar (up to a global phase). Our numerical analysis of the MEBMs of $SU(2)_k$ anyon models with $k = 3, 5, 6, 7$, and $m \in [2, 9]$, shows that the values of $m$ at which the braid group representation fails to be dense agree exactly with the theoretical prediction. For those $m$ that support universality, single-qubit gates are compiled to high precision by a genetic algorithm-enhanced Solovay-Kitaev algorithm (GA-enhanced SKA), and a genetic algorithm (GA) search with progressively increasing braid length yields an approximately the local equivalence class $[CNOT]$. Notably, even-order braiding operations offer a physical advantage by reducing the number of non-Abelian anyons required in braiding-based topological quantum computation (TQC). Our analytical and numerical results together provide strong evidence for identifying which braiding multiplicities $m$ support universal quantum computation in $SU(2)_k$ anyon models.

quant-ph↗

arXiv2025

High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition

We present a systematic numerical construction of a universal quantum gate set for topological quantum computation based on the non-semisimple Ising anyons model. By employing a Genetic Algorithm-enhanced Solovay-Kitaev Algorithm (GA-enhanced SKA), we achieve high-fidelity approximations of standard single-qubit gates (Hadamard H-gate and phase T-gate) with a recursion level of just three, meeting the fidelity requirements for fault-tolerant quantum computation. Our numerical results demonstrate that for the critical parameter range {\alpha} \in [2.001, 2.022], a few braiding operations can approximate the local equivalence class [CNOT] with high precision. Specifically, at {\alpha} =2.012, 2.015, 2.020, and 2.022, we successfully construct a universal gate set {H, T, CNOT} with leakage errors of two-qubit gate below 0.07,0.08,0.09 and 0.10, respectively. This work establishes a new pathway towards universal quantum computation using non-semisimple Ising anyons, overcoming the limitations of traditional Ising models through optimized braiding sequences and Genetic Algorithm-driven compilation.

quant-ph↗

arXiv2025

Long-Range Chiral Pairing enables Topological Superconductivity in Triangular Lattices without Spin-Orbit Coupling and Magnetic Field

This paper demonstrates a pathway to topological superconductivity in monolayer triangular lattices through long-range pairing without requiring spin-orbit coupling and magnetic field, contrasting conventional frameworks reliant on superconductivity and spin-orbit coupling and time-reversal symmetry (TRS) breaking. Berry curvature analysis reveals spontaneous TRS-breaking-induced peaks or valleys under long-range pairing, signaling nontrivial topology superconducting state. Notably, the increase in the long-range pairing strength only changes the size of the energy band-gap, without triggering a topological phase transition. This characteristic is verified by calculating Berry curvature and topological edge states. In zigzag and armchair-edge ribbons of finite width, the topological edge states are regulated by the ribbon boundary symmetry and the interact range of long-range pairing. Under nearest-neighbor pairing, the topological edge states maintain particle-hole symmetry and matches the corresponding Chern number. However, next-nearest-neighbor and third-nearest-neighbor pairings break the particle-hole symmetry of the topological edge states in armchair-edge ribbon. This work proposes a mechanism for realizing topological superconductivity without relying on spin-orbit coupling and magnetic field, offering a theoretical foundation for simplifying the design of topological quantum devices.

physics.comp-ph↗

arXiv2025

The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm

We study systematically numerical method into constructing a universal quantum gate set for topological quantum computation (TQC) using SU(2)k anyon models. The F-matrices and R-symbol were computed through the q-deformed representation theory of SU(2), enabling precise determination of elementary braiding matrices (EBMs) for SU(2)k anyon systems. Quantum gates were derived from these EBMs. One-qubit gates were synthesized using a genetic algorithm-enhanced Solovay-Kitaev algorithm (GA-enhanced SKA), while two-qubit gates were constructed through brute-force search or GA optimization to approximate local equivalence classes [CNOT]. Implementing this framework for SU(2)5, SU(2)6, and SU(2)7 models successfully generated the canonical universal gate set {H-gate, T-gate, CNOT-gate}. These numerical results provide conclusive verification of the universal quantum computation capabilities inherent in SU(2)k anyon models. Furthermore, we get exact implementations of the local equivalence class [SWAP] using nine EBMs in each model.

quant-ph↗

arXiv2025

Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling of Fibonacci anyons

Quantum compiling, which aims to approximate target qubit gates by finding optimal sequences (braidwords) of basic braid operations, constitutes a fundamental challenge in quantum computing. We develop a genetic algorithm (GA)-enhanced Solovay-Kitaev algorithm (SKA) for approximating single-qubit gates using four elementary braiding matrices (EBMs) derived from Fibonacci anyons. The GA-enhanced SKA demonstrates robust performance, efficiently identifying optimal braidwords within exponentially large search spaces. Notably, the approximation precision achieved by our method surpasses that of Monte Carlo (MC)-enhanced SKA and becomes comparable to deep reinforcement learning (RL) approaches when braidword lengths exceed 25. Implementing 2- and 3-order approximations with the GA-enhanced SKA yields optimal braidword (initial braiding lengths l0=50 and 30 respectively) achieving gate distances of 5.9*10-7 - sufficient precision for most quantum computing applications. This work develops an optimized compilation framework for non-Abelian anyon gates, providing an essential methodology for enhancing future topological quantum computation architectures through gate optimization.

quant-ph↗

arXiv2025

Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms

Topological quantum computing holding global anti-interference ability is realized by braiding some anyons, such as well-known Fibonacci anyons. Here, based on $SO(3)_2 $ theory we obtain a total of 6 anyon models utilizing \textit{F}-matrices, \textit{R}-symbols, and fusion rules of metaplectic anyon.We obtain the elementary braiding matrices (EBMs) by means of unconventional encoding. After braiding \textit{X} and $X^\prime$, we insert a pair of \textit{Z} anyons into them to ensure that the initial order of anyons remains unchanged. In this process only fusion is required, and measurement is not necessary. Three of them $\{V^{113}_3,V^{131}_3,V^{133}_1\}$ are studied in detail. We study systematically the compilation of these three models through EBMs obtained analytically. For one-qubit case, the classical \textit{H}- and \textit{T}-gate can be well constructed using the genetic algorithm enhanced Solovay-Kitaev algorithm (GA-enhanced SKA) by $\{V^{113}_3,V^{131}_3,V^{133}_1\}$. The obtained accuracy of the \textit{H}/\textit{T}-gate by $\{V^{113}_3,V^{133}_1\}$ is slightly inferior to the corresponding gates of the Fibonacci anyon model, but it also can meet the requirements of fault-tolerant quantum computing, $V^{131}_3$ giving the best performance of these four models. For the two-qubit case, we use the exhaustive method for short lengths and the GA for long lengths to obtain braidword for $\{V^{113}_3,V^{131}_3,V^{133}_1\}$ models. The resulting matrices can well approximate the local equivalence class of the CNOT-gate, while demonstrating a much smaller error than the Fibonacci model, especially for the $V^{113}_3$.The braiding processes of conventional encoding (using identical anyons) and unconventional encoding (using distinct anyons) are compared. Finally, we attempt to generalize the model to the \textit{N}-qubit case.

quant-ph↗

arXiv2024

Nearest-Neighboring Pairing of Monolayer NbSe2 Facilitates the Emergence of Topological Superconducting States

NbSe2, which simultaneously exhibits superconductivity and spin-orbit coupling, is anticipated to pave the way for topological superconductivity and unconventional electron pairing. In this paper, we systematically study topological superconducting (TSC) phases in monolayer NbSe2 through mixing on-site s-wave pairing (ps) with nearest-neighbor pairing (psA1) based on a tight-binding model. We observe rich phases with both fixed and sensitive Chern numbers (CNs) depending on the chemical potential ({\mu}) and out-of-plane magnetic field (Vz). As the psA1 increases, the TSC phase manifests matching and mismatching features according to whether there is a bulk-boundary correspondence (BBC). Strikingly, the introduction of mixed wave pairing significantly reduces the critical Vz to form TSC phases compared with the pure s-wave paring. Moreover, the TSC phase can be modulated even at Vz=0 under appropriate {\mu} and psA1, which is identified by the robust topological edge states (TESs) of ribbons. Additionally, the mixed pairing influences the hybridization of bulk and edge states, resulting in a matching/mismatching BBC with localized/oscillating TESs on the ribbon. Our finding is helpful for the realization of TSC states in experiment, as well as designing and regulating TSC materials.

cond-mat.supr-con↗

arXiv2018

Lasing and Amplification from Two-Dimensional Atom Arrays

We explore the ability of two-dimensional periodic atom arrays to produce light amplification and generate laser emission when gain is introduced through external optical pumping. Specifically, we predict that lasing can take place for arbitrarily weak atomic scatterers assisted by cooperative interaction among atoms in a 2D lattice. We base this conclusion on analytical theory for three-level scatterers, which additionally reveals a rich interplay between lattice and atomic resonances. Our results provide a general background to understand light amplification and lasing in periodic atomic arrays, with promising applications in the generation, manipulation, and control of coherent photon states at the nanoscale.

cond-mat.mes-hall↗

arXiv2015

Two dimensional topological insulators with tunable band gaps: HgTe and HgSe monolayers

Employing ab initio electronic calculations, we propose a new type of two-dimensional (2D) topological insulator (TI), monolayer (ML) low buckled (LB) mercury telluride (HgTe) and mercury selenide (HgSe), with tunable band gaps. Monolayer LB HgTe undergoes a transition to a topological nontrivial phase under the appropriate in-plane tensile strain (ε > 2.6%) due to the combination effects of strain and spin orbital coupling (SOC). Under the 2.6%< ε <4.2% tensile strain, the band inversion and topological nontrivial gap are induced by the SOC. For ε >4.2%, the band inversion is already realized by strain but the topological gap is induced by SOC. The band gap of monolayer LB HgTe TI phase can be tuned over a wide range from 0 eV to 0.20 eV as the tensile strain increases from 2.6% to 7.4%. Similarly, the topological phase transition of monolayer LB HgSe is induced by strain and SOC as the strain ε >3.1%. The topological band gap can be 0.05 eV as the strain increases to about 4.6%. The large band gap of 2D LB HgTe and HgSe monolayers make this type of material suitable for practical applications at room-temperature.

cond-mat.mes-hall↗

arXiv2015

Direct and quasi-direct band gap silicon allotropes with remarkable stability

In our present work, five previously proposed sp$^3$ carbon crystals were suggested as silicon allotropes and their stabilities, electronic and optical properties were investigated by first-principles method. We find that these allotropes with direct or quasi-direct band gaps in range of 1.2-1.6 eV are very suitable for applications in thin-film solar cells. They display strong adsorption coefficients in the visible range of the sunlight in comparison with diamond silicon. These five silicon allotropes are confirmed possessing positive dynamical stability and remarkable themodynamical stability close to that of diamond silicon. Especially, the direct band gap M585-silicon possessing energy higher than diamond silicon only 25 meV per atom is expected to be experimentally produced for thin-film solar cells.

cond-mat.mtrl-sci↗

arXiv2014

Simple Cubic Carbon Phase C21-sc: A Promising Superhard Carbon Conductor

Traditionally, all superhard carbon phases including diamond are electric insulators and all conductive carbon phases including graphite are mechanically soft. Based on first-principles calculation results, we report a superhard but conductive carbon phase C21-sc which can be obtained through increasing the sp3 bonds in the previously proposed soft and conductive phase C20-sc (Phys. Rev. B 74, 172101 2006). We also show that further increase of sp3 bonds in C21-sc results in a superhard and insulating phase C22-sc with sp3 bonds only. With C20-sc, C21-sc, C22-sc and graphite, the X-ray diffraction peaks from the unidentified carbon material synthesized by compressing the mixture of tetracyanoethylene and carbon black (Carbon, 41, 1309, 2003) can be understood. In view of its positive stability, superhard and conductive features, and the strong possibility of existence in previous experiments, C21-sc is a promising multi-functional material with potential applications in extreme conditions.

cond-mat.mtrl-sci↗