arXiv subjects

Lei-Yi-Nan Liu

Publications and source records attributed to Lei-Yi-Nan Liu.

6 recordsLinked to original sources

arXiv2026

Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum

Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains poorly understood. Here we develop a spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We further reduce the local-unitary optimization to a single-unitary problem and prove that the ordered Schmidt reference state is a local minimum of the SRE for integer $α\geq2$. Applying these results to exponentially and algebraically decaying spectra reveals parametrically distinct relations between entanglement and nonlocal nonstabilizerness. For broad spectra, we introduce a dyadic-shell sandwich construction that determines the asymptotic SRE scaling. At one-dimensional conformal critical points, it yields a universal hierarchy of double-logarithmic scaling laws for integer $α\geq2$. Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems.

quant-ph↗

arXiv2026

Distinct many-body scars and emergent quantum phases driven by competing interactions in two-species Rydberg arrays

Rydberg atom arrays composed of multiple atomic species stand as a highly promising platform for quantum computation. However, the underlying physics of these systems as quantum many-body systems remains poorly understood, owing to the intricate competition between attractive and repulsive interactions, phenomena that entirely defy the Rydberg blockade mechanism. We systematically calculate the ground-state phase diagram of alternating two-species atom arrays and their quench dynamics. Our findings reveal several novel quantum states absent in traditional cold-atom platforms, such as the period-4 product state $|1100...\rangle$, the period-6 product state $|111000...\rangle$, and an order-disorder mixed phase. In the quench dynamics, we confirm $\mathbb{Z}_2$ ordered state qualify as novel quantum many-body scars. Based on our perturbation analysis, the underlying physics ought to be described by a series of Cooper pair states spanning the entire energy spectrum, rather than the PXP low-energy effective model. A detailed analysis is also provided regarding the experimental preparation of those product states. Numerical evidence demonstrates that the proposed scheme exhibits robustness against typical experimental imperfections, thereby confirming its experimental feasibility. Moreover, the ground-state problem of the two-species array naturally maps to more general combinatorial optimization problems, extending the class of optimization tasks accessible to programmable neutral-atom quantum processors. Our work paves a new way for quantum simulation of novel quantum many-body states, which emerge from the interplay between competing interactions among different atom species and quantum fluctuations.

cond-mat.quant-gas↗

arXiv2026

Nonlocal nonstabilizerness for slightly entangled quantum many-body states

Nonlocal nonstabilizerness quantifies the irreducible magic resource encoded in bipartite entanglement, but its evaluation is generally hindered by a highly nonconvex optimization over local unitary transformations. Here we propose a Schmidt-reference-state framework that replaces this optimization by a direct construction from the sorted Schmidt spectrum. We conjecture that the nonlocal stabilizer Rényi entropy (SRE) is given by the SRE of the corresponding reference state, and support this conjecture through analytical and numerical evidences. Our framework makes nonlocal nonstabilizerness efficiently accessible for weakly entangled many-body states whenever the entanglement spectrum is available. Applying it to Haar-random states, critical spin chains, and PXP dynamics, we show that nonlocal SRE captures nonstabilizer structures in the entanglement spectrum that are invisible to conventional entanglement measures. Our results establish entanglement spectra as a powerful window into irreducible nonstabilizer correlations, opening a broadly applicable route to studying nonlocal magic resources of quantum many-body systems in and out of equilibrium.

quant-ph↗

arXiv2026

Preparation of Fractional Quantum Hall States on Quantum Computers

The realization of fractional quantum Hall (FQH) states, characterized by fractional charge and intrinsic topological order, on quantum computers represents a central challenge at the interface of condensed matter physics and quantum information science. Current methods are grouped into two types: methods based on (quasi-)adiabatic evolution of complex parent Hamiltonians to yield target states, and circuit-based approaches for direct state preparation, which are confined to effectively one-dimensional systems near the thin cylinder or torus limit. We introduce a complementary scheme relying on direct quantum circuit construction, which works for arbitrary geometries. Specifically, we present a method to precisely prepare the $ν=1/3$ Laughlin state on the sphere geometry and demonstrate that it significantly reduces the required number of two-qubit gates and circuit depth, compared to variational quantum circuit approaches. In addition, we employ optimal control techniques to design control pulses for both superconducting and Rydberg atom platforms, identifying experimentally feasible protocols for state preparation. Our results provide an efficient and hardware-relevant pathway for realizing generic FQH states on both noisy intermediate-scale and fault-tolerant quantum devices.

quant-ph↗

arXiv2026

Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States

Magic, capturing the deviation of a quantum state from the stabilizer formalism, is a key resource underpinning the quantum advantage. The recently introduced stabilizer Rényi entropy (SRE) offers a tractable measure of magic, avoiding the complexity of conventional methods. We study SRE in translation-invariant matrix product states (MPS), deriving exact expressions for representative states and introducing a numerically stable algorithm, named bond-DMRG, to compute the SRE density in infinite systems. Applying this method, we obtain high-precision SRE densities for the ground state of the one-dimensional Ising model. We also analyze non-local SRE density, showing it is bounded by a universal function of entanglement entropy, and further prove that two-site mutual SRE vanishes asymptotically in injective MPS. Our work not only introduces a powerful method for extracting the SRE density in quantum many-body systems, but also numerically reveals a fundamental connection between magic and entanglement, thereby paving the way for deeper theoretical investigations into their interplay.

quant-ph↗

arXiv2026

Phase diagram of a dual-species Rydberg atom ladder

Dual-species Rydberg atom arrays extend single-species platforms by introducing competing interaction scales and enhanced quantum fluctuations, enabling phenomena beyond homogeneous settings. In this work, we study the ground-state phase diagram of a one-dimensional dual-species Rydberg atom ladder using large-scale density-matrix renormalization group calculations. We identify disordered phases, multiple ordered phases with $\mathbb{Z}_2$, $\mathbb{Z}_3$, and $\mathbb{Z}_4$ symmetry, as well as floating phases characterized by incommensurate wave vectors and algebraically decaying correlations. Importantly, we observe a smooth crossover between distinct $\mathbb{Z}_2$-ordered regimes, reflecting a reorganization of low-energy degrees of freedom rather than a true phase transition, which is absent in single-species Rydberg arrays. We further uncover a multi-critical point at the boundary between the $\mathbb{Z}_2 \otimes \mathbb{Z}_2$ and $\mathbb{Z}_3 \otimes \mathbb{Z}_3$ ordered phases, where Ising, chiral, and first-order transition lines intersect. Our results demonstrate that dual-species Rydberg atom arrays provide a unique platform for realizing crossover physics and multi-critical behavior inaccessible in single-species architectures.

cond-mat.quant-gas↗