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Since Edwin Halls groundbreaking discovery of the Hall effect in 1879, magnetism, spin, and quantization have been expanding the scope of Hall effects, continuously driving transformative progress in science and technology. Among them, the latest nonlinear Hall effect (NLHE), where longitudinal electric field tunes quantum geometry to generate nonlinear Hall voltage, attracts wide attention as a sensitive probe of topological phases across a wide range of materials. Here, we report a new Hall effect member: the magnetic nonlinear Hall effect (MNLHE), characterized by a quadratic Hall conductivity dependence on magnetic field, rather than electric field as in NLHE. This finding relies on an altermagnet, Mn5Si3 thin film, whose alternating-sign Berry curvatures ensure higher-order MNLHE clearly distinguishable from the first-order anomalous Hall effect. The observed quadratic dependence originates from chiral next-nearest-neighbor hopping processes that acquire magnetic-exchange-driven Zeeman energies and Haldane-like chiral flux phases. Remarkably, this MNLHE is non-analytic, as reversing the magnetic field flips the alternating spin-splitting bands and reverses the hopping chirality, which is absent in traditional NLHE. Beyond offering a distinctive transport fingerprint for altermagnet Mn5Si3 thin film, this MNLHE is large and unsaturated up to 60 T, providing opportunities for pulsed high-field sensing technologies in both fundamental researches and engineering applications., Comment: 27 pages, 4 figures

Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating hardware limitations, pinpointing hardware defects, and detecting rare events. However, current methods for decoding repetition codes under circuit level noise are suboptimal, leading to inaccurate error correction thresholds and introducing additional errors in event detection. In this work, we establish that repetition code under circuit level noise has an exact solution, and we propose an optimal maximum likelihood decoding algorithm called planar. The algorithm is based on the exact solution of the spin glass partition function on planar graphs and has polynomial computational complexity. Through extensive numerical experiments, we demonstrate that our algorithm uncovers the exact threshold for depolarizing noise and realistic superconductor SI1000 noise. Furthermore, we apply our method to analyze data from recent quantum memory experiments conducted by Google Quantum AI, revealing that part of the error floor was attributed to the decoding algorithm used by Google. Finally, we implemented the repetition code quantum memory on superconducting systems with a 72-qubit quantum chip lacking reset gates, demonstrating that even with an unknown error model, the proposed algorithm achieves a significantly lower logical error rate than the matching-based algorithm.

The emerging altermagnetic RuO2 with both compensated magnetic moments and broken time-reversal symmetry possesses nontrivial magneto-electronic responses and nonrelativistic spin currents, which are closely related to magnetic easy axis. To probe the N\'eel order in RuO2, we conducted Ru M3-edge X-ray magnetic linear dichroism (XMLD) measurement. For epitaxial RuO2 films, characteristic XMLD signals can be observed in either RuO2(100) and RuO2(110) at normal incidence or RuO2(001) at oblique incidence, and the signals disappear when test temperature exceeds N\'eel temperature. For nonepitaxial RuO2 films, the flat lines in the XMLD patterns of RuO2(100) and RuO2(110) demonstrate that there is no in-plane uniaxial alignment of N\'eel order in these samples, due to the counterbalanced N\'eel order of the twin crystals evidenced by X-ray diffraction phi-scan measurements. Our experimental results unambiguously demonstrate the antiferromagnetism in RuO2 films and reveal the spatial relation of N\'eel order to be parallel with RuO2 [001] crystalline axis. These research findings would deepen our understanding of RuO2 and other attractive altermagnetic materials applied in the field of spintronics., Comment: 16 pages, 4 figures

Due to nonrelativistic altermagnetic spin splitting effect (ASSE), altermagnets can generate time-reversal-odd spin current and spin splitting torque (SST) with spin polarization parallel to the N\'eel vector. Hence the effective manipulation of SST would provide plenty of opportunities for designable spintronic devices, which remains elusive. Here, the electrical control of SST is achieved in altermagnetic RuO2, based on controllable N\'eel vector of RuO2 and N\'eel vector-dependent generation of SST. We demonstrate the current-induced switching of N\'eel vector via spin-orbit torque in RuO2 films, according to the reversible polarity of electrical transport measurements and X-ray magnetic linear dichroism (XMLD). The XMLD also unprecedentedly demonstrates that N\'eel vector really exists in altermagnets. The switching of N\'eel vector to the current direction and resultantly enhanced spin polarization parallel to the N\'eel vector brings about stronger ASSE-induced spin current. Our findings not only enrich the properties of altermagnets but also pave the way for high speed memories and nano-oscillators with excellent controllability and efficiency., Comment: 22 pages, 3 figures

Lithium superionic conductors (LSICs) are crucial for next-generation solid-state batteries, offering exceptional ionic conductivity and enhanced safety for renewable energy and electric vehicles. However, their discovery is extremely challenging due to the vast chemical space, limited labeled data, and the understanding of complex structure-function relationships required for optimizing ion transport. This study introduces a multiscale topological learning (MTL) framework, integrating algebraic topology and unsupervised learning to tackle these challenges efficiently. By modeling lithium-only and lithium-free substructures, the framework extracts multiscale topological features and introduces two topological screening metrics-cycle density and minimum connectivity distance-to ensure structural connectivity and ion diffusion compatibility. Promising candidates are clustered via unsupervised algorithms to identify those resembling known superionic conductors. For final refinement, candidates that pass chemical screening undergo ab initio molecular dynamics simulations for validation. This approach led to the discovery of 14 novel LSICs, four of which have been independently validated in recent experiments. This success accelerates the identification of LSICs and demonstrates broad adaptability, offering a scalable tool for addressing complex materials discovery challenges., Comment: 15 pages and 4 figures

Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the development of accelerated methods that leverage sophisticated models and harness the power of advanced computational hardware. Despite the advancements, a critical challenge persists, the dual demand for both high efficiency and broad generality in solving problems. In this work, we propose a general method, Free-Energy Machine (FEM), based on the ideas of free-energy minimization in statistical physics, combined with automatic differentiation and gradient-based optimization in machine learning. The algorithm is flexible, solving various combinatorial optimization problems using a unified framework, and is efficient, naturally utilizing massive parallel computational devices such as graph processing units (GPUs) and field-programmable gate arrays (FPGAs). We benchmark our algorithm on various problems including the maximum cut problems, balanced minimum cut problems, and maximum $k$-satisfiability problems, scaled to millions of variables, across both synthetic, real-world, and competition problem instances. The findings indicate that our algorithm not only exhibits exceptional speed but also surpasses the performance of state-of-the-art algorithms tailored for individual problems. This highlights that the interdisciplinary fusion of statistical physics and machine learning opens the door to delivering cutting-edge methodologies that will have broad implications across various scientific and industrial landscapes., Comment: Comments are welcome!

Two-dimensional (2D) hybrid organic-inorganic perovskite (HOIP) demonstates great potential for developing flexible and wearable spintronic devices, by serving as spin sources via the bulk Rashba effect (BRE). However, the practical application of BRE in 2D HOIP faces huge challenges, particularly due to the toxicity of lead, which is crucial for achieving large spin-orbit coupling, and the restrictions in 2D HOIP candidates to meet specific symmetry-breaking requirements. To overcome these obstacles, we design a strategy to exploit the interfacial Rashba effect (IRE) of lead-free 2D HOIP (C6H5CH2CH2NH3)2CuCl4 (PEA-CuCl), manifesting as an efficient spin generator at room temperature. IRE of PEA-CuCl originates from the large orbital hybridization at the interface between PEA-CuCl and adjacent ferromagnetic layers. Spin-torque ferromagnetic resonance measurements further quantify a large Rashba effective field of 14.04 Oe per 10^11 A m-2, surpassing those of lead-based HOIP and traditional all-inorganic heterojunctions with noble metals. Our lead-free 2D HOIP PEA-CuCl, which harnesses large IRE for spin generation, is efficient, nontoxic, and economic, offering huge promise for future flexible and wearable spintronic devices.

Quantum anomalous Hall (QAH) effect provides dissipationless chiral channels for spin transport, expected as an outstanding candidate in future low-power quantum computation. The spin-splitting band structure is vital for obtaining QAH effect in topological systems, with ferromagnetism indispensable to manipulate the Chern number. Herein, we challenge this wisdom by proposing tunable QAH effect in spin-splitting antiferromagnets with zero magnetization. Since the spin splitting of these unique magnets originates from the alternate crystal environment, the Chern number can be modulated not only by the conventional magnetic order, but also by the crystal order, opening an additional dimension for tuning QAH effect. Our concept is illustrated based on two-dimensional (2D) MnBi2Te4 (MBT) with even septuple layers (SLs), a typical axion insulator with fully magnetic compensation. By interlayer rotation and translation operations, sublattices of MBT with opposite magnetizations are no longer connected by inversion or mirror symmetries, leading to the transition to the QAH insulator. The flexible stacking of 2D materials enables the reversible Chern number by crystal design. Our work fundamentally reveals the crystal-order-dependent QAH effect in spin-splitting antiferromagnets, which would advance QAH effect-based devices towards high controllability, integration density and operation speed., Comment: 22 pages, 4 figures

Transition metal dichalcogenides (TMDCs) possess valley pseudospin, allowing photon spin to be coupled to electron spin and enabling initialization and readout of both classical and quantum information. Rapid valley-dephasing processes have impeded the development of scalable, high-performance valleytronic devices operating at room temperature. Here we demonstrate that a chiral resonant metasurface can enable room-temperature valley-selective emission, even with linearly polarized excitation. This platform provides circular eigen-polarization states with a high quality factor (Q-factor) and strong chiral near-field enhancement, resulting in unitary emission circular dichroism (i.e. single-handed circularly polarized emission). Our fabricated Si chiral metasurfaces exhibit chiral electromagnetic modes with Q-factors up to 450 at visible wavelengths, spectrally tuned to the exciton energy of MoSe2 monolayers. Using spatially- and spectrally-resolved mapping from temperatures of 100 K to 294 K, we demonstrate degrees of circular polarization (DOP) reaching a record high of 0.5 at room temperature. Reciprocal space mapping of the exciton emission reveals the chiral q-BIC localizes valley-selective emission in the vicinity of the photonic gamma-point. Photon-spin and time-resolved photoluminescence measurements show that the high DOP can be attributed to the significantly increased chiroptical local density of states provided by the metasurface, which enhances valley-specific radiative transition rates by a factor of approximately 13, with lifetimes as short as 189 ps. Our work could facilitate the development of compact chiral classical and quantum light sources and the creation of molecular chiral polaritons for quantum enantioselective synthesis.

The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for $W$-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a distinct set of master integrals (MIs), totaling $27$, $45$ and $15$, respectively. These MIs are analytically calculated using the method of differential equations, with solutions expanded as Taylor series in the dimensional regulator $\epsilon$. For the first two family branches, the differential systems can be successfully transformed into canonical form by adopting appropriate bases of MIs. This enables the MIs of these family branches to be expressed either as Goncharov polylogarithms (GPLs) or as one-fold integrals over GPLs, up to $\mathcal{O}(\epsilon^4)$. In contrast, the differential system for the third family branch can only be cast into a form linear in $\epsilon$ due to the presence of elliptic integrals. The solution to this linear-form differential system is expressed in an iterated form owing to the strictly lower-triangular structure of the coefficient matrices at $\epsilon = 0$. Our analytic expressions for these MIs are verified with high accuracy against the numerical results from the \texttt{AMFlow} package., Comment: 39 pages, 4 figures

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group-subgroup chains is presented. The canonical U(4)->U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4)->SU_S(2)xSU_T(2) coupling coefficients are more specific to nuclear structure studies that utilize Wigner's Supermultiplet Symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series, and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S,T) pair within a single U(4) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators; while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N). It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the \textit{canonical} and the \textit{physical} group-subgroup chains of U(4).

Quantum Computational Superiority boasts rapid computation and high energy efficiency. Despite recent advances in classical algorithms aimed at refuting the milestone claim of Google's sycamore, challenges remain in generating uncorrelated samples of random quantum circuits. In this paper, we present a groundbreaking large-scale system technology that leverages optimization on global, node, and device levels to achieve unprecedented scalability for tensor networks. This enables the handling of large-scale tensor networks with memory capacities reaching tens of terabytes, surpassing memory space constraints on a single node. Our techniques enable accommodating large-scale tensor networks with up to tens of terabytes of memory, reaching up to 2304 GPUs with a peak computing power of 561 PFLOPS half-precision. Notably, we have achieved a time-to-solution of 14.22 seconds with energy consumption of 2.39 kWh which achieved fidelity of 0.002 and our most remarkable result is a time-to-solution of 17.18 seconds, with energy consumption of only 0.29 kWh which achieved a XEB of 0.002 after post-processing, outperforming Google's quantum processor Sycamore in both speed and energy efficiency, which recorded 600 seconds and 4.3 kWh, respectively.

Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical simulation time and challenged the claim of the first-generation quantum advantage experiments. However, in terms of generating uncorrelated samples, time-to-solution, and energy consumption, previous classical simulation experiments still underperform the \textit{Sycamore} processor. Here we report an energy-efficient classical simulation algorithm, using 1432 GPUs to simulate quantum random circuit sampling which generates uncorrelated samples with higher linear cross entropy score and is 7 times faster than \textit{Sycamore} 53 qubits experiment. We propose a post-processing algorithm to reduce the overall complexity, and integrated state-of-the-art high-performance general-purpose GPU to achieve two orders of lower energy consumption compared to previous works. Our work provides the first unambiguous experimental evidence to refute \textit{Sycamore}'s claim of quantum advantage, and redefines the boundary of quantum computational advantage using random circuit sampling., Comment: This work was completed on August 2023. A further 50x improvement has been achieved and will be posted on arXiv shortly

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3)->SO(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and hence provides faster and more accurate output of requested results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Arne Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. A C++ library built on this new methodology will be published in a complementary journal that specializes in the management and distribution of such programs.

Electrical-controllable antiferromagnet tunnel junction is a key goal in spintronics, holding immense promise for ultra-dense and ultra-stable antiferromagnetic memory with high processing speed for modern information technology. Here, we have advanced towards this goal by achieving an electrical-controllable antiferromagnet-based tunnel junction of Pt/Co/Pt/Co/IrMn/MgO/Pt. The exchange coupling between antiferromagnetic IrMn and Co/Pt perpendicular magnetic multilayers results in the formation of interfacial exchange bias and exchange spring in IrMn. Encoding information states 0 and 1 is realized through the exchange spring in IrMn, which can be electrically written by spin-orbit torque switching with high cyclability and electrically read by antiferromagnetic tunneling anisotropic magnetoresistance. Combining spin-orbit torque switching of both exchange spring andexchange bias, 16 Boolean logic operation is successfully demonstrated. With both memory and logic functionalities integrated into our electrical-controllable antiferromagnetic-based tunnel junction, we chart the course toward high-performance antiferromagnetic logic-in-memory., Comment: 20 pages, 4 figures

Anomalous Nernst effect (ANE), a widely investigated transverse thermoelectric effect that converts waste heat into electrical energy with remarkable flexibility and integration capability, has been extended to antiferromagnets with non-collinear spin texture recently. ANE in compensated magnet with collinear N\'eel vector will bring more opportunities to construct magnetic-field-immune and ultrafast transverse thermoelectric converters, but remains unachieved for long. It is due to the degenerated band structure of traditional collinear compensated magnet excludes non-zero Berry curvature. Here, we realize non-volatile ANE in altermagnet Mn5Si3 thin film with collinear Neel vector, whose unique alternating spin-splitting band structure plays vital role in creating non-zero Berry curvature and hotpots of anomalous Nernst conductivity near band intersections. Interestingly, ANE is relatively weak in stoichiometric Mn5Si3, but undergoes a sixfold enhancement through strategically raising the Fermi level by additional Mn doping, indicating sensitive intrinsic influence from specific location of the Fermi level on ANE in altermagnet. Moreover, our investigation reveals a unique Neel-vector-dependent temperature-scaling relationship of anomalous Nernst conductivity in Mn5Si3. Our work not only fills a longstanding gap by confirming the presence of non-volatile ANE in collinear compensated magnet, but also enlightens thermoelectric physics related to exotic spin-splitting band structure in altermagnet., Comment: 25 pages, 4 figures

We introduce the spin dissymmetry factor, a measure of the spin-selectivity in the optical transition rate of quantum particles. This spin dissymmetry factor is valid locally, including at material interfaces and within optical cavities. We design and numerically demonstrate an optical cavity with three-fold rotational symmetry that maximizes spin dissymmetry, thereby minimizing the spin dephasing of a cavity-coupled quantum particle. Our approach emphasizes the difference between spin and chirality in the nearfield and reveals a classical parameter for designing more efficient quantum optical devices., Comment: 11 pages, 1 figure, 1 table

Symmetry plays a fundamental role in condensed matter. The unique entanglement between magnetic sublattices and alternating crystal environment in altermagnets provides a unique opportunity for designing magnetic space symmetry. There have been extensive experimental efforts concentrated on tuning the Neel vector to reconstruct altermagnetic symmetry. However, it remains challenging to modulate the altermagnetic symmetry through the crystal aspect. Here, the crystal design of altermagnetism is successfully realized, by breaking glide mirrors and magnetic mirrors of the (0001) crystallographic plane in CrSb films via crystal distortion. We establish a locking relationship between altermagnetic symmetry and the emergent Dzyaloshinskii-Moriya (DM) vectors in different CrSb films, realizing unprecedentedly room-temperature spontaneous anomalous Hall effect in an altermagnetic metal. The concept of exchange-coupling torques is broadened to include both antiferromagnetic exchange-coupling torque and DM torque. Their relationship is designable, determining electrical manipulation modes, e.g., field-assisted switching for CrSb(1-100)/Pt and field-free switching for W/CrSb(11-20). Particularly, the unprecedentedly field-free 100-percent switching of Neel vectors is realized by making these two torques parallel or antiparallel, dependent on Neel vector orientation. Besides unravelling the rich mechanisms for electrical manipulation of altermagnetism rooted in broadened concept of exchange-coupling torques, we list other material candidates and propose that crystal design of altermagnetism would bring rich designability to magnonics, topology, etc., Comment: 23 pages, 4 figures

Antiferromagnetic spintronics have attracted wide attention due to its great potential in constructing ultra-dense and ultra-fast antiferromagnetic memory that suits modern high-performance information technology. The electrical 180o switching of N\'eel vector is a long-term goal for developing electrical-controllable antiferromagnetic memory with opposite N\'eel vectors as binary "0" and "1". However, the state-of-art antiferromagnetic switching mechanisms have long been limited for 90o or 120o switching of N\'eel vector, which unavoidably require multiple writing channels that contradicts ultra-dense integration. Here, we propose a deterministic switching mechanism based on spin-orbit torque with asymmetric energy barrier, and experimentally achieve electrical 180o switching of spin-splitting antiferromagnet Mn5Si3. Such a 180o switching is read out by the N\'eel vector-induced anomalous Hall effect. Based on our writing and readout methods, we fabricate an antiferromagnet device with electrical-controllable high and low resistance states that accomplishes robust write and read cycles. Besides fundamental advance, our work promotes practical spin-splitting antiferromagnetic devices based on spin-splitting antiferromagnet., Comment: 19 pages, 4 figures

We present a comprehensive analytic calculation of the next-to-next-to-leading order $\text{QCD} \otimes \text{EW}$ corrections to $Z$-boson pair production at electron-positron colliders. The two-loop master integrals essential to this calculation are evaluated using the differential equation method. In this work, we detail the formulation and solution of the canonical differential equations for the two-loop three-point master integrals with two on-shell $Z$-boson external legs and a massive internal quark in the loops. These canonical master integrals are systematically expanded as Taylor series in the dimensional regulator, $\epsilon = (4-d)/2$, up to the order of $\epsilon^4$, with coefficients expressed in terms of Goncharov polylogarithms up to weight four. Upon applying our analytic expressions of these master integrals to the phenomenological analysis of $Z$-pair production, we observe that the $\mathcal{O}(\alpha \alpha_s)$ corrections manifest at a level of approximately one percent compared to the leading-order predictions, underscoring their significance for comparisons with future high-precision experimental data., Comment: 29 pages, 5 figures