arXiv subjects

Shuai Hou

Publications and source records attributed to Shuai Hou.

15 recordsLinked to original sources

arXiv2026

Aicir: A Full-Stack Quantum Circuit Simulator with AscendNPU Support

Quantum computing is a promising way to study problems that are difficult for classical methods, but current quantum hardware still faces limits in scale, noise, and fidelity. Running quantum algorithms on physical machines can also be costly. Quantum circuit simulators therefore remain important because they let researchers design and test algorithms on classical computers before using quantum hardware. Most high-performance simulators provide GPU backends, while few offer native support for NPUs. This gap limits the computing platforms available for quantum-algorithm research. We developed Aicir to provide a full-stack quantum circuit simulator with a native Huawei Ascend NPU backend. Aicir connects circuit construction, several state representations, measurement, differentiation, variational algorithms, quantum machine learning, and quantum architecture search through one programming model. It also supports noise simulation, tensor-network and matrix-product-state engines, and distributed state simulation. On the NPU, paired real tensors, fixed-rank gate views, and hardware-specific formulas keep the tested simulation paths on the device. The same representation lets Aicir partition a state across $2^{p}$ NPUs while retaining reverse-mode differentiation. We validated native execution with CPU fallback disabled and checked distributed communication and gradients on 2, 4, and 8 NPUs. For the tested fused layered circuits, Aicir's CPU runtime is within $0.97$--$1.28\times$ that of Qiskit Aer and $0.76$--$1.10\times$ that of Cirq. These results place its CPU execution in the same range as established simulators for this workload, while the NPU tests establish correct native execution rather than CPU-to-NPU speedup.

quant-ph↗

arXiv2026

Mock-pre-Lie bialgebras

In this paper, we systematically develop the theory of mock-pre-Lie bialgebras from multiple perspectives. We introduce the notion of a phase space of a mock-Lie algebra, and show that a mock-Lie algebra admits a phase space if and only if it is sub-adjacent to a mock-pre-Lie algebra. We introduce the notions of Manin triples of mock-pre-Lie algebras and mock-pre-Lie bialgebras, and prove the equivalences between mock-pre-Lie bialgebras, Manin triples of mock-pre-Lie algebras, certain matched pairs of mock-pre-Lie algebras, certain matched pairs of mock-Lie algebras and phase spaces of a mock-Lie algebra, which lays a theoretical foundation for subsequent research. Next, we investigate coboundary mock-pre-Lie bialgebras, and derive an analogue of the classical Yang-Baxter equation. In addition, we introduce two important special classes of mock-pre-Lie bialgebras: quasi-triangular mock-pre-Lie bialgebras and factorizable mock-pre-Lie bialgebras. We show that quasi-triangular mock-pre-Lie bialgebras naturally induce relative Rota-Baxter operators of weight -1. Finally, we provide a new perspective for the study of triangular and factorizable mock-pre-Lie bialgebras by introducing the concept of quadratic Rota-Baxter mock-pre-Lie algebras of arbitrary weight.

math.RA↗

arXiv2026

Equivariant Nijenhuis Lie Algebras: Extensions to Classical Lie-Theoretic Structures

We develop a theory of equivariant Nijenhuis Lie algebras (ENL algebras), namely Lie algebras equipped with Nijenhuis operators satisfying an equivariance condition with respect to the adjoint representation. This compatibility condition allows classical Lie bialgebra constructions to extend naturally to the operator-equipped setting. Within this framework, we define ENL bialgebras and establish the associated notions of matched pairs, Manin triples, and Drinfel'd doubles. We show that coboundary ENL bialgebras are characterized by EN $r$-matrices satisfying an equivariant classical Yang-Baxter equation. We further introduce EN-relative Rota-Baxter operators and prove that they provide an operator-theoretic realization of such $r$-matrices, leading to descendant ENL algebras and to solutions of the classical Yang-Baxter equation on semidirect ENL algebras. In the quadratic case, this construction recovers Rota-Baxter operators of weight zero. Finally, we extend the EN framework to pre-Lie algebras and show that pre-ENL algebras naturally induce associated ENL structures.

math.RA↗

arXiv2026

Sparsity-Aware Low-Rank Representation for Efficient Fine-Tuning of Large Language Models

Adapting large pre-trained language models to downstream tasks often entails fine-tuning millions of parameters or deploying costly dense weight updates, which hinders their use in resource-constrained environments. Low-rank Adaptation (LoRA) reduces trainable parameters by factorizing weight updates, yet the underlying dense weights still impose high storage and computation costs. Magnitude-based pruning can yield sparse models but typically degrades LoRA's performance when applied naively. In this paper, we introduce SALR (Sparsity-Aware Low-Rank Representation), a novel fine-tuning paradigm that unifies low-rank adaptation with sparse pruning under a rigorous mean-squared-error framework. We prove that statically pruning only the frozen base weights minimizes the pruning error bound, and we recover the discarded residual information via a truncated-SVD low-rank adapter, which provably reduces per-entry MSE by a factor of $(1 - r/\min(d,k))$. To maximize hardware efficiency, we fuse multiple low-rank adapters into a single concatenated GEMM, and we adopt a bitmap-based encoding with a two-stage pipelined decoding + GEMM design to achieve true model compression and speedup. Empirically, SALR attains 50\% sparsity on various LLMs while matching the performance of LoRA on GSM8K and MMLU, reduces model size by $2\times$, and delivers up to a $1.7\times$ inference speedup.

cs.LG↗

arXiv2025

Reynolds Lie bialgebras

In this paper, we establish a bialgebra theory for Reynolds Lie algebras. First we introduce the notion of a quadratic Reynolds Lie algebra and show that it induces an isomorphism from the adjoint representation to the coadjoint representation. Then we introduce the notion of matched pairs, Manin triples and bialgebras for Reynolds Lie algebras, and show that Manin triples, bialgebras and certain matched pairs of Reynolds Lie algebras are equivalent. In particular, we introduce the notion of a Reynolds operator on a quadratic Rota-Baxter Lie algebra which can induce a Reynolds Lie bialgebra naturally. Finally, we introduce the notion of the classical Yang-Baxter equation in a Reynolds Lie algebra whose solutions give rise to Reynolds Lie bialgebras. We also introduce the notion of relative Rota-Baxter operators on a Reynolds Lie algebra and Reynolds pre-Lie algebras, and construct solutions of the classical Yang-Baxter equation in terms of relative Rota-Baxter operators and Reynolds pre-Lie algebras.

math.RA↗

arXiv2023

Quantum Computing for MIMO Beam Selection Problem: Model and Optical Experimental Solution

Massive multiple-input multiple-output (MIMO) has gained widespread popularity in recent years due to its ability to increase data rates, improve signal quality, and provide better coverage in challenging environments. In this paper, we investigate the MIMO beam selection (MBS) problem, which is proven to be NP-hard and computationally intractable. To deal with this problem, quantum computing that can provide faster and more efficient solutions to large-scale combinatorial optimization is considered. MBS is formulated in a quadratic unbounded binary optimization form and solved with Coherent Ising Machine (CIM) physical machine. We compare the performance of our solution with two classic heuristics, simulated annealing and Tabu search. The results demonstrate an average performance improvement by a factor of 261.23 and 20.6, respectively, which shows that CIM-based solution performs significantly better in terms of selecting the optimal subset of beams. This work shows great promise for practical 5G operation and promotes the application of quantum computing in solving computationally hard problems in communication.

cs.NI↗

arXiv2023

Deformations and cohomologies of embedding tensors on 3-Lie algebras

In this paper, first we introduce the notion of an embedding tensor on a 3-Lie algebra, which naturally induces a 3-Leibniz algebra. Using the derived bracket, we construct a Lie 3-algebra, whose Maurer-Cartan elements are embedding tensors. Consequently, we obtain the $L_{\infty}$-algebra that governs deformations of embedding tensors. We define the cohomology theory for embedding tensors on 3-Lie algebras. As applications, we show that if two formal deformations of an embedding tensor on a 3-Lie algebra are equivalent, then their infinitesimals are in the same cohomology class in the second cohomology group. Moreover, an order n deformation of an embedding tensor is extendable if and only if the obstruction class, which is in the third cohomology group, is trivial.

math.RA↗

arXiv2022

$3$-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras

In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras and $3$-post-Lie algebras. A 3-post-Lie algebra consists of a 3-Lie algebra structure and a ternary operation such that some compatibility conditions are satisfied. We show that a relative Rota-Baxter operator of nonzero weight induces a $3$-post-Lie algebra naturally. Conversely, a $3$-post-Lie algebra gives rise to a new 3-Lie algebra, which is called the subadjacent 3-Lie algebra, and an action on the original 3-Lie algebra. Then we construct an $L_\infty$-algebra whose Maurer-Cartan elements are relative Rota-Baxter operators of nonzero weight. Consequently, we obtain the twisted $L_\infty$-algebra that controls deformations of a given relative Rota-Baxter operator of nonzero weight on 3-Lie algebras. Finally, we introduce a cohomology theory for a relative Rota-Baxter operator of nonzero weight on $3$-Lie algebras and use the second cohomology group to classify infinitesimal deformations.

math.RA↗

arXiv2022

Cohomology and the controlling algebra of crossed homomorphisms on 3-Lie algebras

In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a Lie algebra to the semidirect product Lie algebra. We also establish the relationship between crossed homomorphisms and relative Rota-Baxter operators of weight 1 on 3-Lie algebras. Next we construct a cohomology theory for a crossed homomorphism on 3-Lie algebras and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Finally, using the higher derived brackets, we construct an $L_\infty$-algebra whose Maurer-Cartan elements are crossed homomorphisms. Consequently, we obtain the twisted $L_\infty$-algebra that controls deformations of a given crossed homomorphism on 3-Lie algebras.

math.RA↗

arXiv2022

Deformations, cohomologies and abelian extensions of compatible $3$-Lie algebras

In this paper, first we give the notion of a compatible $3$-Lie algebra and construct a bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible $3$-Lie algebras. We also obtain the bidifferential graded Lie algebra that governs deformations of a compatible $3$-Lie algebra. Then we introduce a cohomology theory of a compatible $3$-Lie algebra with coefficients in itself and show that there is a one-to-one correspondence between equivalent classes of infinitesimal deformations of a compatible $3$-Lie algebra and the second cohomology group. We further study 2-order 1-parameter deformations of a compatible $3$-Lie algebra and introduce the notion of a Nijenhuis operator on a compatible $3$-Lie algebra, which could give rise to a trivial deformation. At last, we introduce a cohomology theory of a compatible $3$-Lie algebra with coefficients in arbitrary representation and classify abelian extensions of a compatible $3$-Lie algebra using the second cohomology group.

math.RA↗

arXiv2021

Reynolds $n$-Lie algebras and NS-$n$-Lie algebras

In this paper, first we introduce the notion of a Reynolds operator on an $n$-Lie algebra and illustrate the relationship between Reynolds operators and derivations on an $n$-Lie algebra. We give the cohomology theory of Reynolds operators on an $n$-Lie algebra and study infinitesimal deformations of Reynolds operators using the second cohomology group. Then we introduce the notion of NS-$n$-Lie algebras, which are generalizations of both $n$-Lie algebras and $n$-pre-Lie algebras. We show that an NS-$n$-Lie algebra gives rise to an $n$-Lie algebra together with a representation on itself. Reynolds operators and Nijenhuis operators on an $n$-Lie algebra naturally induce NS-$n$-Lie algebra structures. Finally, we construct Reynolds $(n+1)$-Lie algebras and Reynolds $3$-Lie algebras from Reynolds $n$-Lie algebras and Reynolds commutative associative algebras respectively.

math-ph↗

arXiv2021

Twisted Rota-Baxter operators on 3-Lie algebras and NS-3-Lie algebras

In this paper, first we introduce the notion of a twisted Rota-Baxter operator on a 3-Lie algebra $\g$ with a representation on $V$. We show that a twisted Rota-Baxter operator induces a 3-Lie algebra structure on $V$, which represents on $\g$. By this fact, we define the cohomology of a twisted Rota-Baxter operator and study infinitesimal deformations of a twisted Rota-Baxter operator using the second cohomology group. Then we introduce the notion of an NS-3-Lie algebra, which produces a 3-Lie algebra with a representation on itself. We show that a twisted Rota-Baxter operator induces an NS-3-Lie algebra naturally. Thus NS-3-Lie algebras can be viewed as the underlying algebraic structures of twisted Rota-Baxter operators on 3-Lie algebras. Finally we show that a Nijenhuis operator on a 3-Lie algebra gives rise to a representation of the deformed 3-Lie algebra and a 2-cocycle. Consequently, the identity map will be a twisted Rota-Baxter operator on the deformed 3-Lie algebra. We also introduce the notion of a Reynolds operator on a 3-Lie algebra, which can serve as a special case of twisted Rota-Baxter operators on 3-Lie algebras.

math.RA↗

arXiv2020

Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators

In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an $L_\infty$-algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras by twisting. In particular, we recover the Lie $3$-algebra whose Maurer-Cartan elements are O-operators (also called relative Rota-Baxter operators) on 3-Lie algebras. Then we introduce the notion of generalized matched pairs of 3-Lie algebras using generalized representations of 3-Lie algebras, which will give rise to twilled 3-Lie algebras. The usual matched pairs of 3-Lie algebras correspond to a special class of twilled 3-Lie algebras, which we call strict twilled 3-Lie algebras. Finally, we use O-operators to construct explicit twilled 3-Lie algebras, and explain why an $r$-matrix for a 3-Lie algebra can not give rise to a double construction 3-Lie bialgebra. Examples of twilled 3-Lie algebras are given to illustrate the various interesting phenomenon.

math.RA↗

arXiv2019

3-Lie bialgebras and 3-pre-Lie algebras induced by involutive derivations

In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if $A$ is an $m$-dimensional 3-Lie algebra with an involutive derivation $D$, then there exists a compatible 3-pre-Lie algebra $(A, \{ , , , \}_D)$ such that $A$ is the sub-adjacent 3-Lie algebra, and there is a local cocycle $3$-Lie bialgebraic structure on the $2m$-dimensional semi-direct product 3-Lie algebra $A\ltimes_{ad^*} A^*$, which is associated to the adjoint representation $(A, ad)$. By means of involutive derivations, the skew-symmetric solution of the 3-Lie classical Yang-Baxter equation in the 3-Lie algebra $A\ltimes_{ad^*}A^*$, a class of 3-pre-Lie algebras, and eight and ten dimensional local cocycle 3-Lie bialgebras are constructed.

math.RA↗

arXiv2019

Manin triples of 3-Lie algebras induced by involutive derivations

For any $n$-dimensional 3-Lie algebra $A$ over a field of characteristic zero with an involutive derivation $D$, we investigate the structure of the 3-Lie algebra $B_1=A\ltimes_{ad^*} A^* $ associated with the coadjoint representation $(A^*, ad^*)$. We then discuss the structure of the dual 3-Lie algebra $B_2$ of the local cocycle 3-Lie bialgebra $(A\ltimes_{ad^*} A^*, Δ)$. By means of the involutive derivation $D$, we construct the $4n$-dimensional Manin triple $(B_1\oplus B_2,$ $ [ \cdot, \cdot, \cdot]_1,$ $ [ \cdot, \cdot, \cdot]_2,$ $ B_1, B_2)$ of 3-Lie algebras, and provide concrete multiplication in a special basis $Π_1\cupΠ_2$. We also construct a sixteen dimensional Manin triple $(B, [ \cdot, \cdot, \cdot])$ with $\dim B^1=12$ using an involutive derivation on a four dimensional 3-Lie algebra $A$ with $\dim A^1=2$.

math.RA↗