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Yuanyang Zhou

Publications and source records attributed to Yuanyang Zhou.

17 recordsLinked to original sources
arXiv2026

Engineered dissipation for faster adiabatic state preparation

Adiabatic state preparation is often slowed by nonadiabatic leakage near small spectral gaps. We propose an engineered dissipative protocol that uses a filtered reservoir to induce predominantly downward transitions in the instantaneous energy eigenbasis while leaving the instantaneous ground state dark. The leaked population generated by nonadiabatic driving is therefore continuously relaxed back toward the low-energy sector. An effective avoided-crossing analysis shows that in the regime where the engineered relaxation strength is much larger than the minimum gap, the runtime scaling can improve from the closed-system behavior $\mathcal{O}(\Delta^{-2})$ to $\mathcal{O}(\Delta^{-1})$ Finite-temperature upward transitions introduce a thermal error floor, but the enhancement survives when this heating rate remains below the target error tolerance. Numerical results show improved ground-state preparation over closed-system annealing. We also discuss a possible superconducting-circuit implementation using structured bosonic reservoirs.

quant-ph↗
arXiv2026

Extensions of inertial blocks

In this paper, with suitable assumptions, we generalize the work of K\"ulshammer and Puig on extensions of nilpotent blocks to inertial blocks.

math.GR↗
arXiv2026

Blocks with only one irreducible Brauer character orbit

In this paper, we confirm the Kessar-Linckelmann conjecture for blocks with abelian defect groups. More generally, we prove that if a covered block with abelian defect groups has its irreducible Brauer characters forming a single orbit under the block stabilizer, then the covering block is inertial; we term these blocks with a single irreducible Brauer character orbit. Consequently, we establish Brou\'e's abelian defect conjecture for such blocks. As a byproduct, we show that blocks of finite quasisimple groups with a single irreducible Brauer character orbit necessarily have abelian defect groups. As applications, we verify the blockwise Alperin weight conjecture for blocks with a unique irreducible Brauer character and prove Puig's long-standing conjecture in full generality. All results rely essentially on the Classification of finite simple groups.

math.GR↗
arXiv2026

Inertial 2-blocks with abelian defect groups

L. Puig defined inertial blocks. In this paper, we prove that 2-blocks with defect group $C_{2^{n_1}}\times C_{2^{n_2}}\times...\times C_{2^{n_t}}$ are inertial, where $n_i\geq 2$ for all $i$.

math.GR↗
arXiv2026

Hyperfocal subalgebras of hyperfocal abelian Frobenius blocks

In this paper, we introduce a class of blocks which is called hyperfocal abelian Frobenius blocks.This class of blocks is an analogous version of the block with abelian defect group and Frobenius inertial quotient at hyperfocal level and includes the blocks with Klein four hyperfocal subgroups and cyclic hyperfocal subgroups. We show that there is a stable equivalence of Morita type between the hyperfocal subalgebras of the hyperfocal abelian Frobenius blocks and a group algebra of a Frobenius group associated with the hyperfocal subgroup of the block. As applications, we can partially describe some structures of the blocks with Klein four hyperfocal subgroups and cyclic hyperfocal subgroups,such as the structures of their hyperfocal subalgebras in terms of derived categories and the structures of their characters. As a consequence, we show that Broue's abelian defect group conjecture holds for blocks with Klein four hyperfocal subgroups.

math.GR↗
arXiv2025

A reduction theorem for the blockwise Navarro Alperin weight conjecture via H-triples

The Galois Alperin weight (GAW) conjecture has been reduced to the inductive GAW condition for simple groups. We proceed in two steps to refine this reduction. First, we propose the blockwise Galois Alperin weight (BGAW) conjecture and define its associated inductive BGAW condition. Second, assuming the inductive GAW (respectively, BGAW) condition for simple groups, we establish a stronger version of the GAW (respectively, BGAW) conjecture in terms of central (respectively, block) isomorphism of H-triples.

math.GR↗
arXiv2024

Variational quantum compiling for three-qubit gates design in quantum dots

Semiconductor quantum dots offer a promising platform for controlling spin qubits and realizing quantum logic gates, essential for scalable quantum computing. In this work, we utilize a variational quantum compiling algorithm to design efficient three-qubit gates using a time-independent Hamiltonian composed of only physical interaction terms. The resulting gates, including the Toffoli and Fredkin gates, demonstrate high fidelity and robustness against both coherent and incoherent noise sources, including charge and nuclear spin noise. This method is applicable to a wide range of physical systems, such as superconducting qubits and trapped ions, paving the way for more resilient and universal quantum computing architectures.

quant-ph↗
arXiv2023

A reduction theorem for the Navarro Alperin weight conjecture

The Alperin weight conjecture has been reduced to simple groups by Navarro and Tiep. In this paper, we investigate the Navarro Alperin weight conjecture, which includes Galois automorphisms and group automorphisms in comparison with the original version, and give a reduction to simple groups. As an application, we prove the conjecture for the finite groups with abelian Sylow 2-subgroups.

math.RT↗
arXiv2018

Blocks with the hyperfocal subgroup $Z_{2^n}\times Z_{2^n}$

In this paper, we calculate the numbers of irreducible ordinary characters and irreducible Brauer characters in a block of a finite group $G$, whose associated fusion system over a 2-subgroup $P$ of $G$ (which is a defect group of the block) has the hyperfocal subgroup $\mathbb Z_{2^n}\times \mathbb Z_{2^n}$ for some $n\geq 2$, when the block is controlled by the normalizer $N_G(P)$ and the hyperfocal subgroup is contained in the center of $P$, or when the block is not controlled by $N_G(P)$ and the hyperfocal subgroup is contained in the center of the unique essential subgroup in the fusion system. In particular, Alperin's weight conjecture holds in the considered cases.

math.GR↗
arXiv2018

Finite groups with odd Sylow automizers

Let $p$ be an odd prime number. In this paper, we characterize the nonabelian composition factors of a finite group with odd $p$-Sylow automizers, and then prove that the McKay conjecture, the Alperin weight conjecture and the Alperin-McKay conjecture hold for such group.

math.GR↗
arXiv2013

A remark on Rickard complexes

In this paper, we characterize a Rickard complex, which induces a Rickard equivalence between the block algebras of a block $b$ and its Brauer correspondent and whose vertices have the same order as defect groups of the block $b$. The homology of such a Rickard complex vanishes at all degree but degree $q$, and the homology at degree $q$ induces a basic Morita equivalence between the block algebras in the sense of Puig.

math.RT↗
arXiv2012

Glauberman correspondents and extensions of nilpotent block algebras

The main purpose of this paper is to prove that the extensions of a nilpotent block algebra and its Glauberman correspondent block algebra are Morita equivalent under an additional group-theoretic condition. In particular, Harris and Linckelman's theorem and Koshitani and Michler's theorem are covered. The ingredient to carry out our purpose is the two main results in Külshammer and Puig's work "Extensions of nilpotent blocks"; we actually revisited them, giving completely new proofs of both and slightly improving the second one.

math.GR↗
arXiv2010

On blocks with trivial source simple modules

Motivated by an observation in "Vertices, sources and Green correspondents of the simple modules for the large Mathieu groups", J. of Algebra 322, we determine the source algebra, and therefore all the structure, of the blocks without essential Brauer pairs where the simple modules of all the Brauer corespondents have trivial sources.

math.GR↗