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Yuntao Zhang

Publications and source records attributed to Yuntao Zhang.

6 recordsLinked to original sources

Beyond Monolithic Scaling: Modularity and Heterogeneity as an Architectural Imperative for Utility-Scale Quantum Computing

Scalable quantum computing is fundamentally bottlenecked not by qubit count or fabrication yield, but by a rigid temporal mismatch: macroscopic classical coordination latency ($τ_c$) inevitably grows with system diameter, while microscopic quantum coherence ($τ_q$) remains strictly bounded. Beyond a critical scale, this mismatch breaches the classical control light cone, triggering a superlinear geometric penalty ($ε> 0$) that renders monolithic synchronization physically impossible. We formalize the resulting structural phase transition through a governing scaling law, $1+ε> γ$, which mandates modular decomposition and a shift from global unitaries to Local Operations and Classical Communication (LOCC). To manage the resulting resource contention under strict coherence budgets, we introduce a layered semantic architecture and a time-aware Reserve--Commit protocol. By embedding predictive temporal pre-validation, the protocol acts as an architectural semantic classifier: it preemptively aborts transactions that exceed the causal horizon and explicitly converts scheduling-induced failures into location-known erasure metadata, directly relaxing hardware fidelity thresholds for downstream QEC decoders. Under near-term transduction targets ($η_{\mathrm{trans}} \sim 0.1$), we project a crossover scale at $N_c \sim 10^5$--$10^6$ physical qubits. This threshold marks a profound architectural convergence: the footprint required for modularity aligns precisely with early fault-tolerant utility, establishing time-aware distributed orchestration, rather than monolithic expansion or centralized classical control, as the physical imperative for utility-scale quantum computing.

quant-ph

Star-shaped Curves under Gage's Area-preserving Flow and the CSF

Mayer asks a question what closed, embedded and nonconvex initial curves guarantee that Gage's area-preserving flow (GAPF) exists globally. A folklore conjecture since 2012 says that GAPF evolves smooth, embedded and star-shaped initial curves globally. In this paper, we prove this conjecture by using Dittberner's singularity analysis theory. A star-shaped ``flying wing" curve is constructed to show that GAPF may not always preserve the star-shapedness of evolving curves. This example is also a negative answer to Mantegazza's open problem whether the curve shortening flow (CSF) always preserves the star shape of the evolving curves.

math.DG

Wavelet Prior Attention Learning in Axial Inpainting Network

Image inpainting is the task of filling masked or unknown regions of an image with visually realistic contents, which has been remarkably improved by Deep Neural Networks (DNNs) recently. Essentially, as an inverse problem, the inpainting has the underlying challenges of reconstructing semantically coherent results without texture artifacts. Many previous efforts have been made via exploiting attention mechanisms and prior knowledge, such as edges and semantic segmentation. However, these works are still limited in practice by an avalanche of learnable prior parameters and prohibitive computational burden. To this end, we propose a novel model -- Wavelet prior attention learning in Axial Inpainting Network (WAIN), whose generator contains the encoder, decoder, as well as two key components of Wavelet image Prior Attention (WPA) and stacked multi-layer Axial-Transformers (ATs). Particularly, the WPA guides the high-level feature aggregation in the multi-scale frequency domain, alleviating the textual artifacts. Stacked ATs employ unmasked clues to help model reasonable features along with low-level features of horizontal and vertical axes, improving the semantic coherence. Extensive quantitative and qualitative experiments on Celeba-HQ and Places2 datasets are conducted to validate that our WAIN can achieve state-of-the-art performance over the competitors. The codes and models will be released.

cs.CV

Path Planning Algorithms for a Car-Like Robot visiting a set of Waypoints with Field of View Constraints

This article considers two variants of a shortest path problem for a car-like robot visiting a set of waypoints. The sequence of waypoints to be visited is specified in the first variant while the robot is allowed to visit the waypoints in any sequence in the second variant. Field of view constraints are also placed when the robot arrives at a waypoint, i.e., the orientation of the robot at any waypoint is restricted to belong to a given interval of angles at the waypoint. The shortest path problem is first solved for two waypoints with the field of view constraints using Pontryagin's minimum principle. Using the results for the two point problem, tight lower and upper bounds on the length of the shortest path are developed for visiting n points by relaxing the requirement that the arrival angle must be equal to the departure angle of the robot at each waypoint. Theoretical bounds are also provided on the length of the feasible solutions obtained by the proposed algorithm. Simulation results verify the performance of the bounds for instances with 20 waypoints.

cs.RO

An alternative proof of lower bounds for the first eigenvalue on manifolds

Recently, Andrews and Clutterbuck [AC13] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [AC13]. More precisely, following Ni's method ([Ni13, Section 6]) we give an elliptic proof of this theorem.

math.DG

Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume growth conditions. We also generize it to the manifolds with $k$-th asymptotically nonnegative Ricci curvature by using extensions of Abresch-Gromoll's excess function estimate.

math.DG