Sang Yoon Kim | Searcharxiv

arXiv2026

WingSpan: Concurrency and Dependence for Sparse and Structured Tensor Compilers

Sparse tensors represent data that is mostly zero or some other compressible fill pattern. Such datasets can be massive, so optimized tensor algebra libraries and compilers have been developed to exploit these patterns to improve performance. Existing systems, however, frequently lack support for parallelism, especially when outputs are sparse or multiple inputs are sparse. We propose WingSpan, a sparse tensor language enabling unrestricted parallel programming. WingSpan supports arbitrary composition of parallel loops and data structures, matching or exceeding the performance of hand-optimized parallel routines on critical kernels such as SpGEMM. We also introduce a dependence theory for the safety of parallel programs involving sparse tensors and structures beyond sparsity.

cs.MS↗

arXiv2026

A combinatorial framework for clustering graph states: Algorithms and hardness for rank-integrity

We introduce a new notion of distance between two graph states $|G\rangle$ and $|G'\rangle$ on the same set of qubits. This distance is the minimum number of ancilla qubits in a graph state $|\widehat{G}\rangle$ from which both $|G\rangle$ and $|G'\rangle$ can be ``easily prepared''. (When preparing graph states, we are only allowed to use one-qubit Clifford gates, one-qubit Pauli measurements, and classical communication.) We give a graphical description of this distance through the lens of vertex-minors. We then show how this distance yields quantum network analogs of many graph edit-distance problems. Using this framework, we develop classical algorithms for identifying the ``highly entangled clusters'' of a graph state $|G\rangle$. The ancilla integrity problem asks, given a graph $G$ and integer $k$, for the minimum -- over all graph states $|G'\rangle$ with distance at most $k$ from $|G\rangle$ -- of the maximum component size of $G'$. Up to a factor of $2$ in the number of ancilla qubits, this problem is equivalent to rank integrity, where the distance between $G$ and $G'$ is instead the minimum rank of the sum of their adjacency matrices over $\text{GF}(2)$. We prove that rank integrity is XP parameterized by $k$. We also prove the complementary hardness result that rank integrity is W[1]-hard in $k$. Finally, we give an explicit $\mathcal{O}(n^6)$-time algorithm for ancilla integrity when $G$ has $n$ vertices and $k=1$.

cs.DS↗