Quantum tensor network states and more particularly projected entangled-pair states
provide a natural framework for representing ground states of gapped, topologically ordered …

In this paper we address some algorithmic problems related to computations in finite-
dimensional associative algebras over finite fields. Our starting point is the structure theory …

We analyze algorithms for open construction of a key on some noncommutative group.
Algorithms of factorization and decomposition for associative algebras (of small dimension) …

Starting from the one-way group action framework of Brassard and Yung (Crypto'90), we
revisit building cryptography based on group actions. Several previous candidates for one …

Given linear matrix inequalities (LMIs) L 1 and L 2 it is natural to ask:(Q 1) when does one
dominate the other, that is, does L_1 (X) ⪰ 0 imply L_2 (X) ⪰ 0?(Q 2) when are they mutually …

II Ai”'= B i= l and generalizations, where the Ai and B are given commuting matrices over an
algebraic number field F. In the semigroup membership problem, the variables xi are …

We develop algorithms for writing a polynomial as sums of powers of low degree
polynomials in the non-degenerate case. This problem generalizes symmetric tensor …

Publisher Summary This chapter discusses algebraic complexity theory. Complexity theory,
as a project of lower bounds and optimality, unites two quite different traditions. The first …

It is shown that black-box derandomization of polynomial identity testing (PIT) is essentially
equivalent to derandomization of Noether's Normalization Lemma for explicit algebraic …

We present polynomial time algorithms for some fundamental tasks from representation
theory of finite dimensional algebras. These involve testing (and constructing) isomorphisms …