Related papers: Tree-size complexity of multiqubit states
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…
Nonstabilizerness, also known as magic, quantifies the number of non-Clifford operations needed in order to prepare a quantum state. As typical measures either involve minimization procedures or a computational cost exponential in the…
Many isomorphism problems for tensors, groups, algebras, and polynomials were recently shown to be equivalent to one another under polynomial-time reductions, prompting the introduction of the complexity class TI (Grochow & Qiao, ITCS '21;…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
We consider the numerical taxonomy problem of fitting a positive distance function ${D:{S\choose 2}\rightarrow \mathbb R_{>0}}$ by a tree metric. We want a tree $T$ with positive edge weights and including $S$ among the vertices so that…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
Models of computations over the integers are equivalent from a computability and complexity theory point of view by the Church-Turing thesis. It is not possible to unify discrete-time models over the reals. The situation is unclear but…
Let ${\cal T}=(T,w)$ be a weighted finite tree with leaves $1,..., n$.For any $I :=\{i_1,..., i_k \} \subset \{1,...,n\}$, let $D_I ({\cal T})$ be the weight of the minimal subtree of $T$ connecting $i_1,..., i_k$; the $D_{I} ({\cal T})$…
We prove two results that shed new light on the monotone complexity of the spanning tree polynomial, a classic polynomial in algebraic complexity and beyond. First, we show that the spanning tree polynomials having $n$ variables and defined…
Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…
Binary Tree States (BTS) are states whose decomposition on a quantum register basis formed by a set of qubits can be made sequentially. Such states sometimes appear naturally in many-body systems treated in Fock space when a global symmetry…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…