Related papers: The complexity of approximating the complex-valued…
An emerging insight is that ground states of symmetry-protected topological orders (SPTO's) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the…
The operator approach is applied to investigate the complexity of Bose-Hubbard model. We present a systematic method to expand the quantum complexity in series of coupling constant. We first study 2-sites system. For the ground state we can…
We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set…
Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…
We report on single-cluster Monte Carlo simulations of the Ising, 4-state Potts and 10-state Potts models on quenched ensembles of planar, tri-valent random graphs. We confirm that the first-order phase transition of the 10-state Potts…
This work identifies a necessary condition for any variational quantum approach to reach the exact ground state. Briefly, the norms of the projections of the input and the ground state onto each group module must match, implying that module…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
We derive exact relations between the Potts model partition function, or equivalently the Tutte polynomial, for a network (graph) $G$ and a network obtained from $G$ by (i) by replacing each edge (i.e., bond) of $G$ by two or more edges…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
Approximating a definite integral of product of cosines to within an accuracy of n binary digits where the integrand depends on input integers x[k] given in binary radix, is equivalent to counting the number of equal-sum partitions of the…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
Discrete Morse theory has emerged as a powerful tool for a wide range of problems, including the computation of (persistent) homology. In this context, discrete Morse theory is used to reduce the problem of computing a topological invariant…
A prerequisite to the successful development of quantum computers and simulators is precise understanding of physical processes occurring therein, which can be achieved by measuring the quantum states they produce. However, the resources…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
We unconditionally prove that it is NP-hard to compute a constant multiplicative approximation to the QUANTUM MAX-CUT problem on an unweighted graph of constant bounded degree. The proof works in two stages: first we demonstrate a generic…