Related papers: Testing Permanent Oracles -- Revisited
We present several polynomial- and quasipolynomial-time approximation schemes for a large class of generalized operator norms. Special cases include the $2\rightarrow q$ norm of matrices for $q>2$, the support function of the set of…
Mehring et al. have recently described an elegant nuclear magnetic resonance (NMR) experiment implementing an algorithm to factor numbers based on the properties of Gauss sums. Similar experiments have also been described by Mahesh et al.…
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This…
Testing efficiently whether a finite set with a binary operation over it, given as an oracle, is a group is a well-known open problem in the field of property testing. Recently, Friedl, Ivanyos and Santha have made a significant step in the…
We examine how amplitude noise in queries to the oracle degrades a performance of quantum search algorithm. The Grover search and similar techniques are widely used in various quantum algorithms, including cases where rival parties are…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
We present a new method for solving the hidden polynomial graph problem (HPGP) which is a special case of the hidden polynomial problem (HPP). The new approach yields an efficient quantum algorithm for the bivariate HPGP even when the input…
Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…
Given $\kappa$ databases of unstructured entries, we propose a quantum algorithm to find the common entries between those databases. The proposed algorithm requires $\mathcal{O}(\kappa \sqrt{N})$ queries to find the common entries, where…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
We prove that the logarithm of the permanent of an nxn real matrix A and the logarithm of the hafnian of a 2nx2n real symmetric matrix A can be approximated within an additive error 1 > epsilon > 0 by a polynomial p in the entries of A of…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
This paper investigates learning-augmented algorithms for smooth integer programs, covering canonical problems such as MAX-CUT and MAX-k-SAT. We introduce a framework that incorporates a predictive oracle to construct a linear surrogate of…
A probabilistic version of the Bernstein-Vazirani problem (which is a generalization of the original Bernstein-Vazirani problem) and a quantum algorithm to solve it are proposed. The problem involves finding one or more secret keys from a…
Partitioning oracles were introduced by Hassidim et al. (FOCS 2009) as a generic tool for constant-time algorithms. For any epsilon > 0, a partitioning oracle provides query access to a fixed partition of the input bounded-degree minor-free…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…