Related papers: Polynomial-time Solvable #CSP Problems via Algebra…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
Conic programs arise broadly in physics, quantum information, machine learning, and engineering, many of which are defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers,…
VQC can be understood through the lens of Fourier analysis. It is already well-known that the function space represented by any circuit architecture can be described through a truncated Fourier sum. We show that the spectrum available to…
Holant problems are a general framework to study the computational complexity of counting problems. It is a more expressive framework than counting constraint satisfaction problems (CSP) which are in turn more expressive than counting graph…
Holant problems capture a class of Sum-of-Product computations such as counting matchings. It is inspired by holographic algorithms and is equivalent to tensor networks, with counting CSP being a special case. A classification for Holant…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable if the model-complete core of the template…
An algorithm and its first implementation in C# are presented for assembling arbitrary quantum circuits on the base of Hadamard and Toffoli gates and for constructing multivariate polynomial systems over the finite field Z_2 arising when…
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…
We study polynomial systems whose equations have as common support a set C of n+2 points in Z^n called a circuit. We find a bound on the number of real solutions to such systems which depends on n, the dimension of the affine span of the…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
Exactly solvable models in quantum many body dynamics provide valuable insights into many interesting physical phenomena, and serve as platforms to rigorously investigate fundamental theoretical questions. Nevertheless, they are extremely…
There are two well known types of algorithms for solving CSPs: local propagation and generating a basis of the solution space. For several years the focus of the CSP research has been on `hybrid' algorithms that somehow combine the two…
Choiceless Polynomial Time (CPT) is currently the only candidate logic for capturing PTIME (that is, it is contained in PTIME and has not been separated from it). A prominent example of a decision problem in PTIME that is not known to be…
We design a deterministic subexponential time algorithm that takes as input a multivariate polynomial $f$ computed by a constant-depth circuit over rational numbers, and outputs a list $L$ of circuits (of unbounded depth and possibly with…
Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted…
We review the topological quantum computation scheme of Das Sarma et al. from the perspective of the conformal field theory for the two-dimensional critical Ising model. This scheme originally used the monodromy properties of the…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…