Related papers: Generalized Counting Constraint Satisfaction Probl…
We show that any nonzero polynomial in the ideal generated by the $r \times r$ minors of an $n \times n$ matrix $X$ can be used to efficiently approximate the determinant. For any nonzero polynomial $f$ in this ideal, we construct a small…
In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of…
We study arithmetic proof systems P_c(F) and P_f(F) operating with arithmetic circuits and arithmetic formulas, respectively, that prove polynomial identities over a field F. We establish a series of structural theorems about these proof…
Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and…
In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series,…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique…
Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth-$4$ reduction result by Agrawal and Vinay (FOCS 2008) has made PIT for depth-$4$ circuits an enticing pursuit. A restricted depth-4 circuit computing…
Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems and termed them…
Variational quantum algorithms have been advocated as promising candidates to solve combinatorial optimization problems on near-term quantum computers. Their methodology involves transforming the optimization problem into a quadratic…
For a graph class $\mathcal{G}$, we define the $\mathcal{G}$-modular cardinality of a graph $G$ as the minimum size of a vertex partition of $G$ into modules that each induces a graph in $\mathcal{G}$. This generalizes other module-based…
Discovering the set of closed frequent patterns is one of the fundamental problems in Data Mining. Recent Constraint Programming (CP) approaches for declarative itemset mining have proven their usefulness and flexibility. But the wide use…
The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…
We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that…
We introduce a novel software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each…
Fault tolerant quantum simulation via the phase estimation algorithm and qubitization has a T-gate count that scales proportionally to the 1-norm of the Hamiltonian, the cost of block encoding the Hamiltonian, and inversely proportionally…