Related papers: Tensor Network Contractions for #SAT
This paper explores the Boolean Satisfiability Problem (SAT) in the context of Kolmogorov complexity theory. We present three versions of the distinguishability problem-Boolean formulas, Turing machines, and quantum systems-each focused on…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
\noindent Model building in $\mathsf{SO(10)}$, which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves…
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor…
Bayesian optimization (BO) has been widely used to optimize expensive and black-box functions across various domains. However, existing BO methods have not addressed tensor-output functions. To fill this gap, we propose a novel…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity…
Characterizing the ground-state properties of disordered systems, such as spin glasses and combinatorial optimization problems, is fundamental to science and engineering. However, computing exact ground states and counting their…
The #2-SAT and #3-SAT problems involve counting the number of satisfying assignments (also called models) for instances of 2-SAT and 3-SAT, respectively. In 2010, Zhou et al. proposed an $\mathcal{O}^*(1.1892^m)$-time algorithm for #2-SAT…
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
The Boolean Satisfiability (SAT) problem is a canonical NP-complete problem and a natural candidate for quantum acceleration via search-based algorithms. In Grover-based quantum SAT solvers, the dominant computational cost stems from the…