Related papers: On Efficient Algorithms For Partial Quantifier Eli…
Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability…
With the rapid growth in the use of fine-tuning for large language models (LLMs), optimizing fine-tuning while keeping inference efficient has become highly important. However, this is a challenging task as it requires improvements in all…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…
The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then…
Proton-coupled electron transfer (PCET) is the key step for energy conversion in electrocatalysis. Atomic-scale simulation acts as an indispensable tool to provide a microscopic understanding of PCET. However, consideration of the quantum…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical…
The deductive closure of an ideal knowledge base (KB) contains exactly the logical queries that the KB can answer. However, in practice KBs are both incomplete and over-specified, failing to answer some queries that have real-world answers.…
This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equations and atoms using the conjunction $\wedge$ and the…
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…
Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating…
Low-bit post-training quantization (PTQ) is a practical route to deploy reasoning-capable LLMs under tight memory and latency budgets, yet it can markedly impair mathematical reasoning (drops up to 69.81% in our harder settings). We address…
We observe that fault-tolerant quantum computers have an optimal advantage over classical computers in approximating solutions to many NP optimization problems. This observation however gives nothing in practice.
We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution, that maximally exploits the limited number of qubits in hardware to solve large problem instances. We apply…
In this work, we study the projective quantum eigensolver (PQE) approach to optimizing unitary coupled cluster wave functions on quantum hardware, as introduced in arXiv:2102.00345. The projective quantum eigensolver is a hybrid…
We introduce a continuous analogue of the Learning with Errors (LWE) problem, which we name CLWE. We give a polynomial-time quantum reduction from worst-case lattice problems to CLWE, showing that CLWE enjoys similar hardness guarantees to…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
Generalized quantifiers (e.g., few, most) are used to indicate the proportions predicates are satisfied (for example, some apples are red). One way to interpret quantifier semantics is to explicitly bind these satisfactions with percentage…