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Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
We construct families of cell complexes that generalize expander graphs. These families are called non-$k$-hyperfinite, generalizing the idea of a non-hyperfinite (NH) family of graphs. Roughly speaking, such a complex has the property that…
Quantum algorithms for topological data analysis (TDA) seem to provide an exponential advantage over the best classical approach while remaining immune to dequantization procedures and the data-loading problem. In this paper, we give…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
Quantum coherence profoundly alters classical thermodynamic expectations by modifying the structure and accessibility of probability distributions. Classically, transitions to lower-entropy states (local second-law violations) are…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground…
Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. Approximating a hard CQ by a query from such a fragment can thus allow for an efficient approximate evaluation. While…
This paper proposes a real moment-HSOS hierarchy for complex polynomial optimization problems with real coefficients. We show that this hierarchy provides the same sequence of lower bounds as the complex analogue, yet is much cheaper to…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
This paper introduces a Moment-Quaternion-Sum-of-Squares (QSOS) hierarchy for solving a class of quaternion polynomial optimization problems. This hierarchy is formulated directly in the quaternion domain and consists of a sequence of…
We study the problem of designing worst-case to average-case reductions for quantum algorithms. For all linear problems, we provide an explicit and efficient transformation of quantum algorithms that are only correct on a small (even…
Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…
Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, Physics, Chemistry or Economy. In addition, QP mappings are a…
Currently, quantum computing and artificial intelligence are driving revolutionary advancements in computational science. This study pioneers the integration of quantum kernel networks on smoothed particle hydrodynamics (SPH). SPH has…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
In this paper we present a collection of results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More…
In this paper we show that PSPACE is equal to 4th level in the polynomial hierarchy. We also deduce a lot of important consequences. True quantified Boolean formula is a generalisation of the Boolean Satisfiability Problem, where…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
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…