Related papers: Atom Cavity Encoding for NP-Complete Problems
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
These lecture notes discuss applications of atom-light interactions in cavities to quantum metrology, simulation, and computation. A focus is on nonlocally interacting spin systems realized by coupling many atoms to a delocalized mode of…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…
Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…
A multi-cavity quantization scheme is developed using quasinormal modes (QNMs) of optical cavities embedded in a homogeneous background medium for cases where retardation is significant in the inter-cavity coupling. Using quantities that…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
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…
There has been increasing interest in developing efficient quantum algorithms for hard classical problems. The Network Signal Coordination (NSC) problem is one such problem known to be NP complete. We implement Grover's search algorithm to…
Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and…
Both discrete and continuous systems can be used to encode quantum information. Most quantum computation schemes propose encoding qubits in two-level systems, such as a two-level atom or an electron spin. Others exploit the use of an…
In this paper we consider a model of quantum computation based on n atoms of laser-cooled and trapped linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian interacting with n external (laser) fields. We solve the…
We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…
Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases,…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Quantum cooling has demonstrated its potential in quantum computing, which can reduce the number of control channels needed for external signals. Recent progress also supports the possibility of maintaining quantum coherence in large-scale…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…
We propose a scheme to realize the Heisenberg model of any spin in an arbitrary array of coupled cavities. Our scheme is based on a fixed number of atoms confined in each cavity and collectively applied constant laser fields, and is in a…
We propose a scalable encoding of combinatorial optimization problems with arbitrary connectivity, including higher-order terms, on arrays of trapped neutral atoms requiring only a global laser drive. Our approach relies on modular…
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration…