Related papers: A quantum algorithm for additive approximation of …
Entanglement plays a crucial role in quantum physics and is the key resource in quantum information processing. However, entanglement detection and quantification are believed to be hard due to the operational impracticality of existing…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…
An enriched approximation space is the span of a conventional basis with a few extra functions included, for example to capture known features of the solution to a computational problem. Adding functions to a basis makes it overcomplete…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical"…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case,…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
We study the complexity of approximating the partition function of the $q$-state Potts model and the closely related Tutte polynomial for complex values of the underlying parameters. Apart from the classical connections with quantum…
Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines,…
The near-critical unitary dynamics of quantum Ising spin chains in transversal and longitudinal magnetic fields is studied using an artificial neural network representation of the wave function. A focus is set on strong spatial correlations…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
Quantum simulators and processors are rapidly improving nowadays, but they are still not able to solve complex and multidimensional tasks of practical value. However, certain numerical algorithms inspired by the physics of real quantum…
As we venture into the Intermediate-Scale Quantum (ISQ) era, the proficiency of modular arithmetic operations becomes pivotal for advancing quantum cryptographic algorithms. This study presents an array of quantum circuits, each…
Ising Machine is a promising computing approach for solving combinatorial optimization problems. It is naturally suited for energy-saving and compact in-memory computing implementations with emerging memories. A na\"ive in-memory computing…
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by $d$-linear finite elements on Cartesian grids of a bounded $d$-dimensional domain. An…