Related papers: Simple digital quantum algorithm for symmetric fir…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to…
Two hybrid quantum-classical reservoir computing models are presented to reproduce low-order statistical properties of a two-dimensional turbulent Rayleigh-B\'enard convection flow at a Rayleigh number Ra=1e+5 and a Prandtl number Pr=10.…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
We establish improved complexity estimates of quantum algorithms for linear dissipative ordinary differential equations (ODEs) and show that the time dependence can be fast-forwarded to be sub-linear. Specifically, we show that a quantum…
The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
Quantum reservoir computing (QRC) is a hardware-implementation-friendly quantum neural network scheme with minimal physical system requirements and a proven advantage over classical counterparts. We use an extension of the positive-P phase…
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…