Related papers: Quantum Algorithms for Stochastic Differential Equ…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…

We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr\"odingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system…

In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…

We present a quantum algorithm which allows to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens new possibilities for investigation of macroscopic quantum tunneling and realization of…

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…

Adiabatic Quantum Computing relies on the quantum adiabatic theorem, which states that a quantum system evolves along its ground state with time if the governing Hamiltonian varies infinitely slowly. However, practical limitations force…

We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…

Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…

Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…

We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…

Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…

Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the…

A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a…

Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…

We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…

Since the kinetic and the potential energy term of the real time nonlinear Schr\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence…

Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…