Related papers: A quantum algorithm to solve nonlinear differentia…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Quantum computers can solve specific complex tasks for which no reasonable-time classical algorithm is known. Quantum computers do however also offer inherent security of data, as measurements destroy quantum states. Using shared entangled…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
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 an algorithm for the numerical solution of nonlinear parabolic partial differential equations. This algorithm extends the classical Feynman-Kac formula to fully nonlinear partial differential equations, by using random trees that…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
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…