Related papers: Quantum Algorithm for Computing the Period Lattice…
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes…
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spacial wavefunction of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Quantum algorithms have been identified as a potential means to accelerate computational fluid dynamics (CFD) simulations, with the lattice Boltzmann method (LBM) being a promising candidate for realizing quantum speedups. Here, we extend…
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…
Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of…
Recently, Huggins et. al. [Nature, 603, 416-420 (2022)] devised a general projective Quantum Monte Carlo method suitable for implementation on quantum computers. This hybrid approach, however, relies on a subroutine -the computation of the…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
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…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
As the scope of Computational Fluid Dynamics (CFD) grows to encompass ever larger problem scales, so does the interest in whether quantum computing can provide an advantage. In recent years, Quantum Lattice Gas Automata (QLGA) and Quantum…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
In a recent paper by the same authors, we provided a theoretical foundation for the component-by-component (CBC) construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic…
Quantum error correction (QEC) and fault-tolerant (FT) mechanisms are essential for reliable quantum computing. However, QEC considerably increases the computation size up to four orders of magnitude. Moreover, FT implementation has…
In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables…