Related papers: Quantum algorithms for solving a drift-diffusion e…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…
Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
Solutions of quaternionic quantum mechanics (QQM) are difficult to grasp, even in simple physical situations. In this article, we provide simple and understandable free particle quaternionic solutions, that can be easily compared to complex…
Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…
We propose a simple quantum algorithm for implementing the diffusion step of grid-based Bayesian filters. The method encodes the advected state density and the process noise density into quantum registers and realizes diffusion using a…
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system dynamics, diffusion process and damped system. In this…