Related papers: Compact quantum algorithms for time-dependent diff…
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 algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
In this study, we utilized the quantum flow (QFlow) method to perform quantum simulations of correlated systems. The QFlow approach allows for sampling large sub-spaces of the Hilbert space by solving coupled variational problems in reduced…
Developing quantum algorithms to simulate fluid dynamics has become an active area of research, as accelerating fluid simulations could have significant impact in both industry and fundamental science. While many approaches have been…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
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,…
Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized.…
In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
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…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…