Related papers: H-DES: a Quantum-Classical Hybrid Differential Equ…
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…
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for…
Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning. We consider the general Bayes framework, as introduced by Helstrom, for state…
We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
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…
The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and…
When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…
As quantum computers mature, the applicability in practice becomes more important. Many uses of quantum computers will be hybrid, with classical computers still playing an important role in operating and using the quantum computer. The term…
Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the…
The numerical solution of partial differential equations (PDEs) is essential in computational physics. Over the past few decades, various quantum-based methods have been developed to formulate and solve PDEs. Solving PDEs incur high time…
While the treatment of chemically relevant systems containing hundreds or even thousands of electrons remains beyond the reach of quantum devices, the development of quantum-classical hybrid algorithms to resolve electronic correlation…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…