Related papers: Provably Efficient Quantum Algorithms for Solving …
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
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…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
We explore how a continuous-variable (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Specifically, we construct variational CV quantum circuits…
Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy, intermediate-scale quantum…
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…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
We propose a realistic hybrid classical-quantum linear solver to solve systems of linear equations of a specific type, and demonstrate its feasibility using Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs…
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,…
We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…
Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault…
It is shown that quantum computer can detect the existence of root of a function almost exponentially more efficient than the classical counterpart. It is also shown that a quantum computer can produce quantum state corresponding to the…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…