Related papers: Time-marching based quantum solvers for time-depen…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of…
We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with $\mathcal{O}(\kappa~\text{poly}(\log(\kappa/\epsilon)))$ runtime, where…
The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations…
Finding the solution to linear ordinary differential equations of the form $\partial_t u(t) = -A(t)u(t)$ has been a promising theoretical avenue for \textit{asymptotic} quantum speedups. However, despite the improvements to existing quantum…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\mathbf b$ the task is to find the vector $\mathbf x$ such that $A \mathbf x = \mathbf b$. We…
A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
Differentiable models of physical systems provide a powerful platform for gradient-based algorithms, with particular impact on parameter estimation and optimal control. Quantum systems present a particular challenge for such…