相关论文: All you need is Trotter
Recently, machine learning algorithms have successfully entered large-scale real-world industrial applications (e.g. search engines and email spam filters). Here, the CPU cost during test time must be budgeted and accounted for. In this…
Characterizing quantum systems by learning their underlying Hamiltonians is a central task in quantum information science. While recent algorithmic advances have achieved near-optimal efficiency in this task, they critically rely on…
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algorithms that compute discrete approximations of the scattering…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
Features in the primordial power spectrum require numerical methods that are both accurate and scalable across the wide class of multifield inflationary models that produce them. Sharp turns in the background trajectories, induced by either…
We revisit the classical issue of the controllability/observability cost of linear first order evolution systems, starting with ODEs, before turning to some linear first order evolution PDEs in several space dimensions, including hyperbolic…
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…
Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum…
We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…
Higher-order nonlinear time-evolution equations have widespread applications in science and engineering, such as in solid mechanics, materials science, and fluid mechanics. This paper mainly studies a direct time-parallel algorithm for…
In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…
Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science, and high-energy physics, and could be implemented in noisy intermediate-scale quantum devices. A challenge in building good…
We introduce a novel approach for discriminative classification using evolutionary algorithms. We first propose an algorithm to optimize the total loss value using a modified 0-1 loss function in a one-dimensional space for classification.…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
We show how importance sampling can be used to reconstruct the statistics of rare cosmological fluctuations in stochastic inflation. We have developed a publicly available package, PyFPT, that solves the first-passage time problem of…
This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function…
Based on the generation function of Laguerre polynomials, We proposed a new Laguerre polynomial expansion scheme in the calculation of evolution of time dependent Schr\"odinger equation. Theoretical analysis and numerical test show that the…
The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a…