Related papers: Global space-time update
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…
Analog quantum simulations---simulations of one Hamiltonian by another---is one of the major goals in the noisy intermediate-scale quantum computation (NISQ) era, and has many applications in quantum complexity. We initiate the rigorous…
Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for $1/f$ noise in solid-state quantum information…
While non-Hermitian Hamiltonians enable exotic dynamical phenomena, implementing their nonunitary time evolution on near-term quantum devices remains challenging. We propose a hardware-friendly protocol that simulates non-Hermitian dynamics…
In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
In this work we study the convergence of a classical algorithm called Simulated Quantum Annealing (SQA) on the Spike Hamiltonian, a specific toy model Hamiltonian for quantum-mechanical tunneling introduced by [FGG02]. This toy model…
We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic Hamiltonians…
A recent reformulation [1] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…
Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
Communication-efficient SGD algorithms, which allow nodes to perform local updates and periodically synchronize local models, are highly effective in improving the speed and scalability of distributed SGD. However, a rigorous convergence…
We present an exact spin-elimination technique that reduces the dimensionality of both quadratic and k-local Ising Hamiltonians while preserving their original ground-state configurations. By systematically replacing each removed spin with…