Related papers: Superconvergence of High-order Magnus Quantum Algo…
The computation of the Schr\"odinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require…
Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in…
The numerical simulation of the time-dependent Schr\"odinger equation for quantum systems is a very active research topic. Yet, resolving the solution sufficiently in space and time is challenging and mandates the use of modern…
In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…
We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling…
In multiobjective optimization, inertial gradient systems accelerate convergence toward weakly Pareto optimal solutions. To achieve even faster convergence, we introduce a multiobjective inertial gradient system with time scaling (MITS),…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…
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…
We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a p-summability condition and for integration of functions from Lebesgue…
We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…
We consider a coupled system of Schr\"odinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techniques we study the corresponding classical limit dynamics…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
We prove that a "first-order" Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/\kappa_R)^k$, where $\kappa_R$ is the condition number of the Riemannian…
The quantum k-Local Hamiltonian problem is a natural generalization of classical constraint satisfaction problems (k-CSP) and is complete for QMA, a quantum analog of NP. Although the complexity of k-Local Hamiltonian problems has been well…
We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
Known as no fast-forwarding theorem in quantum computing, the simulation time for the Hamiltonian evolution needs to be $O(\|H\| t)$ in the worst case, which essentially states that one can not go across the multiple scales as the…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…