Related papers: Suggestion for a Fast Heuristic for the Hamiltonia…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
Here we provide a scheme of transforming the one-axis twisting Hamiltonian into the two-axis twisting one based on high order Trotter-Suzuki Approximation. Compared with the paper [Y. C. Liu et al., Phys. Rev. Lett. 107, 013601 (2011)], our…
In this paper we consider the following total functional problem: Given a cubic Hamiltonian graph $G$ and a Hamiltonian cycle $C_0$ of $G$, how can we compute a second Hamiltonian cycle $C_1 \neq C_0$ of $G$? Cedric Smith proved in 1946,…
We propose an efficientmethod to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocol' Hamiltonian may involve terms which are difficult to realize in…
The quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems. One of the most powerful and commonly used heuristics to obtain approximations to the optimal solution of the QAP is simulated…
An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a…
Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and…
Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems…
Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
In this paper we consider the Hamilton cycle problem in the rectangular meshes with at most two faulty nodes.We prove that this problem is solvable in polynomial time with a corresponding algorithm. We provided an entirely new approach to…
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital…
Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
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…
Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…