Related papers: Continuous-time evolution via probabilistic angle …
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…
We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry.…
We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion…
We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call step-truncation methods, are based on performing one time step with a conventional…
Modeling the time evolution of discrete sets of items (e.g., genetic mutations) is a fundamental problem in many biomedical applications. We approach this problem through the lens of continuous-time Markov chains, and show that the…
Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
Multi-objective evolutionary algorithms (MOEAs) have become essential tools for solving multi-objective optimization problems (MOPs), making their running time analysis crucial for assessing algorithmic efficiency and guiding practical…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
Stochastic reduced-order modeling based on time-dependent bases (TDBs) has proven successful for extracting and exploiting low-dimensional manifold from stochastic partial differential equations (SPDEs). The nominal computational cost of…
We present a systematic numerical iteration approach to study the evolution properties of the spin-boson systems, which works well in whole coupling regime. This approach involves the evaluation of a set of coefficients for the formal…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
In this study, we investigate Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions, using quantum computers. We identify different sources of errors prevalent in various quantum processing units and…
This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…