Related papers: Differential Equation Based Path Integral for Syst…
Quantum information processing has greatly increased interest in the phenomenon of environmentally-induced decoherence. The spin boson model is widely used to study the interaction between a spin-modelling a quantum particle moving in a…
Quantum mechanics describes the unitary time evolution of isolated systems. In reality, every quantum system interacts with its environment, leading to an irreversible loss of the phase relation. Path integral based methods provide a…
We develop a new benchmarking scheme for the Decoded Quantum Interferometry (DQI) algorithm quantifying the number of quantum gates required to obtain an optimal solution to a problem amenable to DQI. We apply the benchmarking scheme to the…
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Physical quantum systems are generically coupled to an environment, resulting in open system dynamics. A typical approach to simulating this dynamics is to propagate the density matrix of the system via the Lindblad master equation. This…
We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data.…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional double-barrier step (PDBS) options, the option price changing process is analogous to a particle moving in a finite symmetric…
Path integrals have, over the years, proven to be an extremely versatile tool for simulating the dynamics of open quantum systems. The initial limitations of applicability of these methods in terms of the size of the system has steadily…
The shift in chemical equilibria due to isotope substitution is often exploited to gain insight into a wide variety of chemical and physical processes. It is a purely quantum mechanical effect, which can be computed exactly using…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
We study the quantum dissipative dynamics of a particle coupled linearly to a set of two-level systems (the heat bath) via the master equation method which we extract from the path integral formalism independently from the form of the bath…
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum-classical methods. Specifically, an exact path integral…
Dynamical decoupling (DD) is a low-overhead method for quantum error suppression. Despite extensive work in DD design, finding pulse sequences that optimally decouple computational qubits on noisy quantum hardware is not well understood. In…