Related papers: Efficient Quantum Simulation Algorithms in the Pat…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
Efficient path planning for autonomous mobile robots is a critical problem across numerous domains, where optimizing both time and energy consumption is paramount. This paper introduces a novel methodology that considers the dynamic…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
Inspired by the usefulness of local scaling of time in the path integral formalism, we introduce a new kind of hamiltonian path integral in this paper. A special case of this new type of path integral has been earlier found useful in…
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…
Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum…
In this work, we present a high-fidelity and efficient point-particle direct numerical simulation framework based on a multi-block overset curvilinear grid system, enabling large-scale Lagrangian particle tracking in complex geometries with…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of…
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
Estimating transition rates in open quantum systems is hampered by computing-resource demands that grow rapidly with system size. We present a quantum-simulation framework that enables efficient estimation by recasting the transition rate,…