Related papers: Understanding Traffic Jams Using Lindblad Superope…
We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
Master equations in the Lindblad form describe evolution of open quantum systems that is completely positive and simultaneously has a semigroup property. We analyze a possibility to derive this type of master equations from an intrinsically…
We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, $\mathcal{L} = \sum_{a \in \mathcal{A}} \mathcal{L}_a$, where each $\mathcal{L}_a$ comprises a simple…
We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves…
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…
A simple algorithm for constructing an effective traffic model is presented. The algorithm uses statistically well-defined quantities extracted from the flow-density plot, and the resulting effective model naturally captures and predicts…
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian…
The Lindblad master equation is one of the main approaches to open quantum systems. While it has been widely applied in the context of condensed matter systems to study properties of steady states in the limit of long times, the actual…
Liouvillian dynamics describes the evolution of a density operator in closed quantum systems. One extension towards open quantum systems is provided by the Lindblad equation. It is applied to various systems and energy regimes in solid…
The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
Hybrid traffic modeling and simulation provide an important way to represent and evaluate large-scale traffic networks at different levels of details. The first level, called "microscopic" allows the description of individual vehicles and…
We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental…
We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a…
We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic…
The Lindblad master equation is a fundamental tool for describing the evolution of open quantum systems, but its computational complexity poses a significant challenge, especially for large systems. This article introduces a stochastic…