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Related papers: Lower Bounds for the Trotter Error

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To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…

Numerical Analysis · Mathematics 2019-07-09 Yusuke Imoto

Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Despite…

Quantum Physics · Physics 2025-10-20 Wenjun Yu , Xiaogang Li , Qi Zhao , Xiao Yuan

Adiabatic evolution is a central paradigm in quantum physics. Digital simulations of adiabatic processes are generally viewed as costly, since algorithmic errors typically accumulate over the long evolution time, requiring exceptionally…

Quantum Physics · Physics 2025-10-15 Yangyu Lu , Yifei Huang , Dong An , Qi Zhao , Dingshun Lv , Xiao Yuan

Accurate simulations of vibrational molecular spectra are expensive on conventional computers. Compared to the electronic structure problem, the vibrational structure problem with quantum computers is less investigated. In this work we…

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…

Quantum Physics · Physics 2017-05-04 R. Yousefjani , S. Salimi , A. S. Khorashad

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…

Methodology · Statistics 2010-07-06 Robert B. Gramacy , Herbert K. H. Lee

The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a…

Finding minimal time and establishing the structure of the corresponding optimal controls which can transfer a given initial state of a quantum system into a given target state is a key problem of quantum control. In this work, this problem…

Quantum Physics · Physics 2025-02-21 L. V. Lokutsievskiy , A. N. Pechen , M. I. Zelikin

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…

Optimization and Control · Mathematics 2007-07-26 Paulo Tabuada , Aaron D. Ames , Agung Julius , George J. Pappas

Trotter-Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error---the Trotter error. The Trotter…

Quantum Physics · Physics 2020-01-08 Andrew Tranter , Peter J. Love , Florian Mintert , Nathan Wiebe , Peter V. Coveney

Conventional classical sensors are approaching their maximum sensitivity levels in many areas. Yet these levels still are far from the ultimate limits dictated by quantum mechanics. Quantum sensors promise a substantial step ahead by taking…

Quantum Physics · Physics 2020-12-02 Aaron Z. Goldberg , Andrei B. Klimov , Gerd Leuchs , Luis L. Sanchez-Soto

We present upper bounds for the numerical errors introduced when using operator splitting methods to integrate transport and non-linear chemistry processes in global chemical transport models (CTM). We show that (a) operator splitting…

Numerical Analysis · Mathematics 2015-11-09 Mauricio Santillana , Ling Zhang , Robert Yantosca

Obtaining prescribed accuracy bounds in super-twisting sliding mode control loops often falls short in terms of the applicability of the controller in high-performance systems. This is due to the fact that the selection of the controller…

Systems and Control · Electrical Eng. & Systems 2022-06-29 Dimitrios Papageorgiou

We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…

Probability · Mathematics 2014-09-15 Jasper Goseling , Richard J. Boucherie , Jan-Kees van Ommeren

Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…

Quantum Physics · Physics 2026-05-15 Yu-Xia Wu , Yun-Zhuo Fan , Dan-Bo Zhang

Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the…

From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences. Particularly in quantum mechanics, the amount of information needed for specifying the state of a…

Quantum Physics · Physics 2016-07-06 Yudong Cao , Sabre Kais

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…

Quantum Physics · Physics 2026-03-31 Qiuhao Chen , Yuling Jiao , Yinan Li , Xiliang Lu , Jerry Zhijian Yang

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…

Quantum Physics · Physics 2011-01-24 Takanori Sugiyama , Peter S. Turner , Mio Murao

Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an…

Quantum Physics · Physics 2020-11-25 Quntao Zhuang