Related papers: Lie-algebraic classical simulations for quantum co…
We estimate the run-time and energy consumption of simulating non-equilibrium dynamics on neutral atom quantum computers in analog mode, directly comparing their performance to state-of-the-art classical methods, namely Matrix Product…
The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in…
Recent demonstrations of D-Wave's annealing-based quantum simulators have established new benchmarks for quantum computational advantage [arXiv:2403.00910]. However, the precise location of the classical-quantum computational frontier…
We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schr\"{o}dinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a…
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond…
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It…
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their…
Modeling and simulation is essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We…
According to the Gottesman-Knill theorem, quantum algorithms which utilise only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states,…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
In the recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state-of-the-art classical simulators are only limited to binary quantum systems, which…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as Boson sampling, where classical counterparts fail. In another field of…
The structure and dynamics of quantum many-body systems are the result of a delicate interplay between underlying interactions, which leads to intricate entanglement structures. Despite this apparent complexity, symmetries emerge and have…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, LOWESA (low weight efficient simulation…