Related papers: Enabling Lie-Algebraic Classical Simulation beyond…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…
Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To…
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…
We emphasize the usefulness of the Lie brackets in the context of classical and quantum mechanics. By way of examples we show that many dynamical systems, especially the ones with (gauge) constraints, can equally be treated in their time…
The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative…
Quantum-classical hybrid dynamics is crucial for accurately simulating complex systems where both quantum and classical behaviors need to be considered. However, coupling between classical and quantum degrees of freedom and the exponential…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
Simulating dynamics of physical systems is a key application of quantum computing, with potential impact in fields such as condensed matter physics and quantum chemistry. However, current quantum algorithms for Hamiltonian simulation yield…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
Existing cosmological simulation methods lack a high degree of parallelism due to the long-range nature of the gravitational force, which limits the size of simulations that can be run at high resolution. To solve this problem, we propose a…
Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules.…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
Simulating quantum many-body dynamics is important both for fundamental understanding of physics and practical applications for quantum information processing. Therefore, classical simulation methods have been developed so far.…
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…