Related papers: On model reduction for quantum dynamics: symmetrie…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce…
We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in many-body systems and…
Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum…
Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter…
Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and…
Simulating the dynamics of complex quantum systems is a central application of quantum devices. Here, we propose leveraging the power of measurements to simulate short-time quantum dynamics of physically prepared quantum states in classical…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
Inspired by path integral molecular dynamics, we build a spin model, in terms of spin coherent states, from which we can compute the quantum expectation values of a spin in a constant magnetic field, at finite temperature. This formulation…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…
We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system…
It has been assumed that it is possible to approximate the interactions of quantized BPS solitons by quantising a dynamical system induced on a moduli space of soliton parameters. General properties of the reduction of quantum systems by a…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…