Related papers: Random unitaries from Hamiltonian dynamics
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…
In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using…
We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are…
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that…
We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
In arXiv:0710.5653v1 M. Znojil claims that he has found and corrected an error in my paper: [Phys. Lett. B \textbf{650}, 208 (2007), arXiv:0706.1872v2] and that it is possible to escape its main conclusion, namely that the unitarity of the…
In this work we combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
This thesis explores the concept of realizing quantum gates using physical systems like atoms and oscillators perturbed by electric and magnetic fields. The basic idea is that if a time-independent Hamiltonian $H_0$ is perturbed by a…
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and…
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic…
The Hamiltonian of an isolated quantum mechanical system determines its dynamics and physical behaviour. This study investigates the possibility of learning and utilising a system's Hamiltonian and its variational thermal state estimation…
Given a time-independent Hamiltonian $\widetilde H$, one can construct a time-dependent Hamiltonian $H_t$ by means of the gauge transformation $H_t=U_t \widetilde H \, U^\dagger_t-i\, U_t\, \partial_t U_t^\dagger$. Here $U_t$ is the unitary…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
We study the sampling complexity of a probability distribution associated with an ensemble ofidentical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice.With uniform nearest-neighbor hopping we show that…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
Characterizing quantum systems by learning their underlying Hamiltonians is a central task in quantum information science. While recent algorithmic advances have achieved near-optimal efficiency in this task, they critically rely on…