Related papers: State-dependent Trotter Limits and their approxima…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
We discuss real time evolution for the quantum Ising model in one spatial dimension with $N_s$ sites. In the limit where the nearest neighbor interactions $J$ in the spatial directions are small, there is a simple physical picture where…
We report on our recent efforts to perform realistic simulations of large quantum devices in the time domain. In contrast to d.c. transport where the calculations are explicitly performed at the Fermi level, the presence of time-dependent…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary…
Many-body entangled quantum spin systems exhibit emergent phenomena such as topological quantum spin liquids with distinct excitation spectra accessed in inelastic neutron scattering (INS) experiments. Here we simulate the dynamics of a…
This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing…
Stabilizer states constitute a set of pure states which plays a dominant role in quantum error correction, measurement--based quantum computation, and quantum communication. Central in these applications are the local symmetries of these…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an…
The entangled quantum states play a key role in quantum information. The association of the quantum state vector with each individual physical system in an attributive way is a source of many false paradoxes and inconsistencies. The…
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where…
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent…