相关论文: Quantum simulation of time-dependent Hamiltonians …
For many quantum models an apparent non-Hermiticity of observables corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent…
Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. In contrast to time-independent Hamiltonian…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
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…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology.…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analysing a sequence of finite-size cases? We present a model for which such an approach gives completely misleading results: a translationally…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…
It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
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…
We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e.,…
Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with…
A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…