Related papers: Krylov Subspace Methods for Quantum Dynamics with …
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…
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 propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
Quantum speed limit focuses on the minimum time scale for a fixed mission and hence is important in quantum information where fast dynamics is usually beneficial. Most existing tools for the depiction of quantum speed limit are the…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
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 review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
This paper presents a study of the inherent structural properties of Krylov subspaces, in particular for the self-adjoint class of operators, and how they relate with the important phenomenon of `Krylov solvability' of linear inverse…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
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…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
A new control method that considers all sources of uncertainty and noises that might affect the time evolutions of quantum physical systems is introduced. Under the proposed approach, the dynamics of quantum systems are characterised by…
We develop Cresson's non-differentiable embedding to quantum problems of the calculus of variations and optimal control with time delay. Main results show that the dynamics of non-differentiable Lagrangian and Hamiltonian systems with time…
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…