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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…
The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore…
Conventional manipulations over quantum systems for such as coherent population trapping and unidirectional transfer focus on Hamiltonian engineering while regarding the system's manifold geometry and constraint equation as secondary…
Quantum control plays a crucial role in enhancing precision scaling for quantum sensing. However, most existing protocols require perfect control, even though real-world devices inevitably have control imperfections. Here, we consider a…
We present a general formalism based on the variational principle for finding the time-optimal quantum evolution of mixed states governed by a master equation, when the Hamiltonian and the Lindblad operators are subject to certain…
Bounds of the minimum evolution time between two distinguishable states of a system can help to assess the maximal speed of quantum computers and communication channels. We study the quantum speed limit time of a composite quantum states in…
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz,…
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
The minimal evolution time between two distinguishable states is of fundamental interest in quantum physics. Very recently Mirkin et al. argue that some most common quantum-speed-limit (QSL) bounds which depend on the actual evolution time…
The speed limits on entanglement are defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and…
We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the…
Sudden changes of quantum correlations in the Bell-diagonal states are well-known effects. They occur when the set of optimal parameters that determine the quantum correlation consists of isolated points and optimal parameters during the…
In this paper, we consider a general time-inconsistent optimal control problem for a non homogeneous linear system, in which its state evolves according to a stochastic differential equation with deterministic coefficients, when the noise…
We derive lower bounds on the time needed for a quantum annealer to prepare the ground state of a target Hamiltonian. These bounds do not depend on the annealing schedule and can take the local structure of the Hamiltonian into account.…
We cast observable measure of quantum coherence or asymmetry as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together.…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…