Related papers: Optimized Dynamical Decoupling for Time Dependent …
We study the relationship between disturbance decoupling (DD) and H2 optimal control for linear time-invariant (LTI) systems, revealing a fundamental gap between DD subspace constraints and semi-definite program (SDP)-based H2 minimization.…
We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this…
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 analyze the robust character against non-static noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in ^{87}\textrm{Rb}. The emergence of features specific to the…
The loss of quantum information due to interaction with external degrees of freedom, which is known as decoherence, remains one of the main obstacles for large-scale implementations of quantum computing. Accordingly, different measures are…
In this paper we introduce a method for finding a time independent Hamiltonian of a given dynamical system by canonoid transformation. We also find a condition that the system should satisfy to have an equivalent time independent…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
Reducing decoherence is an essential step toward realizing general-purpose quantum computers beyond the present noisy intermediate-scale quantum (NISQ) computers. To this end, dynamical decoupling (DD) approaches in which external fields…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide…
We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…
High-fidelity control of quantum systems is crucial for quantum information processing, but is often limited by perturbations from the environment and imperfections in the applied control fields. Here, we investigate the combination of…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most AC sensing sequences involve a periodic echo-like…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of…
We introduce a high-order dynamical decoupling (DD) scheme for arbitrary system-bath interactions in the weak-coupling regime. Given any decoupling group $\mathcal G$ that averages the interaction to zero, our construction yields pulse…