Related papers: Time-optimal control of SU(2) quantum operations
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing…
In complex engineered systems, completing an objective is sometimes not enough. The system must be able to reach a set performance characteristic, such as an unmanned aerial vehicle flying from point A to point B, \textit{under 10 seconds}.…
The control of quantum dynamics via specially tailored laser pulses is a long-standing goal in physics and chemistry. Partly, this dream has come true, as sophisticated pulse shaping experiments allow to coherently control product ratios of…
Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their…
Unitary control and decoherence appear to be irreconcilable in quantum mechanics. When a quantum system interacts with an environment, control strategies usually fail due to decoherence. In this letter, we propose a time-optimal unitary…
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…
We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for…
We introduce a simple yet versatile protocol to inverse engineer the time-dependent Hamiltonian in two- and three level systems. In the protocol, by utilizing a universal SU(2) transformation, a given speedup goal can be obtained with large…
In this series of lectures, we would like to introduce the audience to quantum optimal control. The first lecture will cover basic ideas and principles of optimal control with the goal of demystifying its jargon. The second lecture will…
We present a number of new physical systems that may be addressed using methods of time dependent transformation. A recap of results available for two-state systems is given, with particular emphasis on the AC stark effect. We give some…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast, high fidelity transport can be achieved using protocols designed with differentiable programming. Building on this,…
In this article, the sufficient Pontryagin's maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function.…
High fidelity quantum state transfer is an essential part of quantum information processing. In this regard, we address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann…
In this article we analyze the optimal control strategy for rotating a monitored qubit from an initial pure state to an orthogonal state in minimum time. This strategy is described for two different cost functions of interest which do not…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Li\'enard system to its limit cycle using a bounded external force. To tackle…
This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex,…
Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further…