6 problems
Open problems
Specific, well-posed questions in quantum optimal control. Each one is stated precisely and comes with the paper that poses it, the known partial results and the references — in the spirit of the open problem zoo of quantum information.
6 problems.
-
Open
How many pulses does universal dynamical decoupling of a qubit need?
To cancel an arbitrary interaction between a qubit and its environment up to order \(K\) in the total time, with ideal instantaneous pulses, are about \(K^2\) pulses necessary — as for quadratic dynamical decoupling — or do \(O(K)\) pulses suffice?
-
Open
Time-optimal cooling of two qubits through one decay channel
Two qubits, only one of which decays, are cooled using arbitrarily fast unitary control. Can every achievable rate of change of the eigenvalues of the state be obtained, up to convex combinations, by simply permuting the eigenbasis? If so, the time-optimal cooling protocol for this system is known explicitly.
-
Partial progress
Does a classical speed limit survive quantization?
If a classical particle driven by a controlled potential cannot be steered across its phase space in arbitrarily short time, is the corresponding Schrödinger equation also not controllable in arbitrarily short time?
-
Partial progress
Ensemble controllability with a single control beyond two-level systems
A continuum of qubits whose resonance frequencies are known only up to an interval can be steered simultaneously, to any family of target gates, by one real-valued control field. Does the same hold for systems with more than two levels?
-
Partial progress
Traps in the control landscapes of controllable multilevel systems
For a completely controllable closed \(N\)-level system with \(N \ge 3\), unconstrained controls and a long enough control time, can a standard objective — a transition probability, an expectation value or a gate fidelity — have a trap, that is, a local maximum that is not a global one?
-
Solved
A universal gap for the minimum control time of finite-dimensional systems
Is there a constant \(\delta > 0\), independent of the dimension, such that every finite-dimensional quantum control system whose drift has unit norm can either be controlled in arbitrarily short time or needs at least time \(\delta\)?