32 problems

Irrational-angle counterexample conjecture. It is impossible to find a counterexample satisfying $\varphi_0\notin 2\pi\mathbb{Q}$.

Let $\phi\in\mathscr{P}_\beta$ be a Bernstein-type pulse function, let $h$ be the step size parameter, and let $\Omega_j(h)$ denote the $j$th Magnus term. Let $\omega$ denote the f…

Lower-rate dynamical decoupling conjecture. In this setting, dynamical decoupling should still work, but its convergence speed in the number $N$ of steps may be lower, of order

Constant-$\theta$ time-optimality conjecture. For symmetric-space controls in $\mathfrak p$ with holonomy targets in $\mathfrak k$, constant-$\theta$ paths are time-optimal.

Constant inverse-velocity conjecture. Local variation of the total time should yield Euler–Lagrange equations implying that

Let $\Delta^3$ denote the probability simplex, let $\mathsf{derv}(\lambda)$ be the set of achievable derivatives at $\lambda$, let $S_4$ be the permutation group on four elements,…

Relaxation conjecture. Assumption 3 can be relaxed for measurement-free systems with drift.

Consider finite-dimensional quantum control systems with control schemes given by $\text{Sp}(\frac{n}{2})$ and $\text{S}(\text{U}(p)\times\text{U}(q))$, and let the corresponding a…

Threshold conjecture. This phenomenon holds in general: condition (21) sets a corresponding threshold on the signal-to-thermal-noise ratio. The conjecture predicts that the restric…

Let QGASS denote the stochastic-optimization framework introduced in the paper for training parametric feedback policy networks. Let QND MFC denote a quantum nondemolition measurem…

Structured-perturbation smoothing conjecture. Added structured perturbations may have a smoothing effect on the optimization landscape, resulting in either filtration or creation o…

Let a quantum spin-$J$ system be controlled by feedback controls of the particular form considered in the source, and let the target be an eigenstate of the measurement operator. E…

Lloyd's alternating-sequence conjecture. Any unitary $\mathcal{U}\in U(d)$ can be performed by an alternating operator sequence $\mathcal{W}(\vec{t},\vec{\tau})$ of the displayed f…

Exponential stabilization conjecture. The first controller almost surely exponentially stabilizes $(\rho_t,\hat{\rho}_t)$ to $(\boldsymbol\rho_{\bar n},\boldsymbol\rho_{\bar n})$ w…

Controllability-diameter conjecture. For every such Hamiltonian, the implication

Classical-to-quantum controllability conjecture. If the classical system is not small-time controllable, then the corresponding quantum system is not small-time controllable either…

Let $H_0,\ldots,H_m$ be selfadjoint operators on a separable Hilbert space $\mathcal H$, with $H_0$ bounded or unbounded and having non-degenerate, rationally independent pure poin…

Let $\Sigma$ be a finite-dimensional quantum control system on $\mathbb{C}^n$ of the form … where $A$ and the $B_i$ are skew-adjoint matrices, and normalize the drift by…

Minimum pumped-crystal conjecture. Three pumped crystals are the minimum number required for constructing a desired locally dissipative system.

Let $V$ be the covariance matrix of an $N$-mode pure Gaussian state, expressed in the factored form above. A linear quantum system generating this state must satisfy the necessary…

Optimal-angle no-improvement conjecture. At the optimal homodyne angle,

No-improvement conjecture. The coherent-classical estimation cost satisfies

Let $SU(n)$, for $n\geq 2$, carry a Randers metric, and consider the set of infinitely many geodesic vectors of this Finsler metric. Connectedness conjecture. This set is connected…

Let $u>0$ and $\kappa>0$, let $r>1$ be an integer, and consider the master equation … Let $\bar\rho$ be a steady density operator supported on the span of the coherent states…

Wigner-function convergence conjecture. For every initial Wigner function $W_0=W^{\rho_0}$ with finite energy,