8 problems

Bounded-degree logarithmic-depth conjecture. For all sufficiently large $p$, there exists $c_p>0$, $\zeta>0$, and $\delta>0$ such that, if $D_n\leq\delta\log n$, then

Quantum spin-glass circuit-complexity conjecture. Near-ground states of quantum $p$-spin glasses cannot be prepared by polynomial-size circuits, even with arbitrary ancillas.

Fixed-average-degree NLTS conjecture. For all sufficiently large constant $\zeta$, the minimum circuit depth is in fact $\Omega(\log n)$.

Let $r_N(\boldsymbol{\xi},\boldsymbol{\xi})$ be the self-overlap, let $\varrho$ denote the Parisi order parameter, and let the Parisi variational formula contain an infimum over Pa…

Let $q$ be the Edwards–Anderson parameter … Here $b$ is the transverse-field parameter, and $\beta$ is the inverse temperature. Large-field absence conjecture. For the quantum Sher…

Let the quantum generalized random energy model (QGREM) have multiple phase transitions, with critical field strengths denoted by $\Gamma_k$, and let $\pmb{\sigma_k}$ denote the co…

Field-destabilisation conjecture. The longitudinal and transversal fields should destabilise the glass phase in the quantum SK model.

For the quantum $p$-spin model, let the phase diagram be the one described by Figure, and consider its behavior at low temperatures as the interaction order $p$ varies. Smooth…