7 problems

Let $\boldsymbol{\rho}^\star$ be the MPO state considered in the recovery results, and let the results in the Frobenius-norm recovery guarantee and the recovery-error bounds for va…

Let $Q$ be the number of Haar-random rank-one POVMs and $M$ the number of measurements performed for each POVM. The statistical recovery bound in the paper requires a total number…

Let $\mathcal{A}^{Q}:\mathbb{C}^{d^n\times d^n}\rightarrow\mathbb{R}^{KQ}$ be the linear map induced by $Q$ random unitary matrices, and let $\overline{\mathbb{X}}_{\overline{r}}$…

Let the Lee-Yang C-weak Hopf algebra be the algebra described in Example, and let the associated RFP MPDOs be the renormalization fixed-point matrix product density operators const…

Let RFP MPDOs be the renormalization fixed-point matrix product density operators constructed from biconnected C-weak Hopf algebras. The general phase classification of these state…

Quantum Gibbs-state preparation conjecture. The sufficient number of elementary quantum gates for preparing a one-dimensional quantum Gibbs state should also be quasi-linear, as in…

A stationary state $\rho$ of a primitive Liouvillian is assumed to have a Log-Sobolev constant. A constant-bond-dimension approximation conjecture asserts that, for a given error,…