The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. I will study operator-algebraic forms of stability for unitary representations of groups and quantum synchronous strategies for non-local games. In particular, I will present how simple spectral gap estimates can lead to strong quantitative forms of stability. For example, the direct product of two (flexibly) Hilbert-Schmidt stable groups is again (flexibly) Hilbert-Schmidt stable, provided that one of them has Kazhdan's property (T). I will also provide a simple form and simple analysis of a non-local game with few questions, with the property that synchronous strategies with large value are close to perfect strategies involving large Pauli matrices. This simplifies one of the steps (the question reduction) in the recent announced resolution of Connes' embedding problem by Ji, Natarajan, Vidick, Wright and Yuen.