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Thermalization in highly excited quantum many-body system does notnecessarily mean a complete memory loss of the way the system was formed. Thiseffect may pave a way for a quantum computing, with a large number of qubits$n\simeq 100$--1000, far beyond the quantum chaos border. One of themanifestations of such a thermalized non-equilibrated matter is revealed by astrong asymmetry around 90$^\circ $ c.m. of evaporating proton yield in theBi($\gamma$,p) photonuclear reaction. The effect is described in terms ofanomalously slow cross symmetry phase relaxation in highly excited quantummany-body systems with exponentially large Hilbert space dimensions. In theabove reaction this phase relaxation is about eight orders of magnitude slowerthan energy relaxation (thermalization).

Anomalously Slow Cross Symmetry Phase Relaxation, Thermalized Non-Equilibrated Matter and Quantum Computing Beyond the Quantum Chaos Border