Quantum Future-Trial Computing (QFTC) v2: Geometric Time Control, Noise-Consistent Rollback, and Complexity-Theoretic Positioning Beyond BQP

Quantum Future-Trial Computing (QFTC) v2 introduces a geometric reinterpretation of computational time and formalizes rollback as an active computational resource rather than a passive property of unitarity. Instead of treating time as an external parameter, QFTC models computational evolution as controlled motion in projective Hilbert space via the Fubini–Study metric. This geometric formulation enables forward exploration, exact unitary rollback, and coherent selective commit without measurement collapse. Version 2 strengthens the framework by incorporating: • Bounded-noise rollback analysis under CPTP maps • Trace-distance stability bounds with linear accumulation control • Continuous-time open-system modeling via Lindblad dynamics • Definition of physical rollback capacity C_phys • Explicit constructibility constraints for the commit operator • Complexity-theoretic positioning between BQP and PostBQP QFTC does not modify quantum mechanics or introduce nonlinearity. All operations remain unitary. The potential computational advantage arises from macro-structural use of reversibility, not from postselection or hidden oracle amplification. The model defines QFTC_ε as a physically realizable subclass constrained by rollback stability conditions. A strict separation from BQP remains a formal hypothesis, pending lower-bound proof of non-simulability of rollback-induced amplitude steering. QFTC v2 therefore establishes a structured, noise-consistent, thermodynamically coherent framework for geometric time control in quantum computation.