Homeostatic Quantum Computing: Beyond Darwinian Selection to Geometric Flow

AbstractCurrent quantum computing architectures predominantly follow a redundancy-basedparadigm inspired by Quantum Darwinism, where environmental selection andinformation proliferation determine pointer-state emergence and classicality. This paperproposes Homeostatic Quantum Computing (HQC) as a complementary frameworkgrounded in Homeostatic Adaptive Teaming Intelligence (HATI) principles. HQCreframes pointer-state emergence as convergence to stable attractors within thedissipative geometry of Lindblad dynamics, rather than as outcomes of environmentalwitnessing contests.Through analysis of the Lindblad master equation, we identify two qualitatively distinctdynamical regimes—Darwinian selection dominated by discrete dephasing events, andgeometric flow characterised by smooth convergence toward engineered attractorbasins—separated by a dimensionless homeostatic control parameter. We deriveconditional recovery-time bounds and present falsifiable predictions distinguishingHQC-governed dynamics from standard dephasing-dominated evolution, testable oncurrent transmon and fluxonium hardware. Historical parallels with the audio industry’stransition from vacuum-tube proliferation to transistor-based precision engineeringillustrate the potential efficiency advantages of quality-first scaling. No new postulatesare introduced beyond standard open quantum systems theory; all results follow fromestablished GKSL formalism under specific parameter regimes. Dedicated to Stephen Hodgson Keywords: quantum computing, homeostatic control, Lindblad dynamics, attractor convergence,error resilience, geometric flow, HATI framework