BT‑PEC Full‑Stack Computing Framework: A Steady-State Dynamic Scheduling Model for Open Quantum Systems

This paper proposes the BT-PEC full-stack computing framework to address the challenge that traditional static resource scheduling and fixed error correction strategies fail to adapt to time-varying noise and dynamic decoherence of coherent resources in the NISQ era for open quantum systems. The framework includes a quantum living-state architecture, a quantum operating system, and a unified programming language system, with falsifiable engineering predictions and simulation verification schemes. Four core operators are defined: the B basis operator representing underlying hardware quantum resources; the T transition operator describing coherent energy input and quantum state evolution; the P power consumption operator for resource and energy costs from gate operations and entanglement generation; and the EC entropy-causal closure operator implementing error correction, feedback compensation and causal recording constraints. A global steady-state order parameter Ω=tr(BT)−tr(PEC) is introduced. Three system phases are classified by threshold ϵ=0.05: survival state (Ω_Q>0.05), critical state (|Ω_Q|≤0.05), and extinction state (Ω_Q<−0.05). The Lindblad master equation is adopted to model open quantum system dynamics, combined with an exponential fidelity decay model and binary information entropy proxy function. The phase transition critical decoherence parameter γ_c≈0.42 is obtained from simulation, which is only valid within this model and not a universal physical constant. The full-stack hardware-software co-design consists of a topology-logic two-layer quantum hardware architecture, the BT-PEC/OS quantum operating system kernel with Ω_Q-aware task scheduling, and Omega-IR intermediate representation together with a multi-paradigm unified programming language. The FEA cross-language adaptation layer enables compatibility with Python, C++ and other programming environments. Numerical simulations are implemented on QuTiP with five controlled repeatable experiments. Eight quantifiable, falsifiable engineering predictions are presented with explicit falsification criteria. Limitations of the model are clarified: γ_c is simulation-specific; BT and PEC operator matrices need instantiation for individual hardware; Omega-IR currently only has semantic specifications without a production-grade compiler and virtual machine; performance advantages are validated only by numerical simulation pending physical quantum hardware tests; causal chain integrity under high concurrency remains an engineering challenge. The BT-PEC framework unifies quantum hardware, operating system and compilation system under one steady-state evaluation system, offering a verifiable engineering theoretical model for hardware-software co-design of quantum computers under dynamic NISQ noise environments. Future work includes completing the Omega-IR compiler, scaling up simulations, and preparing validation experiments on small-scale physical quantum processors.