Mitigation Potential Geometry for Quantum Computing: Submodular Placement of Error Mitigation Under Budget Constraints

Mitigation Potential Geometry for Quantum Computing: Submodular Placement of Error Mitigation Under Budget Constraints  Quantum chips are noisy and mitigation resources (shots, depth, post-processing) are limited. Most workflows spread mitigation evenly or use ad-hoc rules, so effort is spent where it has little effect. Mitigation Potential Geometry (MPG) provides a simple alternative:      Score each circuit layer with a “mitigation potential” MtM_tMt: how much fixing that layer should improve the final answer.     Allocate a fixed budget using a submodular optimizer (greedy) with a (1−1/e)(1-1/e)(1−1/e)-style guarantee under stated conditions.     Stay honest in practice via an online curvature check γ\gammaγ: when structure deviates, MPG switches to local search or halts conservatively.     Model real devices with tensor-network / MPO locality to handle correlated and time-varying noise (drift), not just i.i.d. errors.     Plug-and-play with existing tools by placing ZNE, PEC, virtual distillation, symmetry checks, and DD exactly where they matter most.     Balance trade-offs (fidelity vs. shots/depth/time) through a multi-objective formulation and Pareto reporting.    What’s in this recordThe methods paper and supporting materials describing MPG 2.x: the core objects (MtM_tMt, the noise direction cone, transfer coefficients), the placement algorithm with the γ\gammaγ check and fallbacks, scalable estimators (sectorized tensor networks, stochastic quadrature), and a front-loaded validation roadmap (benchmarks, baselines, statistics, failure-mode policy). Plain-English executive summary included.  What this does not claimThis is a methods contribution; it reports no hardware results and is not yet peer-reviewed. The record includes a clear plan for empirical validation on real devices and guidance for integration into existing compiler stacks (Qiskit/Cirq/LLVM-based).  Who should read thisTeams hitting mitigation plateaus (ZNE/PEC/VD), compiler developers seeking budget-aware passes, and researchers exploring device-aware placement under realistic (non-Markovian, drifting) noise.  How to engage (written only)If you want to try MPG on your workloads, please share (in writing): (1) your benchmark (e.g., QAOA/VQE size), (2) device/provider and drift context, (3) current mitigation baselines, and (4) acceptable overheads. The paper provides a short diagnostic + pilot design you can run in-house.We are open to custom consultancy or research assignments (including refinement for your devices/workloads); collaboration can be fully asynchronous and in writing.  Keywords (bullet list)      Quantum computing     Error mitigation     NISQ     Mitigation Potential Geometry (MPG)     Submodular optimization     Online curvature check (γ\gammaγ)     Tensor networks (TN)     Matrix Product Operators (MPO)     Non-Markovian noise     Device drift (T1/T2)     Zero-Noise Extrapolation (ZNE)     Probabilistic Error Cancellation (PEC)     Virtual distillation     Symmetry verification     Dynamical decoupling (DD)     QAOA / VQE     Compiler optimization (Qiskit, Cirq, LLVM)     Resource allocation / Pareto frontier   Research consultancy