Josephson Entanglers and Encoded Error Correction with Four-Tool Control

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We study two-qubit control and quantum error correction with a specified three-node Josephson-circuit Hamiltonian, Gaussian-waveform shaping, and Gaussian–T3–solid-torus–Möbius bookkeeping. The cumulative R01–R20 source retains number-sector and spectral-notch identities, charge-basis truncation residuals, flux-coupler inversion, native- entangler and CNOT compilation, and stochastic decoder bounds. Exact gate algebra establishes that two calibrated native entanglers, but not one, are sufficient for a logical CNOT with suitable one-qubit operations. Finite five- and six-level projected CNOT fidelity calculations reach approximately 0.999985, while physical replacement of the ideal local operations requires separately verified microwave controls. R18 derives non-RWA charge-drive and flagged-Steane calculations; their limited timing and stochastic-error budgets do not certify a working encoded device. R19–R20 establish an infinite-horizon O(log2 t) resource-growth theorem conditional on a joint space–time decoding graph with a uniform local-stochastic bound, and derive a bounded-spread reduction for correlated primitive faults. R21 proves an unprojected coherent-leakage-return inequality, an exact Pauli-plus-leakage channel identity after explicit randomization and sector dephasing, and a corrected history-conditioned reset bound. R22 resolves a previously silent control-frame mismatch: laboratory-frame intervals compose correctly only when transformed with their absolute time boundaries. A new independently executable eight-interval matrix test verifies exact frame telescoping to below 10−15 and exhibits a large error from naive segmentwise resetting. The historical high-fidelity R22 Josephson candidates remain exploratory because their complete control-waveform/replay … [excerpt; full original in PDF]

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