극저온 초전도 플럭소니움(Fluxonium) 큐비트 초고인덕턴스 조셉슨 접합 어레이(Superinductance) 자속 바이어스 및 분극 서보 C# 실시간 SIMD 엔진

3. Zero-Allocation C# SIMD 플럭소니움 자속 서보 구현

판독 공진기의 복소 투과 계수 $S_{21}$ 주파수 분광 데이터를 수신하여 온칩 초전도 마그넷 DAC 전류를 10,000 Hz로 실시간 보정하는 C# .NET 9.0 엔진입니다.

using System;
using System.Runtime.CompilerServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;

namespace ZeliDesk.Quantum.FluxoniumQubit
{
    public readonly ref struct FluxoniumCavityTelemetry
    {
        public readonly float ReadoutCavityFreqShiftKhz; // Dispersive shift
        public readonly float QubitTransitionFreqGhz;    // omega_01 ~ 1.25 GHz
        public readonly float MeasuredT1LifetimeMicrosec; // T1 relaxation
        public readonly float CurrentFluxBiasOffsetMicroPhi0;
        public readonly float CryostatTempMillikelvin;   // 15 mK

        public FluxoniumCavityTelemetry(float cavShift, float qFreq, float t1, float fluxOffset, float tempMilliK)
        {
            ReadoutCavityFreqShiftKhz = cavShift;
            QubitTransitionFreqGhz = qFreq;
            MeasuredT1LifetimeMicrosec = t1;
            CurrentFluxBiasOffsetMicroPhi0 = fluxOffset;
            CryostatTempMillikelvin = tempMilliK;
        }
    }

    public ref struct FluxoniumServoCommands
    {
        public float OnChipFluxDacCurrentOffsetMicroAmps;
        public float TargetFluxBiasMilliPhi0;
        public float EstimatedDephasingTimeT2StarMicrosec;
        public float QuantumAnharmonicityMhz;
        public bool SweetSpotLocked;
    }

    public static class SuperconductingFluxoniumEngine
    {
        private const float NominalHalfFluxSweetSpotFreqGhz = 1.2450f; // 1.245 GHz at phi_ext = pi
        private const float FluxDacSensitivityUaPerMicroPhi0 = 0.085f; // 85 nA / uPhi0

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void MaintainSweetSpotLock(
            in FluxoniumCavityTelemetry telemetry,
            ref FluxoniumServoCommands output)
        {
            // 1. Quadratic Minimum Frequency Tracking: omega_01 = omega_min + k * (Delta Phi)^2
            float freqError = telemetry.QubitTransitionFreqGhz - NominalHalfFluxSweetSpotFreqGhz;

            // Invert flux error: Delta Phi = sign(cavity_shift) * sqrt(2 * freqError / k)
            float kCurvature = 4.2e-6f; // GHz / (uPhi0)^2
            float deltaPhiEstimate = MathF.Sign(telemetry.ReadoutCavityFreqShiftKhz) * MathF.Sqrt(MathF.Max(0.0f, freqError / kCurvature));

            // 2. Closed-Loop DAC Nulling Current Feedback
            float targetFluxCorrection = -deltaPhiEstimate * 0.45f;
            output.TargetFluxBiasMilliPhi0 = 500.0f + (telemetry.CurrentFluxBiasOffsetMicroPhi0 + targetFluxCorrection) * 1.0e-3f; // 500 mPhi0 = 0.5 Phi0

            float dacCurrentStepUa = targetFluxCorrection * FluxDacSensitivityUaPerMicroPhi0;
            output.OnChipFluxDacCurrentOffsetMicroAmps = Math.Clamp(dacCurrentStepUa, -15.0f, 15.0f);

            // 3. Anharmonicity Calculation (omega_12 - omega_01)
            // For Fluxonium: omega_01 ~ 1.25 GHz, omega_12 ~ 3.85 GHz -> Anharmonicity ~ +2.6 GHz (Huge!)
            output.QuantumAnharmonicityMhz = +2600.0f; // 2.6 GHz positive anharmonicity

            // 4. Pure Dephasing Time T2* Prediction
            // T2* improves drastically at sweet spot (deltaPhi < 1 uPhi0)
            float absDeltaPhi = MathF.Abs(deltaPhiEstimate);
            float t2Star = (absDeltaPhi < 1.0f) ? 1250.0f : (1250.0f / (absDeltaPhi * absDeltaPhi));
            output.EstimatedDephasingTimeT2StarMicrosec = Math.Clamp(t2Star, 10.0f, 1800.0f);

            // Sweet spot lock criteria: deltaPhi < 0.8 uPhi0
            output.SweetSpotLocked = (absDeltaPhi <= 0.8f && telemetry.MeasuredT1LifetimeMicrosec > 800.0f);
        }
    }
}