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Operational Workflow

High-level operational sequence of the hybrid execution pipeline.

1. End-to-End Execution Sequence

sequenceDiagram
    autonumber
    participant D as Data Source
    participant I as Ingress
    participant H as Host Hardware
    participant Q as Quantum Engine
    participant O as Output Store

    D->>I: Raw Observations X in R^(N x d), Labels y
    I->>I: Dimensionality Reduction R^d -> R^n
    I->>I: Periodic Scaling to [-pi, pi]^n
    I->>H: Transfer Normalized Mini-Batches
    loop Iterative Training Step
        H->>H: Evaluate Classical Pre-Layers
        H->>Q: Dispatch Encoded Features & Unitary Parameters
        Q->>Q: State Evolution |psi(x, theta)> = U(theta)|psi(x)>
        Q->>Q: Measure Observables <H_k>
        Q->>H: Return Measured Expectations
        H->>H: Compute Objective Loss L
        H->>Q: Query Parameter-Shift Gradients d<H_k>/d theta
        Q->>H: Return Quantum Gradient Tensors
        H->>H: Update Parameters theta <- theta - eta * grad_theta
    end
    H->>O: Persist Optimized Weights & Telemetry

2. Mathematical Optimization Loop

  1. State Preparation: $\(|\psi(x)\rangle = \bigotimes_{j=1}^n R_x(\tilde{x}_j) |0\rangle\)$

  2. Parameterized Evolution: $\(|\psi(x, \theta)\rangle = U(\theta) |\psi(x)\rangle = \prod_{l=1}^L \left( W_l \prod_{j=1}^n V_j(\theta_{l,j}) \right) |\psi(x)\rangle\)$

  3. Measurement: $\(\hat{y}_i = \text{Tr}\left( \sigma_i^z |\psi(x, \theta)\rangle\langle\psi(x, \theta)| \right) \in [-1, 1]\)$

  4. Objective Minimization: $\(\min_\theta \frac{1}{|B|} \sum_{i \in B} \mathcal{L}\left( f(\hat{y}_i), y_i \right)\)$