Fit a Quantum Kernel Ridge Regression (Pillar 6)

Closed-form dual solution $$\boldsymbol{\alpha} = (K + \lambda I)^{-1}\mathbf{y}$$ using the quantum Gram matrix from quantum_kernel(). Works both for regression (y numeric) and binary classification (encode y \in \{-1, +1\} and threshold the prediction at zero).

Usage

quantum_krr_fit(X, y, reps = 2L, lambda = 0.1)

Arguments

X

Feature matrix already rescaled to [0, pi] — quantum_scale() is the recommended preprocessor.

y

Numeric response vector (or \pm 1 for classification).

reps

Integer, encoding depth of the ZZFeatureMap.

lambda

Numeric ridge regulariser (> 0).

Value

An edaphos_quantum_krr object.

Examples

# \donttest{
  set.seed(1)
  X <- quantum_scale(matrix(runif(60), ncol = 3L))
  y <- sign(X[, 1L] - mean(X[, 1L]))
  fit <- quantum_krr_fit(X, y, reps = 2L, lambda = 0.1)
  mean(predict(fit, X, type = "class") == y)  # training accuracy
#> [1] 1
# }