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Quantum kernel Gram matrix via ZZFeatureMap overlap

Source: R/quantum_kernel.R
quantum_kernel.Rd

Computes the Havlicek-et-al. quantum kernel $$K(\mathbf{x}_i, \mathbf{x}_j) \;=\; \bigl|\langle \phi(\mathbf{x}_j) \mid \phi(\mathbf{x}_i)\rangle\bigr|^2$$ over one or two datasets whose rows are feature vectors in [0, pi] (see quantum_scale()). The result is a positive semi-definite matrix with ones on the diagonal.

Usage

quantum_kernel(X, Y = NULL, reps = 2L, backend = c("rcpp", "r"))

Arguments

X

Numeric matrix or data frame (rows = samples, columns = features). Features are mapped 1-1 to qubits; the number of qubits equals ncol(X). The current pure-R simulator scales to about 8 qubits comfortably.

Y

Optional numeric matrix / data frame with the same number of columns as X. When NULL (default), the symmetric Gram matrix K(X, X) is returned.

reps

Integer encoding depth — forwarded to quantum_feature_map().

backend

One of "rcpp" (default, 10-50x faster; requires the package to be properly installed so the compiled code is available) or "r" (pure-R reference implementation, kept for audit and fallback).

Value

Numeric matrix with nrow(X) rows and nrow(Y %||% X) columns; all values lie in [0, 1].

References

Havlicek, V. et al. (2019). Supervised learning with quantum-enhanced feature spaces. Nature 567, 209-212.

Examples

set.seed(1)
X <- matrix(runif(20, 0, pi), nrow = 5)
K <- quantum_kernel(X, reps = 2L)
stopifnot(isSymmetric(K))
stopifnot(all(abs(diag(K) - 1) < 1e-8))