Fig. 1. Schematics of resonant quantum PCA algorithm.

(A) The energy structure of the coupled probe-register system with H = ∣1〉〈1∣ ⊗ ρ. ∣λ_i〉 is the ith eigenstate of ρ, and λ_i ∈ [0,1] is the corresponding eigenvalue. After introducing the probe qubit’s Hamiltonian, the energy of lowest level moves to the green dashed line. Once the scanning frequency ω ≈ λ_i, the Rabi oscillations of the probe qubit is induced. (B) The quantum circuit of RqPCA using the Suzuki-Trotter decomposition (NΔt = τ). The projective measurement of the probe qubit in the state ∣1〉 indicates success of the algorithm, with principal component being distilled in the register.