Fig. 3: Numerical results for the channel equalization (CE) task with Hamiltonian ansatz.
From: Overcoming the coherence time barrier in quantum machine learning on temporal data
a Error rates on test messages for the CE task with a Hamiltonian ansatz (2 + 4)-qubit QRC for two distinct connectivities shown in (b) The fully-connected QRC in red has Jacobian rank RJ = 2R − 1 = 15 and is shown for both S → ∞ (circles) and finite S = 105 (⋆), whereas the split QRC has RJ = 2(22 − 1) = 6 and only S → ∞ is plotted in magenta. These are compared with the error rates of naive rounding (black dash-dots) and logistic regression on the current signal (yellow +, see Supplementary Note 6), and the exact channel inverse (blue dashed). c Performance of connected QRC on SNR = 20dB test signals (solid) of increasing length Nts ≤ 5000, with shots S = 105. Training error on N = 100-length messages is indicated for comparison in dashed lines. Without reset (red) or using 4 ancilla qubit ansatz with quantum non-demolition (QND) readout (proposed in ref. 30, green), the algorithms both fail, approaching the random guessing error rate and showing that both architectures suffer from the thermalization problem. Performance is only slightly reduced from the dissipation-free case (blue) when strong decay T1 = 10τ is included (purple). All error rates in (c) are averaged over 8 different test messages.
