Quantum Kernel Estimation With Neutral Atoms For Supervised
  Classification: A Gate-Based Approach
Marco Russo Edoardo Giusto Bartolomeo Montrucchio
Quantum Kernel Estimation (QKE) is a technique based on leveraging a quantum
computer to estimate a kernel function that is classically difficult to
calculate, which is then used by a classical computer for training a Support
Vector Machine (SVM). Given the high number of 2-local operators necessary for
realizing a feature mapping hard to simulate classically, a high qubit
connectivity is needed, which is not currently possible on superconducting
devices. For this reason, neutral atom quantum computers can be used, since
they allow to arrange the atoms with more freedom. Examples of
neutral-atom-based QKE can be found in the literature, but they are focused on
graph learning and use the analogue approach. In this paper, a general method
based on the gate model is presented. After deriving 1-qubit and 2-qubit gates
starting from laser pulses, a parameterized sequence for feature mapping on 3
qubits is realized. This sequence is then used to empirically compute the
kernel matrix starting from a dataset, which is finally used to train the SVM.
It is also shown that this process can be generalized up to N qubits taking
advantage of the more flexible arrangement of atoms that this technology
allows. The accuracy is shown to be high despite the small dataset and the low
separation. This is the first paper that not only proposes an algorithm for
explicitly deriving a universal set of gates but also presents a method of
estimating quantum kernels on neutral atom devices for general problems using
the gate model.