Achieving fast, high fidelity single qubit gates for the Kerr-Cat Qubit

The Kerr-Cat Qubit is a biased noise qubit realised by coherent states in an oscillator. We investigated the effect of a detuning and a single photon drive on this qubit. 

Both of which cause the coherent states │±α〉 defined by the two photon drive and Kerr nonlinearity to be no longer eigenstates of our Hamiltonian. 

For a small detuning and single photon drive strength the difference to the eigenstates is small enough so that these states are a good approximation of the eigenstates. 

However this limits us to the regime in which X and Z rotations which are realised by a detuning and a single photon drive respectively are slow. 

Increasing these terms will speed up the gates but will result in considerably lower fidelities as the coherent states are deformed over time. 

Using coherent states that are better approximations of eigenstates than │±α〉 can result in fast, high fidelity gates. 

These displaced states have a semi periodic deformation in them, which needs to be considered carefully and gives rise to a discrete set of detunings and Kerr nonlinearities that produce high fidelity rotations.