Stabilizing the Kerr arbitrary cat states and holonomic universal control

TL;DR

This paper introduces a novel Hamiltonian for Kerr nonlinear resonators that stabilizes arbitrary cat states, enables their manipulation in phase space, and facilitates holonomic quantum computing with potential superconducting circuit implementation.

Contribution

It proposes a new Hamiltonian for stabilizing and controlling arbitrary cat states, and develops a universal holonomic quantum computing protocol using these states.

Findings

Demonstrates stabilization of arbitrary cat states with a new Hamiltonian.

Shows control over superposed states allowing phase space manipulation.

Develops a feasible superconducting circuit implementation.

Abstract

The interference-free double potential wells realized by the two-photon driving Kerr nonlinear resonator (KNR) can stabilize cat states and protect them from decoherence through a large energy gap. In this work, we use a parametrically driving KNR to propose a novel engineering Hamiltonian that can stabilize arbitrary cat states and independently manipulate the superposed coherent states to move arbitrarily in phase space. This greater degree of control allows us to make the two potential wells collide and merge, generating a collision state with many novel properties. Furthermore, the potential wells carrying quantum states move adiabatically in phase space produce quantum holonomy. We explore the quantum holonomy of collision states for the first time and propose a holonomy-free preparation method for arbitrary cat states. Additionally, we develop a universal holonomic quantum computing protocol utilizing the quantum holonomy of coherent and collision states, including single-qubit rotation gates and multi-qubit control gates. Finally, we propose an experimentally feasible physical realization in superconducting circuits to achieve the Hamiltonian described above. Our proposal provides a platform with greater control degrees of freedom, enabling more operations on bosonic modes and the exploration of intriguing physics.