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Bulletin of the American Physical Society

An experimental implementation for stabilizing Schrödinger cat states in a Kerr nonlinear resonator - Basic concepts

Nicholas Frattini, Alexander Grimm, Shantanu Mundhada, Shruti Puri, Steven Touzard, Mazyar Mirrahimi

Published Mar 5, 2019• 0 citations
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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.

arXiv:2406.13390•Jun 19, 2024•0 citations
Abstract Photonic cat states stored in high-Q resonators show great promise for hardware efficient universal quantum computing. We propose an approach to efficiently prepare such cat states in a Kerr-nonlinear resonator by the use of a two-photon drive. Significantly, we show that this preparation is robust against single-photon loss. An outcome of this observation is that a two-photon drive can eliminate undesirable phase evolution induced by a Kerr nonlinearity. By exploiting the concept of transitionless quantum driving, we moreover demonstrate how non-adiabatic initialization of cat states is possible. Finally, we present a universal set of quantum logical gates that can be performed on the engineered eigenspace of such a two-photon driven resonator and discuss a possible realization using superconducting circuits. The robustness of the engineered subspace to higher-order circuit nonlinearities makes this implementation favorable for scalable quantum computation.
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.