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arXiv:2108.13225 · New Journal of Physics

Fast generation of cat states in Kerr nonlinear resonators via optimal adiabatic control

Jiao-Jiao Xue, Ke-Hui Yu, Wenxiao Liu, Xin Wang, Hongrong Li

Published Apr 14, 2022• 12 citations
arXivHTMLPDF

Abstract

Abstract Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their applications in quantum information processing. In this paper, we propose a quantum speed-up method for the creation of cat states in a Kerr nonlinear resonator (KNR) via optimal adiabatic control. By simultaneously adiabatic tuning the cavity-field detuning and driving field strength, the width of the minimum energy gap between the target trajectory and non-adiabatic trajectory can be widened, which allows us to accelerate the evolution along the adiabatic path. Compared with the previous proposal, preparing cat states only by controlling two-photon pumping strength, our method can prepare the target state with a shorter time, a high-fidelity and a large non-classical volume. It is worth noting that the cat state prepared here is also robust against single-photon loss. Moreover, when we consider the KNR with a large initial detuning, our proposal will create a large-size cat state successfully. This proposal for preparing cat states can be implemented in superconducting quantum circuits, which provides a quantum state resource for quantum information encoding and fault-tolerant quantum computing.

DOI
10.1088/1367-2630/ac6765

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Abstract Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their applications in quantum information processing. In this paper, we propose a quantum speed-up method for the creation of cat states in a Kerr nonlinear resonator (KNR) via optimal adiabatic control. By simultaneously adiabatic tuning the cavity-field detuning and driving field strength, the width of the minimum energy gap between the target trajectory and non-adiabatic trajectory can be widened, which allows us to accelerate the evolution along the adiabatic path. Compared with the previous proposal, preparing cat states only by controlling two-photon pumping strength, our method can prepare the target state with a shorter time, a high-fidelity and a large non-classical volume. It is worth noting that the cat state prepared here is also robust against single-photon loss. Moreover, when we consider the KNR with a large initial detuning, our proposal will create a large-size cat state successfully. This proposal for preparing cat states can be implemented in superconducting quantum circuits, which provides a quantum state resource for quantum information encoding and fault-tolerant quantum computing.
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.
Schrödinger cat states, quantum superpositions of macroscopically distinct classical states, are an important resource for quantum communication, quantum metrology and quantum computation. Especially, cat states in a phase space protected against phase-flip errors can be used as a logical qubit. However, cat states, normally generated in three-dimensional cavities and/or strong multi-photon drives, are facing the challenges of scalability and controllability. Here, we present a strategy to generate and preserve cat states in a coplanar superconducting circuit by the fast modulation of Kerr nonlinearity. At the Kerr-free work point, our cat states are passively preserved due to the vanishing Kerr effect. We are able to prepare a 2-component cat state in our chip-based device with a fidelity reaching 89.1% under a 96 ns gate time. Our scheme shows an excellent route to constructing a chip-based bosonic quantum processor.
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.
Schrödinger cat states, quantum superpositions of macroscopically distinct classical states, are an important resource for quantum communication, quantum metrology and quantum computation. Especially, cat states in a phase space protected against phase-flip errors can be used as a logical qubit. However, cat states, normally generated in three-dimensional cavities, are facing the challenges of scalability and controllability. Here, we present a novel strategy to generate and store cat states in a coplanar superconducting circuit by the fast modulation of Kerr nonlinearity. At the Kerr-free work point, our cat states are passively preserved due to the vanishing Kerr effect. We are able to prepare a 2-component cat state in our chip-based device with a fidelity reaching 89.1% under a 96 ns gate time. Our scheme shows an excellent route to constructing a chip-based bosonic quantum processor.
The purpose of this Bachelor thesis is to study methods to engineer Schrödinger’s cat states in microwave resonators, as proposed in the paper Engineering quantum states of light by S. Puri et al. The thesis starts by introducing relevant notions and concepts. Thereafter, it provides several analytical as well as numerical derivations of the main equations and results in the paper by S. Puri et al. The Kerr non-linear resonator (KNR) is explored as a means to adiabatically generate cat states. The Hamiltonian of the KNR is modified by detuning and orthogonal drive modes to achieve faster initialisation. Some images are also replicated with Matlab and the Python toolbox QuTiP. Finally, we also construct a number of quantum gates using coherent states.
In optical and solid-state architectures, low-order nonlinearities are commonly exploited for quantum state preparation due to their practical accessibility and controllability, while higher-order contributions are typically much weaker and treated as unwanted perturbations. Here, we alternatively show that detuned Rydberg ensembles provide a natural platform where higher-order Kerr nonlinearities can become comparable in strength to lower-orders near multiphoton resonances. We demonstrate that these nonlinearities can be harnessed as a resource for the rapid preparation of non-Gaussian states, with the coexistence of multiple Kerr orders substantially accelerating the evolution of an initial coherent state into Schrödinger cat states. Furthermore, by combining the nonlinear dynamics with a controllable linear drive, we can gain the full control over the evolution trajectory, thereby achieving cat-state generation directly from vacuum on timescales beyond the genuine Kerr evolution. Our results establish a paradigm in which naturally occurring higher-order nonlinearities are transformed from unwanted imperfections into a valuable resource for quantum state engineering.