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arXiv:2408.00471 · Advanced Quantum Technologies

Preparation of High‐Fidelity Entangled Cat States with Composite Pulses

Ge‐Ge Gu, Dong-Sheng Li, Ye‐Hong Chen, Bi‐Hua Huang, Yan Xia

Published Feb 17, 2025• 7 citations
arXivHTMLPDF

Abstract

Abstract A protocol is proposed for the preparation of high‐fidelity entangled cat states with composite pulses. The physical model contains two Kerr‐nonlinear resonators and a cavity. By properly designing the parameters, each Kerr‐nonlinear resonator is confined in the cat‐state subspace and the entangled cat states can be generated efficiently. Composite two‐photon drives are introduced with multiple amplitudes and frequencies to improve the fidelity of the entangled cat states in the presence of parameter errors. The performance of the protocol is estimated by taking into account the parametric errors and decoherence. Numerical simulation results show that, the protocol is robustness to timing error, detuning error, and decoherence. It is hoped that the protocol may provide a method for preparing stable entangled cat states.

DOI
10.1002/qute.202400518

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Abstract A protocol is proposed for the preparation of high‐fidelity entangled cat states with composite pulses. The physical model contains two Kerr‐nonlinear resonators and a cavity. By properly designing the parameters, each Kerr‐nonlinear resonator is confined in the cat‐state subspace and the entangled cat states can be generated efficiently. Composite two‐photon drives are introduced with multiple amplitudes and frequencies to improve the fidelity of the entangled cat states in the presence of parameter errors. The performance of the protocol is estimated by taking into account the parametric errors and decoherence. Numerical simulation results show that, the protocol is robustness to timing error, detuning error, and decoherence. It is hoped that the protocol may provide a method for preparing stable entangled cat states.
ABSTRACT We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing time‐averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high‐order three‐photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three‐photon state and the qubit excited state in the squeezed picture. Numerical simulations confirm that the target state can be prepared with a population close to 1 under ideal conditions, and even in the presence of realistic environmental noise, an appreciable state fidelity of 0.77 and an entanglement concurrence of 0.71 can still be preserved, demonstrating the high robustness of our protocol. Our method provides a practical pathway for generating complex non‐Gaussian entangled states, which are of significant value for fault‐tolerant quantum computation and quantum metrology beyond the standard quantum limit.
We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.
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 Optimal coherent control of many qubits is critical to quantum information processing. Here, an efficient scheme is proposed for implementing state swap and creating an entanglement with two superconducting qubits in a circuit quantum electrodynamics (QED). Two qutrits of Cooper‐pair box (CPB) circuits are placed into a cavity field and are driven by individual classical microwaves. In the two‐photon resonance with a large detuning, each CPB is reduced into a qubit effectively. Within a composite system composed of qubit states and cavity photons, two‐qubit state swap and entanglement can be fast obtained using the technique of shortcuts to adiabaticity with counterdiabatic drivings. Benefited from the shorter duration times and less sensitivity to timing errors and parameter imperfections, high‐fidelity quantum operations can be performed with the accessible decoherence rates. The present protocol could offer a feasible route towards optimized operations on superconducting qubits in a circuit QED.
Abstract The cat state, known as the superposition of coherent states, has broad applications in quantum computation and quantum metrology. Increasing the number of optical cat states is crucial to implement complex quantum information tasks based on them. Here, two optical cat states are prepared simultaneously based on a nondegenerate optical parametric amplifier. By subtracting one photon from each of two squeezed vacuum states, two odd cat states with orthogonal superposition direction in phase space are prepared simultaneously, which have similar fidelity of 60% and amplitude of 1.2. Compared with the traditional method to generate two odd optical cat states based on two degenerate optical parametric amplifiers, only one nondegenerate optical parametric amplifier is applied in this experiment, which saves half of the quantum resources of nonlinear cavities. The presented results make a step toward preparing the four‐component cat state, which has potential applications in fault‐tolerant quantum computation.
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.