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Nonadiabtic robust pulses for creating superposition states in a resonant three-level system

Lin Wan, Joel Moser, Ying Lin Yan

Published Dec 18, 2019• 0 citations
Publisher

Abstract

We proposed new light pulses to create a quantum coherent superposition state by using the invariant-based inverse engineering in a resonant three-level system, where physical imperfections such as the frequency detuning and variations in Rabi frequencies were concerned. Simulation results show that the fidelity of creating a superposition state of more than 98% can be achieved over a frequency detuning of ±18 MHz in 4 μs. The pulses are robust against the spatial inhomogeneity or instantaneous fluctuations in laser intensity. Comparisons of our pulses with other pulses show that our pulses are much more robust in terms of both the frequency detuning and laser intensity variations. Such features make our pulses an effective alternative as the spectral hole-burning pulses to reduce the number of repetitions of pulses, and can also be applied to initialize the multiple qubits where the driving frequency varies with time or position in superconducting transmon qubit systems.

DOI
10.1117/12.2547414

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We proposed new light pulses to create a quantum coherent superposition state by using the invariant-based inverse engineering in a resonant three-level system, where physical imperfections such as the frequency detuning and variations in Rabi frequencies were concerned. Simulation results show that the fidelity of creating a superposition state of more than 98% can be achieved over a frequency detuning of ±18 MHz in 4 μs. The pulses are robust against the spatial inhomogeneity or instantaneous fluctuations in laser intensity. Comparisons of our pulses with other pulses show that our pulses are much more robust in terms of both the frequency detuning and laser intensity variations. Such features make our pulses an effective alternative as the spectral hole-burning pulses to reduce the number of repetitions of pulses, and can also be applied to initialize the multiple qubits where the driving frequency varies with time or position in superconducting transmon qubit systems.
Abstract We propose a method to engineer the light matter interaction while initializing a qubit present of physical constraints utilizing the inverse engineering. Combining the multiple degrees of freedom in the pulse parameters with the perturbation theory, we develop pulses to initialize the qubit within a tightly packed frequency interval to an arbitrary superposition state with high fidelity. Importantly, the initialization induces low off-resonant excitations to the neighboring qubits, and it is robust against the spatial inhomogeneity in the laser intensity. We apply the method to the ensemble rare-earth ions system, and simulations show that the initialization is more robust against the variations in laser intensity than the previous pulses, and reduces the time that ions spend in the intermediate excited state by a factor of 17. The method is applicable to any systems addressed in frequency such as nitrogen-vacancy centers, superconducting qubits, quantum dots, and molecular qubit systems.
High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
Abstract Optimal generation of photon Fock states is of significance to quantum science and technology. Here we develop a theoretical scheme for fast generating microwave photon Fock states in a circuit quantum electrodynamics (QED) via invariant-based shortcuts to adiabaticity. A superconducting transmon qubit is dispersively coupled to a cavity field of transmission line resonator. Two classical drivings are applied to a composite system, consisting of a transmon qubit and cavity field. In the two-photon resonance with a large intermediate-level detuning, a single-photon Fock state can be fast created by inversely engineering Rabi couplings. With the assistance of auxiliary driving, qubit state can be initialized for inducing multi-photon Fock states in the shortcut manner. Due to negligible leakage effects and high robustness, our scheme offers a potential way to rapidly prepare photon Fock states with a superconducting qubit in circuit QED.
Entanglement generation via optimal drivings is of significance for quantum information science and engineering. Here, an efficient scheme is proposed for creating entangled states between two transmon qubits via shortcuts to adiabaticity with constant Rabi drivings. Two three-level atoms of Cooper-pair box circuits are coupled to a common cavity field of transmission-line resonator and individually driven by adjustable classical microwaves. In the regime of large detuning, we obtain an effective three-state system consisting of qubits and cavity photons. By the invariant-based shortcuts with time-independent Rabi drivings, two-qubit entangled states can be rapidly induced from an easily prepared product state. Compared to the entanglement creation with time-dependent Rabi drivings, our protocol not only becomes more feasible in experiment but also needs shorter times. Moreover, high-fidelity quantum operations can be realized with the accessible decoherence rates. The scheme could pave a promising avenue towards optimal generation of entangled states between superconducting qubits.
Coherent manipulation of three-level systems is of critical significance to quantum information processing. Here, we propose a scheme to achieve quantum state engineering in arbitrary three-level systems, in which the controlling Hamiltonian can be inversely engineered based on Lewis-Riesenfeld invariants and a gauge transformation. With well-designed control pulses, the three-level system continually evolves from the initial state to a desired final state in one step. The proposed scheme allows diverse optimizations, which gives it a significant advantage in robustness and fidelity over the commonly used resonant-pulse multistep method. The scheme can also be extended to produce multiqubit entangled states provided with a similar state subspace. In a particular application, we demonstrate numerically that our protocol can reliably and robustly prepare qutrit states as well as three-qubit entangled WWW states within superconducting circuits.