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New Journal of Physics

High-fidelity quantum gates via optimizing short pulse sequences in three-level systems

Cheng Zhang, Yang Liu, Jie Song, Yan Xia, Zhi‐Cheng Shi

Published Jan 1, 2024• 15 citations
Publisher

Abstract

Abstract We propose a robust and high-fidelity scheme for realizing universal quantum gates by optimizing short pulse sequences in a three-level system. To alleviate the sensitivity to the errors, we recombine all elements of error matrices to construct a cost function with three types of weight factors. The modulation parameters are obtained by searching for the minimum value of this cost function. The purposes of introducing the weight factors are to reduce the detrimental impact of high-order error matrices, suppress population leakage to the third state, correct the operational error in the qubit space, and optimize the total pulse area of short pulse sequences. The results demonstrate that the optimized sequences exhibit strong robustness against errors and effectively reduce the total pulse area. Therefore, this work presents a valuable method for achieving exceptional robustness and high speed in quantum computations.

DOI
10.1088/1367-2630/ad1a2a

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Abstract We propose a robust and high-fidelity scheme for realizing universal quantum gates by optimizing short pulse sequences in a three-level system. To alleviate the sensitivity to the errors, we recombine all elements of error matrices to construct a cost function with three types of weight factors. The modulation parameters are obtained by searching for the minimum value of this cost function. The purposes of introducing the weight factors are to reduce the detrimental impact of high-order error matrices, suppress population leakage to the third state, correct the operational error in the qubit space, and optimize the total pulse area of short pulse sequences. The results demonstrate that the optimized sequences exhibit strong robustness against errors and effectively reduce the total pulse area. Therefore, this work presents a valuable method for achieving exceptional robustness and high speed in quantum computations.
Many realizations of solid-state qubits involve couplings to leakage states lying outside the computational subspace, posing a threat to high-fidelity quantum gate operations. Mitigating leakage errors is especially challenging when the coupling strength is unknown, e.g., when it is caused by noise. Here we show that simple pulse sequences can be used to strongly suppress leakage errors for a qubit embedded in a three-level system. As an example, we apply our scheme to the recently proposed charge quadrupole (CQ) qubit for quantum dots. These results provide a solution to a key challenge for fault-tolerant quantum computing with solid-state elements.
In this work, we exploit the idea of composite pulses to achieve robust population inversion in a three-level quantum system. The scheme is based on the modulation of the coupling strength, while the other physical parameters remain unchanged. The composite pulses sequence is designed by vanishing high-order error terms, and can compensate the systematic errors to any desired order. In particular, this scheme keeps a good performance under the disturbance of waveform deformations. This trait ensures that population inversion can be nearly obtained even when the pulse sequence has a short jump delay. As an example, we employ the designed composite pulse sequence to prepare the WWW state in a robust manner in the superconducting circuits. The numerical results show that the fidelity can still maintain a high level in a decoherence environment.
Abstract In this work, we propose a composite pulses (CPs) scheme by modulating phases to achieve high fidelity population transfer in three-level systems. To circumvent the obstacle that not enough variables are exploited to eliminate the systematic errors in the transition probability, we put forward a cost function to find the optimal value. The cost function is independently constructed either in ensuring an accurate population of the target state, or in suppressing the population of the leakage state, or both of them. The results demonstrate that population transfer is implemented with high fidelity even when existing the deviations in the coupling coefficients. Furthermore, our CPs scheme can be extensible to arbitrarily long pulse sequences. As an example, we employ the CPs sequence for achieving the three-atom singlet state in an atom-cavity system with ultrahigh fidelity. The final singlet state shows robustness against deviations and is not seriously affected by waveform distortions. Also, the singlet state maintains a high fidelity under the decoherence environment.
We propose a protocol for robust quantum state engineering using composite pulses (CPs) in four-level systems. The analytical expression of the propagator is derived for the implementation of universal single-qubit gates and the maximum superposition state. By carefully designing the relative phases between pulses, the CP sequences can compensate for the pulse area error to any desired order. We present two classes of CP sequences, one generating robust population inversion and the other generating robust superposition states. As applications, we employ the well-designed CP sequences to achieve the conversion of the W and Greenberger-Horne-Zeilinger states with high fidelity in a Rydberg atomic system. It is shown that the CP sequences yield excellent robustness with respect to the pulse area errors, and they possess a short evolution time.
We determine the optimal quantum manipulation protocols for implementing high-fidelity, fast single-qubit gates. We demonstrate that the time-optimal pulse sequence is a ``bang-bang'' sequence: discrete pulses of either positive or negative maximum amplitude or zero. The non-adiabatic bang-bang pulse sequence minimizes gate duration providing a speedup for low-frequency architectures. We first derive the protocol for a transversally driven two-level system, extracting exact analytic expressions for minimum gate times. We then extend this framework to general multilevel architectures, identifying conditions that enable the coherent suppression of leakage errors. Using the fluxonium circuit as a representative case study, we optimize X/2X/2X/2 and Y/2Y/2Y/2 gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of 1/f1/f1/f flux noise and dissipation.
In this work, we put forward an approach of constructing the optimal composite pulse sequence for robust population transfer in two-level systems. This approach is quite universal and applicable to a variety of systems, because the modulation parameters of composite pulses are obtained by minimizing the homemade cost function rather than nullifying the error coefficients of the transition probability. Specifically, we design different forms of the cost function for implementing optimal robustness with respect to the single or multiple errors. When slightly adjusting the constraints of the cost function, this approach can be easily extended to achieve arbitrary population transfer. The numerical results demonstrate that the optimized sequences are immune from various systematic errors, allowing us to produce a broadening excitation range of the transition probability. Therefore, this work offers an optimal robust design for controlling quantum states in error-prone environments.