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Physical Review A

Universal composite pulses for robust quantum state engineering in four-level systems

Zhi‐Cheng Shi, Jian-Hui Wang, Cheng Zhang, Jie Song, Yan Xia

Published Feb 29, 2024• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.109.022441

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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.
Abstract A scheme is proposed for achieving robust population inversion in five‐level systems by means of composite pulses. An example of such a system consists of the magnetic sublevels with angular momenta and . Through elaborately constructing the relative phases of pulse pairs, the composite sequences perform well in suppressing the uncorrelated pulse area errors. In particular, the five pulse‐pair sequence possesses good robustness and a short evolution time. The composite sequences are further designed to compensate for a single type of pulse area errors to any desired order. This work provides a high‐efficiency way for robust quantum state manipulation in five‐level systems.
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.
A number of composite pulse (CP) sequences for four basic quantum phase gates---the Z, S, T, and general phase gates---are presented. The CP sequences contain up to 18 pulses and can compensate up to eight orders of experimental errors in the pulse amplitude and duration. The short CP sequences (up to eight pulses) are calculated analytically and the longer ones numerically. The results demonstrate the remarkable flexibility of CPs accompanied by extreme accuracy and robustness to errors. These CP sequences, in particular the Z, S, and T gates, can be very useful quantum control tools in quantum information applications, because they provide a variety of options to find the optimal balance among ultrahigh fidelity, error range, and speed, which may be different in different physical applications.
Composite pulses are an efficient tool for robust quantum control. In this work, we derive the form of the composite pulse sequence to implement robust single-qubit gates in a three-level system, where two low-energy levels act as a qubit. The composite pulses can efficiently cancel the systematic errors up to a certain order. We find that the three-pulse sequence cannot completely eliminate the first order of systematic errors, but still availably makes the fidelity resistant to variations in a specific direction. When employing more pulses in the sequence (N>3N>3N>3), the fidelity can be insensitive to the variations in all directions and the robustness region becomes much wider. Finally we demonstrate the applications of composite pulses in quantum information processing, e.g., robust quantum information transfer between two qubits.
Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequency), and duration errors. Our construction uses two complementary strategies: (i) derivative-based cancellation of error terms in the full unitary (not just the transition probability), formulated via the Cayley-Klein parametrization, and (ii) direct minimization of the average gate infidelity over prescribed error ranges. We derive symmetric five-pulse solutions with closed-form phases that cancel all first-order terms (including the mixed derivative), and numerically optimize longer sequences -- up to 15 pulses -- to achieve higher-order suppression. We also show that standard ``universal'' five-pulse sequences (U5a/U5b) emerge as simple phase-shifted instances of our symmetric solutions, yielding broad robustness to both detuning and amplitude errors. Finally, we construct variable-area sequences for Rx(π/2)R_x(π/2)Rx​(π/2), which, up to virtual Z rotations, benchmark the Hadamard gate. Across all families we observe the expected trade-off between sequence length and robustness window, with substantial boosts in fidelity over large error domains.
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.