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arXiv:2501.02847 · Quantum Science and Technology

Robust Mølmer-Sørensen gate against symmetric and asymmetric errors

Wenhao Zhang, Gaoxiang Tang, Kecheng Liu, Xiao Yuan, Yangchao Shen, Yukai Wu, Xiao‐Ming Zhang

Published Apr 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract To achieve the entangling gate fidelity above the quantum error correction threshold, it is critical to suppress errors due to experimental imperfection. We consider the Mølmer-Sørensen gates in trapped-ion systems, and develop a general approach to suppress a family of noise sources that appeared as either symmetric or asymmetric errors. Using the time-average displacement minimization technique, both symmetric error and displacement-dependent part of the asymmetric errors are eliminated. Then, by analyzing the tangent space of displacement- independent errors, we obtain the analytic form of the generators of the correction operator to the remaining error terms. We then develop a compensation pulse to fully suppress the remaining displacement-independent errors. The effectiveness of our scheme is further verified by numerical analysis, through which we observe a significant reduction of entangling gate infidelity. Our findings enhance gate fidelity and robustness to noise for ion trap quantum computing.

DOI
10.1088/2058-9565/adce29

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Abstract To achieve the entangling gate fidelity above the quantum error correction threshold, it is critical to suppress errors due to experimental imperfection. We consider the Mølmer-Sørensen gates in trapped-ion systems, and develop a general approach to suppress a family of noise sources that appeared as either symmetric or asymmetric errors. Using the time-average displacement minimization technique, both symmetric error and displacement-dependent part of the asymmetric errors are eliminated. Then, by analyzing the tangent space of displacement- independent errors, we obtain the analytic form of the generators of the correction operator to the remaining error terms. We then develop a compensation pulse to fully suppress the remaining displacement-independent errors. The effectiveness of our scheme is further verified by numerical analysis, through which we observe a significant reduction of entangling gate infidelity. Our findings enhance gate fidelity and robustness to noise for ion trap quantum computing.
High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits; however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the renowned Mølmer-Sørensen gate by using multitone drives. We experimentally implemented several of the proposed gates on ^{88}Sr^{+} ions trapped in a linear Paul trap and verified their resilience.
Trapped ion hardware has made significant progress recently and is now one of the leading platforms for quantum computing. To construct two-qubit gates in trapped ions, experimental manipulation approaches for ion chains are becoming increasingly prevalent. Given the restricted control technology, how implementing high-fidelity quantum gate operations is crucial. Many works in current pulse design optimization focus on ion-phonon and effective ion-ion coupling while ignoring the higher-order expansion impacts of these two terms brought on by experiment defects. This paper proposed a novel robust quantum control optimization method in trapped ions. By introducing the higher-order terms caused by the error into the optimization cost function, we generated an extremely robust Molmer-Sorensen gate with infidelity below 10−310^{-3}10−3 under drift noise range ±10\pm 10±10 kHz and time noise range ±0.02\pm 0.02±0.02. Our work reveals the vital role of higher-order coupling terms in trapped ion pulse control optimization, especially the higher ion-ion coupling order, and provides a robust optimization scheme for realizing more efficient entangled states in trapped ion platforms.
Abstract Trapped ion hardware has made significant progress recently and is now one of the leading platforms for quantum computing. To construct two-qubit gates in trapped ions, experimental manipulation approaches for ion chains are becoming increasingly prevalent. Given the restricted control technology, how implementing high-fidelity quantum gate operations is crucial. Many works in current pulse design optimization focus on ion–phonon and effective ion–ion couplings while ignoring the first-order derivative terms expansion impacts of these two terms brought on by experiment defects. This paper proposes a novel robust quantum control optimization method in trapped ions. By introducing the first-order derivative terms caused by the error into the optimization cost function, we generate an extremely robust Mølmer–Sørensen gate with infidelity below 10−3 under a drift noise range of ±10 kHz, the relative robustness achieves a tolerance of ±5%, compared to the 200-kHz frequency spacing between phonon modes, and for time noise drift, the tolerance reached to 2%. Our work reveals the vital role of the first-order derivative terms of coupling in trapped ion pulse control optimization, especially the first-order derivative terms of ion–ion coupling. It provides a robust optimization scheme for realizing more efficient entangled states in trapped ion platforms.
Constructing a large-scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of Mølmer-Sørensen gate protects against infidelity caused by heating of the motional mode used during the gate. Furthermore, we show how the same technique simultaneously provides significant protection against slow fluctuations and mis-sets in the secular frequency. Since this parameter sensitivity is worsened in cases where the ions are not ground-state cooled, our method provides a path towards relaxing ion cooling requirements in practical realizations of quantum computing and simulation.
Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. However, one of the pressing challenges is improving the fidelity of two-qubit entangling gates. These operations are often implemented by addressing individual ions with laser pulses using the M\o{}lmer-S\o{}rensen protocol. Amplitude modulation (AM) is a well-studied extension of this protocol, where the amplitude of the laser pulses is controlled as a function of time. We present an analytical study of AM, using a Fourier series expansion to maintain the generality of the laser amplitude's functional form. We then apply this general AM method to gate-timing errors by imposing conditions on these Fourier coefficients, producing trade-offs between the laser power and fidelity at a fixed gate time. The conditions derived here are linear and can be used, in principle, to achieve arbitrarily high orders of insensitivity to gate-timing errors. Numerical optimization is then employed to identify the minimum-power pulse satisfying these constraints. Our central result is that the leading-order dependence on gate-timing errors is improved from $O(\mathrm{\ensuremath{\Delta}}{t}^{2})$ to $O(\mathrm{\ensuremath{\Delta}}{t}^{6})$ with the addition of one linear constraint on the Fourier coefficients and to $O(\mathrm{\ensuremath{\Delta}}{t}^{10})$ with two linear constraints without a significant increase in the average laser power. The increase approaches zero as more Fourier coefficients are included. In further studies, this protocol can be applied to other error sources and used in conjunction with other error-mitigation techniques to improve two-qubit gates.
We demonstrate a simple pulse shaping technique designed to improve the fidelity of spin-dependent force operations commonly used to implement entangling gates in trapped ion systems. This extension of the Mølmer-Sørensen gate can theoretically suppress the effects of certain frequency and timing errors to any desired order and is demonstrated through Walsh modulation of a two qubit entangling gate on trapped atomic ions. The technique is applicable to any system of qubits coupled through collective harmonic oscillator modes.