We present an entangling gate scheme that achieves high-fidelity operations with excited motional states, despite multiple error sources. While we demonstrate this approach for trapped-ion chains, the underlying principles are applicable to a wide range of quantum computing platforms. Our scheme incorporates all relevant motional modes and exhibits enhanced robustness against both motional heating effects and detuning errors, critical features for building robust and scalable quantum computers.
We present an entangling gate scheme that achieves high-fidelity operations with excited motional states, despite multiple error sources. While we demonstrate this approach for trapped-ion chains, the underlying principles are applicable to a wide range of quantum computing platforms. Our scheme incorporates all relevant motional modes and exhibits enhanced robustness against both motional heating effects and detuning errors, critical features for building robust and scalable quantum computers.
Abstract Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for a few ions, how to maintain the high fidelity for large scale trapped-ions remains an open problem. Here, we present an analysis of arbitrary scale ion chains and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal under the phase insensitive configuration. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases in of the Hilbert space dimension. For the motional heating error, we derive a much tighter bound of gate infidelity than previously estimated O ( N Γ τ ) , and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.
Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which creates a new interaction, that enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.
Entangling gates of trapped ions are typically mediated by collective motional degrees of freedom. Weak coupling between qubit and motional degrees of freedom and the resulting harmonic dynamics give access to a broad range of gate schemes, but also impose strict limitations on achievable gate times. In this paper, we devise optimally designed driving schemes for the realization of fast, high-fidelity entangling gates mediated by anharmonic dynamics. The driving can also be optimized to achieve resilience to multiple system imperfections, and the anharmonicity in the motional dynamics can be used to enhance such resilience.
Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to 50 ions with fidelities approaching 99.9%.
Near-term quantum algorithms require high-performance entangling gates in a scalable quantum processor, and M\o{}lmer-S\o{}rensen (MS) gates on trapped ions have achieved some of the highest entanglement fidelities to date. However, technical noise that induces small changes in the motional frequencies of the ion chain is a dominant error source in these gates that limits scalability. Here, we report an improved MS-gate design that mitigates the impact of motional-frequency changes by using a class of laser waveforms with three salient features: a spectrally compact Fourier transform, a constant frequency that balances contributions to the MS-gate rotation angle from all motional modes, and a simple parameterization. Together, these features suppress residual coherent displacement of the motional modes, generate robustness to rotation-angle error, and provide low technical complexity and computational overhead. As a proof of concept, we implement this gate design on a four-ion chain, achieving a $<1\mathrm{%}$ fidelity reduction over a $\ifmmode\pm\else\textpm\fi{}10$ kHz range of frequency offset from the calibrated detuning. We also analyze the applicability of our gate design to longer ion chains through numerical simulations of our gate design on chains of up to 33 ions. This robustness to motional-frequency changes represents an order-of-magnitude improvement over the more complicated waveform-shaping techniques that currently dominate the robust-gate literature, and our simulations predict that a high level of robustness can be maintained in these systems for longer ion chains. In addition, the robustness and simplicity of our approach promises to accelerate the development of quantum architectures that invoke long algorithmic runtimes and frequent calibration.
Trapped-ion processors are leading candidates for scalable quantum computation. However, motional heating remains a key obstacle to fault-tolerant operation, especially when system size increases. Heating error is particularly challenging to suppress due to is incoherence nature, and no general methods currently exist for mitigating their impact in large systems with multiple phonon modes. In this work, based on a careful analysis about the dependence of heating-induced infidelity on phase-space trajectories, we present a simple yet comprehensive framework for suppressing heating errors in large trapped-ion quantum processors. Our approach is flexible, allowing various control pulse bases, ion numbers, and noise levels. Our approach is also compatible with existing error-mitigation techniques, including those targeting laser phase and frequency noise. Crucially, it relies on an efficiently computable cost function that avoids the exponential overhead of full fidelity estimation. We perform numerical simulations for systems with up to 55 qubits, demonstrating up to a fivefold reduction in infidelities compared with the conventional method in typical regimes. We further show that our framework simultaneously reduces the sensitivity of the gate rotation angle to detuning errors, leading to an improvement in detuning-error tolerance. These results offer a practical route toward robust, large-scale quantum computation with trapped ions.