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arXiv:1802.03640 · Physical Review A

Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear Paul trap

Yukai Wu, Sheng-Tao Wang, Luming Duan

Published Jun 19, 2018• 69 citations
arXivHTMLPDF

Abstract

The realization of high-fidelity quantum gates in a multiqubit system, with a typical target set at $99.9%$, is a critical requirement for the implementation of fault-tolerant quantum computation. To reach this level of fidelity, one needs to carefully analyze the noises and imperfections in the experimental system and optimize the gate operations to mitigate their effects. Here, we consider one of the leading experimental systems for the fault-tolerant quantum computation, ions in an anharmonic linear Paul trap, and optimize entangling quantum gates using segmented laser pulses with the assistance of all the collective transverse phonon modes of the ion crystal. We present detailed analyses of the effects of various kinds of intrinsic experimental noises as well as errors from imperfect experimental controls. Through explicit calculations, we find the requirements on these relevant noise levels and control precisions to achieve the targeted high fidelity of $99.9%$ for the entangling quantum gates in a multi-ion crystal.

DOI
10.1103/physreva.97.062325

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The realization of high-fidelity quantum gates in a multiqubit system, with a typical target set at 99.999.9%99.9, is a critical requirement for the implementation of fault-tolerant quantum computation. To reach this level of fidelity, one needs to carefully analyze the noises and imperfections in the experimental system and optimize the gate operations to mitigate their effects. Here, we consider one of the leading experimental systems for the fault-tolerant quantum computation, ions in an anharmonic linear Paul trap, and optimize entangling quantum gates using segmented laser pulses with the assistance of all the collective transverse phonon modes of the ion crystal. We present detailed analyses of the effects of various kinds of intrinsic experimental noises as well as errors from imperfect experimental controls. Through explicit calculations, we find the requirements on these relevant noise levels and control precisions to achieve the targeted high fidelity of 99.999.9%99.9 for the entangling quantum gates in a multi-ion crystal.
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal gate set on the logical level in order to perform arbitrary calculations to in principle unlimited precision. In this paper we characterize the recent demonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler et al., Nature (London) 605, 7911 (2022)] and identify aspects to improve the design of experimental setups to reach an advantage of logical over physical qubit operation. We show that various criteria to assess the break-even point for fault-tolerant quantum operations are within reach for the ion trap quantum computing architecture under consideration. Furthermore, we analyze the influence of crosstalk in entangling gates for logical state preparation circuits. These circuits can be designed to respect fault tolerance for specific microscopic noise models. We find that an experimentally informed depolarizing noise model captures the essential noise dynamics of the fault-tolerant experiment that we consider, and crosstalk is negligible in the currently accessible regime of physical error rates. For deterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initialization circuit, which can be realized without in-sequence measurement and feed-forward of classical information. Additionally, we show that nondeterministic state preparation schemes, i.e., repeat until success, for logical Pauli and magic states perform with higher logical fidelity over their deterministic counterparts for the current and anticipated future regime of physical error rates. Our results offer guidance on improvements of physical qubit operations and validate the experimentally informed noise model as a tool to predict logical failure rates in quantum computing architectures based on trapped ions.
High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\ensuremath{\pi}$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the M\o{}lmer-S\o{}rensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant 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.
Ion trap is one of the most promising candidates for quantum computing. High-fidelity gates have been demonstrated in small ion crystals and schemes like ion shuttling have been proposed for larger systems. This thesis discusses the possibility of direct quantum computing on a large ion crystal in a Paul trap, without any shuttling of the ions. We first review a scheme to entangle two ions in a small ion crystal mediated by the collective phonon modes and analyze the gate errors. The generalization to larger systems is divided into three parts. (1) We present numerical methods to solve all the normal modes of the ion crystal, including the micromotion, up to arbitrary precision. The stability of the crystal under infinitesimal perturbation is ensured when all the normal modes have real frequencies. For finite disturbance, direct molecular dynamics simulation will be needed; after discussing some potential problems in the simulation, we give a rule of thumb for the ion crystal to be stable at a given temperature. (2) We show that when designing an entangling gate between two nearby ions, all the ions far away can be neglected, so that only a small number of normal modes are relevant. Similarly, distant entangling gates can be applied in parallel and the crosstalk is shown to decay cubically with the distance between these gates. (3) Then we present numerical methods to include the solved micromotion into the design of the entangling gates efficiently, again up to arbitrary precision. Thus we conclude that the design and the implementing of entangling gates are scalable in a large ion crystal. Finally we consider a near-term application to simulate an all-to-all coupled Ising model in a small to medium-sized ion crystal.
An ion trap is one of the most promising candidates for quantum computing. Current schemes mainly focus on a linear chain of up to about 100 ions in a Paul trap. To further scale up the qubit number, one possible direction is to use 2D or 3D ion crystals (Wigner crystals). In these systems, ions are generally subjected to large micromotion due to the strong fast-oscillating electric field, which can significantly influence the performance of entangling gates. In this paper, we develop an efficient numerical method to design high-fidelity entangling gates in a general 3D ion crystal. We present numerical algorithms to solve the equilibrium configuration of the ions and their collective normal modes. We then give a mathematical description of the micromotion and use it to generalize the gate scheme for linear ion chains into a general 3D crystal. The involved time integral of highly oscillatory functions is expanded into a fast-converging series for accurate and efficient evaluation and optimization. As a numerical example, we show a high-fidelity entangling gate design between two ions in a 100-ion crystal, with a theoretical fidelity above 99.9%.
Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits, N , in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as N 2 , the gate duration scales as N , leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path toward scaling up quantum computers based on ion-crystals with hundreds of qubits.