Trapped-ion quantum computing: Progress and challenges

Abstract

Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented. We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits. In addition, we discuss what is being done, and what may be required, to increase the scale of trapped ion quantum computers while mitigating decoherence and control errors. Finally, we explore the outlook for trapped-ion QC. In particular, we discuss near-term applications, considerations impacting the design of future systems of trapped ions, and experiments and demonstrations that may further inform these considerations. CONTENTS

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

“…This makes them a reliable solution for quantum information processing satisfying all of the required DiVincenzo criteria (for a comprehensive recent Review on the state-of-theart of this technology focused on quantum computing, we refer to ref. [74]). Today, digital quantum processors with up to 11 programmable ions in a linear Paul trap have been made available, [131] also through spin-off companies such as IonQ offering restricted cloud access (see https://ionq.com/, accessed 2019-09-01).…”

“…Among the different possibilities, particularly advanced appear the technologies based on 40 Ca + as optical qubits, [135,136] and 43 Ca + or 171 Yb + as hyperfine qubits, [137,138] respectively, although several other atomic species with a single outer electron can be successfully trapped. [72,74] In fact, irrespective of the specific qubit realization, initialization and readout of their quantum state is performed through coherent manipulation, for example, by using external lasers of suitable frequency to optically pump the ion state into the desired one (preparation), or by detecting resonantly scattered radiation from an optical transition (readout). The qubits' individual control (i.e., single-qubit operations) can be performed by directly coupling the |0⟩ and |1⟩ eigenenergy levels, for which the required tools inevitably depend on the qubit type (e.g., hyperfine qubits require microwave control or stimulated Raman coupling, while the optical qubits internal states are directly coupled through a resonant laser).…”

“…In particular, when working with isolated or pairs of trapped ions, single-qubit operations with fidelities in the order of 99.9999% have been shown, [142] as well as two-qubit gates reaching fidelities in excess of 99.9% even in different experimental setups. [137,143] Typical duration for single-qubit gates varies between 100 ns and few tens of µs, while two qubit gating times range in the µs to few hundred µs interval [74,137,144] ; readout is typically performed in hundreds of µs with fidelities in the 99.99% range. [145] Recent advances on ultra-fast gating times have also been reported.…”

“…Targeted strategies to mitigate these issues will become crucial to further improve the trapped ion quantum hardware. [74] A couple of recent results are worth being mentioned: entanglement of a subset of trapped ions has been reported with suppressed crosstalk errors, [152] and gate fidelities above the physical limits have been obtained by applying error mitigation techniques. [129] On a quantitative level, it has recently been reported that the fidelity of multi-qubit entangling Mølmer-Sørensen gates degrades from 99.6% with 2 optical qubits down to 86% when the same quantum hardware is loaded with 10 optical qubits.…”

“…In terms of actual quantum hardware, we will focus on reviewing the main experimental achievements obtained in the last decade, specifically dealing with the simulation accuracy of targeted spin Hamiltonians on different quantum platforms. While several alternatives are currently being pursued to realize actual non-error corrected quantum processors, [70] from photonic integrated circuits [57] to spins in semiconductors, [71] we concentrate upon two leading architectures that have been dominating the scene: trapped ions manipulated through external microwave or optical fields, [72][73][74] and superconducting circuits working at microwave frequencies. [75][76][77][78] Given the recent developments, [63] we anticipate that interesting results on quantum simulations might already be within reach in NISQ processors, despite the relatively small number of useful operations and non-error corrected qubits currently available on such devices.…”