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Scientific Insights

Ion Trap Quantum Computers Part 1: 1-Qubit Gates

Bernd Baumann

Published May 27, 2025• 0 citations
Publisher

Abstract

Ions offer a promising approach to physically realize qubits. The present text extensively elucidates the physics of 1-qubit gates for use in quantum computers based on ion qubits. To keep the discussion as simple as possible, ions are treated mechanically as rigid rotors. The discussed system is excellently suited to practice important elementary methods of quantum physics using a practical application example. For didactic reasons, contrary to the usual approach, a typographical distinction is made between states and operators on the one hand and column vectors and matrices on the other. The article is aimed at readers with basic knowledge of quantum physics, i.e., those familiar with terms like Schrödinger equation, wave function, bra and ket, Pauli matrices, and the like. Rudimentary knowledge of quantum computers is also assumed (qubit, gate, ...).

DOI
10.64897/si.2025v1i2.006

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Ions offer a promising approach to physically realize qubits. The present text extensively elucidates the physics of 1-qubit gates for use in quantum computers based on ion qubits. To keep the discussion as simple as possible, ions are treated mechanically as rigid rotors. The discussed system is excellently suited to practice important elementary methods of quantum physics using a practical application example. For didactic reasons, contrary to the usual approach, a typographical distinction is made between states and operators on the one hand and column vectors and matrices on the other. The article is aimed at readers with basic knowledge of quantum physics, i.e., those familiar with terms like Schrödinger equation, wave function, bra and ket, Pauli matrices, and the like. Rudimentary knowledge of quantum computers is also assumed (qubit, gate, ...).
Present-day computers are essentially non-quantum mechanical in operation. The logic gates of a classical computer are irreversible in nature. For easy understanding, elementary quantum mechanics is reviewed including the Schrödinger’s equation, the particle-in-a-box problem, state superposition and collapsing. Bloch sphere representation of a quantum bit is explained. The qubits display interesting properties of quantum superposition, entanglement and interference, characteristic of atomic and subatomic particles. Measurements carried out on qubits cause their wave functions to collapse forcing them into a definite 0 or 1 state. Qubit decoherence on interaction with the environment is a major problem in quantum computing Three types of quantum computing devices are discussed including silicon, superconducting and trapped qubit devices. Among silicon devices, gate-controlled silicon quantum dots and phosphorous donor implanted Si substrates are considered. Superconducting qubit archetypes and their realization techniques are explained. The transmon qubit design is preferred for charge noise mitigation. Under the trapped ion qubit devices, construction and operation of Paul ion traps is discussed, and the types of trapped ion qubits are elucidated.
The Cirac-Zoller mechanism is generally used for the implementation of CNOT gates in ion trap quantum computers. We present here a highly detailed quantum physical description of this approach. To keep the presentation simple, the qubits are modeled as rigid rotors and the radiation field of each of the lasers is treated as a classical field. In combination with the corresponding first part (Ion Trap Quantum Computer Part 1: 1-Qubit Gates), this results in the complete quantum theory of a universal set of quantum gates. This presentation is intended for readers with basic knowledge of quantum physics and assumes familiarity with Part 1.
This is the second paper in a series of papers providing an overview of different quantum computing hardware platforms from an industrial end-user perspective. It follows our first paper on neutral-atom quantum computing. In the present paper, we provide a survey on the current state-of-the-art in trapped-ion quantum computing, taking up again the perspective of an industrial end-user. To this end, our paper covers, on the one hand, a comprehensive introduction to the physical foundations and mechanisms that play an important role in operating a trapped-ion quantum computer. On the other hand, we provide an overview of the key performance metrics that best describe and characterise such a device's current computing capability. These metrics encompass performance indicators such as qubit numbers, gate times and errors, native gate sets, qubit stability and scalability as well as considerations regarding the general qubit types and trap architectures. In order to ensure that these metrics reflect the current state of trapped-ion quantum computing as accurate as possible, they have been obtained by both an extensive review of recent literature and, more importantly, from discussions with various quantum hardware vendors in the field. We combine these factors and provide - again from an industrial end-user perspective - an overview of what is currently possible with trapped-ion quantum computers, which algorithms and problems are especially suitable for this platform, what are the relevant end-to-end wall clock times for calculations, and what might be possible with future fault-tolerant trapped-ion quantum computers.
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.
In this paper we describe one of the most promising platforms for the construction of a universal quantum computer, which consists of a chain of NNN ions trapped in a harmonic potential, whose internal states work out as qubits, and are coupled to collective vibrational modes of the chain. From such coupling, it is possible to build interactions between different ions of the chain, that is, qubit-qubit interactions that, together with individual operations on the ions, allow building a quantum computer as first proposed by Cirac and Zoller in the 1990s [Phys. Rev. Lett. 74, 4091 (1995)]. Here we discuss from the physics involved in trapping ions in electromagnetic potentials to the Hamiltonian engineering needed to generate a universal set of logic gates, fundamental for the execution of more complex quantum algorithms. Finally, we present the current state of the art of quantum computing in trapped ion systems, highlighting recent advances made by companies and government projects that use such architecture, such as IonQ and AQTION.
Ion trap is one of the leading physical platforms to implement quantum computation. Currently, high-fidelity elementary quantum operations above the fault-tolerant threshold, including state preparation, measurement and universal gates, have been demonstrated for tens of ionic qubits. One important future research direction is to further enlarge the qubit number to the scale required for solving practical problems while maintaining the high performance of individual qubits. This paper introduces the current mainstream schemes for scalable ion trap quantum computation like quantum charge-coupled device (QCCD) and ion-photon quantum network, and describes the main limiting factors in current research. Then we further explore new schemes to scale up the qubit number like two-dimensional ion crystals and dual-type qubit, and discuss the future research directions.