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arXiv:quant-ph/0212079 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Quantum information processing with trapped ions

David J. Wineland, M. D. Barrett, J. Britton, John Chiaverini, Brian DeMarco, Wayne M. Itano, B. M. Jelenkovic, C. Langer, Dietrich G. Leibfried, V. Meyer, Till Rosenband, T. Schätz

Published Jul 15, 2003• 174 citations
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Abstract

Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single-qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.

DOI
10.1098/rsta.2003.1205

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•Jan 1, 2014•0 citations
Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single-qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.
The basic requirements for quantum computing and quantum simulation (single‐ and multi‐qubit gates, long memory times, etc.) have been demonstrated in separate experiments on trapped ions. Construction of a large‐scale information processor will require synthesis of these elements and implementation of high‐fidelity operations on a very large number of qubits. This is still well in the future. NIST and other groups are addressing part of the scaling issue by trying to fabricate multi‐zone arrays of traps that would allow highly‐parallel and scalable processing. In the near term, some simple quantum processing protocols are being used to aid in quantum metrology, such as in atomic clocks. As the number of qubits increases, Schrödinger’s cat paradox and the measurement problem in quantum mechanics become more apparent; with luck, trapped ion systems might be able to shed light on these fundamental issues.
The role of trapped atomic ions in the field of quantum information processing is briefly reviewed. We discuss some of the historical developments that enabled ions to enter the field and then summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We describe potential pathways to reach fault-tolerant error levels and large-scale devices, and highlight some of the main problems that will be faced in achieving these goals. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are discussed.
This chapter reviews the basic experimental techniques which enable quantum information processing (QIP) with trapped ions and, more briefly, with trapped atoms. In particular, it is explained how the fundamental concepts of quantum computing, such as quantum bits (qubits), qubit rotations, and quantum gates, translate into experimental procedures in a quantum optics laboratory. Furthermore, the recent progress of quantum computing with ions and atoms is summarised, and new approaches to meet the future challenges of scaling up QIP and of atom-photon qubit interfacing are discussed. The chapter is intended to provide an intuitive understanding of the subject and enable the non-specialist student to appreciate the paradigmatic role and the potential of trapped single ions and atoms in the field of quantum computation or, more generally, of quantum optical information technology.
Quantum information processing combines information theory with laws of quantum mechanics to provide an interesting new study that promises significant technological advances in the field of computation. The quest for a physical quantum information processor not only tests the limits of quantum mechanics but also motivates the development of new control techniques for quantum systems. This thesis documents the implementation of the necessary components of a quantum computer in a new atomic ion species, while demonstrating an entangling procedure that is uniquely insensitive to certain types of phase noise. Quantum bits are stored in the ground state hyperfine levels of individual trapped cadmium ions, and the collective vibration of the ions in the trap potential form a quantum databus through which information can be transferred. Quantum state measurements and initialization processes are accomplished through optical pumping, and quantum logic operations are performed through interactions with applied electromagnetic fields. The spin-dependent force, which is the underlying principle of many entanglement schemes for trapped ions, is investigated in detail in a series of Schrodinger cat experiments that generates entangled wavepackets well separated in the momentum-position phase space (alpha = 6). Phase control of the interaction in the gate scheme proposed by Molmer and Sorensen results in phase coherence between single-qubit rotations and a robust two-qubit entangling logic gate that can operate on magnetic-field insensitive clock qubits at finite temperature. The coherence time of the clock qubit (∼ 1s) is long compared to the gate time (∼ 100mus). Finally, quantum state tomography is performed on two ions, featuring a set of universal quantum logic gates that is sufficient for any quantum computation, with an entangling gate fidelity of 0.83. The combination of the tools developed here is sufficient to perform universal quantum computation. With the advent of scalable, multi-zone ion trap structures, the concept of a quantum computation device may become reality in the not so distant future.
Quantum technology with atomic, molecular and optical systems has advanced to a stage that single particles can be manipulated precisely so that quantum information processing is no longer elusive. In fact, a great number of quantum information protocols have been demonstrated with small scaled systems. The remaining task is to build large scale practical devices. However it turns out that scaling up is highly nontrivial in the quantum world. A protocol valid in principle could face enormous technical challenges when the system size is increased. Therefore new ideas and smart designs that bypass the technical obstacles are extremely useful in this field. In this dissertation we tackle several specific problems in quantum information processing with trapped ions and cold atomics gases. For ions, we first present a scalable implementation scheme for the recently proposed concept of Boson sampling, which holds the promise of outperforming classical computers in the near future. The scheme is based on the technically mature linear Paul trap and the transverse motional phonons of the ions are manipulated with laser to perform sampling. A complete recipe is provided and the technical requirements are discussed. Then we go back to the conventional circuit model for computation and discuss a method to perform individual ion addressing quantum gates with Gaussian beams. We describe the so-called spatial refocusing technique to significantly narrow down the beams with coherent interference. We also extend the original quantum gate formalism to include the effect of micromotion. We demonstrate high fidelity gates in the presence of significant micromotion. This paves the way to the development of a two dimensional ion crystal quantum processor with hundreds of ions inside a single trap. On the other hand, we explore precision measurement with a cold atom interferometer. Combining a spin-spin interaction Hamiltonian and coherent spin rotation pulses, we construct optimized pulse sequences for spin squeezing to approach the Heisenberg limit of noise. Finally we investigate the general problem of state detection with faulty detectors. We develop a statistical procedure to recover the true correlation from noisy data.