ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS

QUANTUM COMPUTING

QUANTUM COMPUTING WITH TRAPPED IONS

A. Physical approach and perspective

Ion trap quantum computation is based on schemes devised by Cirac and Zoller [1]. A quantum register is provided by strings of ions, each representing a physical qubit. The system satisfies in principle all DiVincenzo criteria and most of the criteria have been experimentally demonstrated. While the originally proposed system is scalable in principle, practical scalability requires additional techniques such as interconnecting via photons (flying qubits) or moving one or more ions to operate as a messenger for quantum information. A more comprehensive summary of ion trap QIP is contained in the US QIST roadmap [2].

Currently, experimental ion trap QIP is pursued by around 10 groups worldwide, 7 of which are located in Europe [R. Blatt (Innsbruck, A), M. Drewsen (Aarhus, Dk), P. Gill (Teddington, UK), W. Lange (Sussex, UK), A. Steane (Oxford, UK), R. C. Thompson (Imperial College, UK), Ch. Wunderlich (Maynooth, Ei)], 3 more groups are currently setting up ion trap experiments for QIP in Europe [J. Eschner (Barcelona, E), T. Schaetz (MPQ Garching, D), F. Schmidt-Kaler (Ulm, D)].

On the theory side there is J.I. Cirac (MPQ Garching, D), K. Molmer (Aarhus, DK) and P. Zoller (Innsbruck, A).

B. State of the art (November 2004)

With trapped ions, qubits are implemented using either two levels out of the Zeeman- or hyperfine manifold or employing a forbidden optical transition of alkaline earth, or alkaline earth-like ions. The DiVincenzo criteria are currently met as follows:

1. Strings of two and three trapped ions are routinely loaded to a linear trap.
2. Ion strings can be cooled to the ground state of the trapping potential, and thus are prepared for implementing the Cirac-Zoller scheme. Using various techniques of individual ion manipulation, the register can be initialized to arbitrary internal and external states.
3. Qubit decay times for individual hyperfine qubits of more than 10 minutes have been observed, however, this requires magnetic-field "insensitive" transitions. For optical transitions, decoherence is limited by spontaneous decay which, however, is orders of magnitudes slower than a single gate operation.
4. Individual ion manipulation (pulsed Rabi oscillations), as well as two-qubit gate operations (Cirac-Zoller gate, geometric phase gate) have been demonstrated.
5. State-sensitive light scattering (observation of quantum jumps) is routinely used with trapped ions and detection efficiencies of more than 99.9% are readily obtained.
6. For converting stationary (ion) qubits into flying (photon) qubits, the techniques of cavity quantum electrodynamics (CQED) are used and several experiments are currently under way, no results are available at this time.
7. Faithful transmission of photonic qubits between two quantum computer nodes was theoretically shown to be feasible; a transfer protocol is available, however, at this time no experimental work is carried out yet. Instead, over short distances, and for the transfer of quantum information within a quantum processor, ions can be moved and/or teleportation protocols may be used.

C. Strengths and weaknesses

At present, ion trap QIP provides most of the requirements for first-generation quantum computation experiments. In particular, the long coherence times of the ionic two-level systems provide a robust quantum memory. Moreover, the near-unity state detection and the availability and operability of a universal set of gate operations make it already a test-bed for small-scale quantum computation. Furthermore, techniques to build large-scale ion trap quantum computers were outlined and their function was shown in first steps.

On the downside, motional decoherence by stochastically fluctuating fields (originating from trap electrodes) is not completely understood and must be reduced. Spontaneous emission must be avoided by all means; therefore decoherence-free subspaces need to be explored. Current technical constraints, such as the availability of laser sources, their respective stability and purity as well as fast optical detection and switching, need to be improved.

However, aside from the technical difficulties of scaling ion trap QIP up to larger devices, there is no fundamental problem in sight.

D. Short-term goals (next 3-5 years) (cf. also [2])

• Improve coherence of qubits by using magnetic field "insensitive" transitions, or decoherence free subspaces (for optical qubits).
• Reduce trap size and thus increase speed of operations.
• Identify and reduce sources of motional decoherence (needed for smaller traps).
• Implement error correction with 3 and 5 qubits, correct for phase and spin flip errors.
• Develop an "ion chip" as the basic building block for scaling ion trap QIP.
• Improve laser intensity and phase stability to reach fault-tolerant limits.
• Realize a "logical" qubit including error correction, i.e. encode a stable logical qubit in 5 physical qubits ("keeping a logical qubit alive").
• Interface stationary and flying qubits.
• Demonstrate more quantum algorithms.
• Logical qubit operations (single L-qubits operations, gates between L-qubits).
• Identify an optimal ion.

E. Long-term goals (2010 and beyond) (cf. also [2])

• Develop ion chips with integrated optics and electronics.
• Operations with several L-qubits.
• Fault-tolerant operations with multiple qubits.

F. Key references

[1] J.I. Cirac and P. Zoller, Quantum computation with cold trapped ions, Phys. Rev. Lett. 74, 4091 (1995).

[2] D. Wineland, Ion trap approaches to quantum information processing and quantum computing, in 'A Quantum Information Science and Technology Roadmap, Part 1: Quantum Computation', Version 2.0, section 6.2 and references therein; available from http://qist.lanl.gov.