Publications by the group
return to main page

Ion Traps and Quantum Information,
Andrew Steane and Derek Stacey Group,
Department of Physics, University of Oxford.

Our research interests are summarised on another page. This is a list of articles, grouped under four headings:

1. `Fundamentals of Quantum Theory.' This includes quantum information theory and quantum computing.
2. `Ion/Atom Trapping and Laser Cooling.' This includes both theory and experiment, both atoms and ions.
3. `Atomic Matter waves.' This overlaps with the previous heading, but means things related to atom `optics' rather than cooling techniques.
4. Miscellaneous: atomic clock, diffraction theory.

Within each group, the articles are listed in reverse order of publication (ie most recent first). They are not yet available on the web, I'm afraid, but almost all the recent ones can be found in preprint form on the LANL archive, The quickest way to find these is to go to LANL search archive and do a search for author Steane. The list below also gives lanl references. Please mail me if you are interested in further information, at a.steane@physics.ox.ac.uk

Coworkers. Experimental work published before 1993 was carried out in Oxford with C. J. Foot. Publications between 1993 and 1995 mostly represent work done by A.M.S. at the Laboratoire Kastler Brossel of the Ecole Normale Superieure, Paris. Thus those papers do not originate from our group, but they reflect our research interests.

Fundamentals of Quantum Theory

Includes quantum computation

Back to top

• A. M. Steane and D. M. Lucas
  Quantum computing with trapped ions, atoms and light
  submitted to Fortshritte der Physik.
  Preprint: quant-ph/0004053
  Abstract We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and immediate prospects for quantum information processing in ion traps. We discuss decoherence and gate rates in ion traps, comparing methods based on the vibrational motion with a method based on exchange of photons in cavity QED. We then sketch the main features of a quantum computer designed to allow an algorithm needing 10^6 Toffoli gates on 100 logical qubits. We find that around 200 ion traps linked by optical fibres and high-finesse cavities could perform such an algorithm in a week to a month, using components at or near current levels of technology.

• A. Steane
  A quantum computer only needs one universe
  Preprint: quant-ph/0003084
  Abstract: I give an informal discussion of the nature of quantum computation, arguing that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to "perform many computations simultaneously" except in a highly qualified and to some extent misleading sense. Quantum computation is therefore not well described by interpretations of quantum mechanics which invoke the concept of vast numbers of parallel universes. Rather, entanglement makes available types of computation process which, while not exponentially larger than classical ones, are unavailable to classical systems.

• A. M. Steane and W. van Dam, Physicists triumph at Guess My Number
  , Physics Today 53 No. 2, 35-39 (2000).
  Abstract: Quantum entanglement looks like telepathy when three physicists get together on a game show.

• A. Steane and E. Reiffel
  Beyond bits: The Future of Quantum Information Processing
  Computer 33, No. 1, 38--45 (2000).
  Summary: Introduction to quantum computing, and commentary on its prospects, aimed at a computer scientist readership.

• M. Mosca, R. Jozsa, A. Steane and A. Ekert
  Quantum-enhanced information processing
  Phil. Trans. R. Soc. Lond. A 358, 261-279 (2000).
  Summary: A fairly non-technical discussion of quantum computing aimed at the general physicist. Part of a millenial publication looking at the future of physics.

• A. Steane
  ``Bit of a hype'' (letter to the editor), Physics World, 1999, Vol.12, No.9, pp.17-18
  This is a short letter commenting on science journalism and progress towards quantum computing.
  Text

• A. M. Steane:
  Efficient fault-tolerant quantum computing
  Nature, vol. 399, 124-126 (May 1999)
  Preprint: quant-ph/9809054
  N.B. the preprint contains a lot of additional information further to the letter to Nature.
  Abstract: Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This permits a new analysis of the permissible error rates and minimum overheads for robust quantum computing. It is found that, under the standard noise model of ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an order of magnitude larger than the logical machine contained within it in order to be reliable. For example, a scale-up by a factor of 22, with gate error rate of order $10^{-5}$, is sufficient to permit large quantum algorithms such as factorization of thousand-digit numbers.

• A. M. Steane:
  Enlargement of Calderbank Shor Steane quantum codes
  IEEE Trans. Inf. Theory 45, 2492-2495 (1999).
  Preprint: quant-ph/9802061
  Abstract: It is shown that a classical error correcting code C = [n,k,d] which contains its dual, C^{\perp} \subseteq C, and which can be enlarged to C' = [n,k' > k+1, d'], can be converted into a quantum code of parameters [[n,k+k' - n, min(d, 3d'/2 )]]. This is a generalisation of a previous construction, it enables many new codes of good efficiency to be discovered. Examples based on classical Bose Chaudhuri Hocquenghem (BCH) codes are discussed.

• A. M. Steane:
  Introduction to quantum error correction
  Phil. Trans. Roy. Soc. Lond. A, 356, 1739-1758.
  Abstract: An introduction to quantum error correction (QEC) is given, and some recent developments are described. QEC consists of two parts: the physics of error processes and their reversal, and the construction of quantum error correcting codes. Errors are caused both by imperfect quantum operations, and by coupling between the quantum system and its enviroment. Any such process can be analysed into a sum of `error operators,' which are tensor products of Pauli spin operators. These are the analogue of classical error vectors. A quantum error correcting code is a set of orthogonal states, `quantum codewords', which behave in a certain useful way under the action of the most likely error operators. A computer or channel which only uses such states can be corrected by measurements which determine the error while yielding no information about which codeword or superposition of codewords is involved. Powerful codes can be found using a construction based on classical error correcting codes. An analysis which allows even the corrective operations to be themselves imperfect yields powerful and counter-intuitive results: the quantum coherence of a long quantum computation can be preserved even though every qubit in the computer relaxes spontaneously many times before the computation is complete.

• D. Stevens, J. Brochard and A. M. Steane:
  Simple experimental methods for trapped ion quantum processors
  Phys. Rev. A. 58, 2750-2759 (1998).
  See under Laser Cooling and Trapping , below.

• Andrew Steane:
  Quantum Error Correction
  in Introduction to Quantum Computation and Information, H-K. Lo, T. Spiller and S. Popescu, eds (World Scientific 1998).
  Abstract: Quantum error correction is a central component of quantum information theory. It is a powerful general method to restore the state of a quantum system after it has been subject to noise. The theory of quantum error correction is introduced, starting from the principles of error correction for classical communication channels. The treatment concentrates on the construction of quantum error correcting codes, and on the syndrome extraction operation, by which the quantum state is recovered after errors have occurred.

• Andrew Steane:
  Quantum Computing
  Rep. Prog. Phys. 61, 117-173 (1998).
  Preprint: quant-ph/9708022
  To get the full text, including completed figures and much better presentation, I recommend downloading from the IOP Electronic Journals site Click on Reports on Progress in Physics "Journal menu" then select volume 61, page 117.
  There is one mistake in the text which I am aware of, brought to my attention by Antoine Schoeb. The derivation of the channel capacity in equations (13) to (15) should use p(y=0|x=0) not p(x=0|y=0) etc, leading to I(X:Y)=S(Y)-H(p).
  Substance: This is a fairly lengthy review paper introducing quantum information theory.
  Abstract: The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and quantum algorithms. The common theme of all these ideas is the use of quantum entanglement as a computational resource. Experimental methods for small quantum processors are briefly sketched, concentrating on ion traps, high Q cavities, and NMR. The review concludes with an outline of the main features of quantum information physics, and avenues for future research.

• Andrew Steane:
  Space, time, parallelism and noise requirements for reliable quantum computing
  Fortschritte Der Physik (Fortschr. Phys.) 46, 443-457 (1998)
  Preprint: quant-ph/9708021
  Abstract: Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and degree of parallelism. I present an analysis of error correction with block codes, made fault-tolerant through the use of prepared ancilla blocks. The preparation and verification of the ancillas is described in detail. It is shown that the ancillas need only be verified against a small set of errors. This, combined with previously known advantages, makes this `ancilla factory' the best method to apply error correction, whether in concatenated or block coding. I then consider the resources required to achieve $2 \times 10^{10}$ computational steps reliably in a computer of 2150 logical qubits, finding that the simplest $[[n,1,d]]$ block codes can tolerate more noise with smaller overheads than the $7^L$-bit concatenated code. The scaling is such that block codes remain the better choice for all computations one is likely to contemplate.

• Andrew Steane:
  Active stabilisation, quantum computation and quantum state synthesis
  Phys. Rev. Lett. 78 , 2252 (1997)
  Preprint: quant-ph/9611027
  Abstract: Active stabilisation of a quantum system is the active suppression of noise (such as decoherence) in the system, without disrupting its unitary evolution. Quantum error correction suggests the possibility of achieving this, but only if the recovery network can suppress more noise than it introduces. A general method of constructing such networks is proposed, which gives a substantial improvement over previous fault tolerant designs. The construction permits quantum error correction to be understood as essentially quantum state synthesis. An approximate analysis implies that algorithms involving very many computational steps on a quantum computer can thus be made possible.

• Andrew Steane:
  Quantum Reed-Muller codes
  IEEE Trans. Inf. Theory 45, 1701-1703 (1999).
  Preprint: quant-ph/9608026
  Abstract: A set of quantum error-correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[ 2^r, 2^r - C(r,x) - 2 \sum_{t=0}^{x-1} C(r,t), 2^x + 2^{x-1} ]].

• Andrew Steane:
  The Ion Trap Quantum Information Processor
  Appl. Phys. B. 64 , 623-642 (1997) (Invited paper)
  Preprint: quant-ph/9608011
  Abstract: An introductory review of the linear ion trap is given, with particular regard to its use for quantum information processing. The discussion aims to bring together ideas from information theory and experimental ion trapping, to provide a resource to workers unfamiliar with one or the other of these subjects. It is shown that information theory provides valuable concepts for the experimental use of ion traps, especially error correction, and conversely the ion trap provides a valuable link between information theory and physics, with attendant physical insights. Example parameters are given for the case of calcium ions. Passive stabilisation will allow about 200 computing operations on 10 ions; with error correction this can be greatly extended.

• Andrew Steane:
  Simple quantum error correcting codes
  Phys. Rev. A, 54 , 4741 (1996).
  Preprint: quant-ph/9605021
  Abstract: Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe $C_2^{\perp} \subseteq C_1$, where $C_1$ and $C_2$ are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing $C_1$ to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error correcting codes for 3, 4 and 5 information qubits with block lengths of 8, 10 and 11 qubits respectively.

• Andrew Steane:
  Quantum Error Correction
  Proceedings of XXXIst Moriond Conference, 1996: "Dark matter in cosmology, quantum measurement, experimental gravitation".
  Substance: A brief introduction to quantum error correction. Click on the title to see it.

• Andrew Steane:
  Multiple particle interference and quantum error correction
  Proc. Roy. Soc. Lond. A. 452, 2551 (1996) (submitted November 1995)
  Preprint: quant-ph/9601029
  Abstract: The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of error correction in the quantum regime are presented, and their limitations assessed. It is shown that exponential suppression of decoherence is possible, with only a polynomial increase in the computing resources. Therefore quantum computation is possible. The methods also allow suppression of noise and evesdropping in quantum communication (quantum privacy amplification).

• Andrew Steane:
  Error correcting codes in quantum theory
  Phys. Rev. Lett. 77, 793-797 (1996)
  (submitted 4th October 1995).
  Abstract: This discusses classical error correcting codes appearing in the form of state superpositions in quantum mechanics. Some basic results in this area are established. Error correction can be used to make the interference between macroscopically different states observable (cf Schrodinger cat paradox).

• Andrew Steane:
  Which path information and interference phase
  Unpublished article.
  Substance: This a `tutorial' type of article discussing the familiar problem of loss of interference when `which path' information is available. Two ways of understanding the loss of interference patterns are commonly employed. One is in terms of an entanglement which prevents two states from interfering, the other is in terms of a randomisation of the phase of the interference. The paper shows that these two descriptions are equivalent---they are not alternatives.

• Andrew Steane:
  Proposed solution of the quantum measurement problem
  J. Phys. A 23, 2905 (1990).
  Substance: This is a speculative idea in which the results of measurement-like processes in quantum mechanics become definite because of Godelian incompleteness. At the moment I think the idea is probably wrong, but it suggests interesting ways of reasoning.

Ion/Atom Trapping and Laser Cooling

Back to top

• A. M. Steane and D. M. Lucas
  Quantum computing with trapped ions, atoms and light
  submitted to Fortshritte der Physik.
  Preprint: quant-ph/0004053
  See under Fundamentals of quantum theory , above.

• C. J. S. Donald, D. M. Lucas, P. A. Barton, M. J. McDonnell, J. P. Stacey, D. A. Stevens, D. N. Stacey and A. M. Steane
  Search for correlation effects in linear chains of trapped ions
  Submitted to Europhys. Lett
  Preprint: physics/0003085
  Abstract We report a precise search for correlation effects in linear chains of 2 and 3 trapped Ca+ ions. Unexplained correlations in photon emission times within a linear chain of trapped ions have been reported, which, if genuine, cast doubt on the potential of an ion trap to realize quantum information processing. We observe quantum jumps from the metastable 3d 2D_{5/2} level for several hours, searching for correlations between the decay times of the different ions. We find no evidence for correlations: the number of quantum jumps with separations of less than 10 ms is consistent with statistics to within errors of 0.05%; the lifetime of the metastable level derived from the data is consistent with that derived from independent single-ion data at the level of the experimental errors 1%; and no rank correlations between the decay times were found with sensitivity to rank correlation coefficients at the level of |R| = 0.024.

• A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler and R. Blatt
  Speed of ion trap quantum information processors
  Preprint: quant-ph/0003087
  This work was done in collaboration with Innsbruck University.
  Abstract We investigate theoretically the speed limit of quantum gate operations for ion trap quantum information processors. The proposed methods use laser pulses for quantum gates which entangle the electronic and vibrational degrees of freedom of the trapped ions. Two of these methods are studied in detail and for both of them the speed is limited by a combination of the recoil frequency of the relevant electronic transition, and the vibrational frequency in the trap. We have experimentally studied the gate operations below and above this speed limit. In the latter case, the fidelity is reduced, in agreement with our theoretical findings.

• P. A. Barton, C. J. S. Donald, D. M. Lucas, D. A. Stevens, A. M. Steane, D. N. Stacey
  Measurement of the lifetime of the 3d D_{5/2} state in 40Ca+
  Phys. Rev. A.,
  Preprint: physics/0002026
  Abstract We report a measurement of the lifetime of the $3d D_{5/2} metastable level in 40Ca+, using quantum jumps of a single cold calcium ion in a linear Paul trap. The 4s S_{1/2}--3d D_{5/2} transition is significant for single-ion optical frequency standards, astrophysical references, and tests of atomic structure calculations. We obtain tau=1.168 +- 0.007 seconds from observation of nearly 64,000 quantum jumps during 32 hours. Our result is more precise and significantly larger than previous measurements. Experiments carried out to quantify systematic effects included a study of a previously unremarked source of systematic error, namely excitation by the broad background of radiation emitted by a semiconductor diode laser. Combining our result with atomic structure calculations yields 1.20 +- 0.01 s for the lifetime of 3d D_{3/2}. We also use quantum jump observations to demonstrate photon anti-bunching, and to estimate background pressure and heating rates in the ion trap.

• D. Stevens, J. Brochard and A. M. Steane:
  Simple experimental methods for trapped ion quantum processors
  Phys. Rev. A. 58, 2750-2759 (1998).
  Preprint: quant-ph/9802058
  Abstract: Two techniques are described that simplify the experimental requirements for measuring and manipulating quantum information stored in trapped ions. The first is a new technique using electron shelving to measure the populations of the Zeeman sublevels of the ground state, in an ion for which no cycling transition exists from any of these sublevels. The second technique is laser cooling to the vibrational ground state, without the need for a trap operating in the Lamb-Dicke limit. This requires sideband cooling in a sub-recoil regime. We present a thorough analysis of sideband cooling on one or a pair of sidebands simultaneously.

• Andrew Steane:
  The Ion Trap Quantum Information Processor
  Appl. Phys. B. 64 , 623-642 (1997) (Invited paper)
  Preprint: quant-ph/9608011
  See under Fundamentals of quantum theory , above.

• C. G. Townsend, N. H. Edwards, C. J. Cooper, K. P. Zetie, C. J. Foot; A. M. Steane, P. Szriftgiser, H. Perrin and J. Dalibard:
  Phase-space density in the magneto-optical trap
  Phys. Rev. A vol 52, pp 1423 (1995).
  Substance: General discussion of the MOT under a wide range of parameters.

• J. Werner, H. Wallis, G. Hillenbrand and A. M. Steane:
  Laser cooling by sigma+ / sigma- polarized beams of unequal intensities
  J. Phys. B vol 26, 3063 (1993).
  Substance: Theory of 1D corkscrew molasses with unbalanced beams. Useful for understanding the magneto-optical trap, and, more particularly, the TROOP (trap relying on optical pumping).

• A. M. Steane, G. Hillenbrand and C. J. Foot:
  Polarisation gradient cooling in a one-dimensional sigma+ / sigma- configuration for any atomic transition
  J. Phys. B vol 25, 4721 (1992).
  Substance: One dimensional laser cooling theory for any angular momentum J of the atomic state. Rather than giving merely a formal calculation, we discuss the details of what is going on, giving physical insight into the process.

• A. M. Steane and C. J. Foot:
  Laser cooling below the Doppler limit in a magneto-optical trap
  Europhys. Lett. vol 14, 231 (1991).
  Substance: This is the original demonstration that the MOT works by means of optical pumping, not merely Doppler and Zeeman effects.