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Quantum Computing Technology

A quantum computer is a device in which data can be stored in a network of quantum mechanical two-level systems ("qubits"), such as spin-1/2 particles or two level atoms. The quantum mechanical nature of such systems allows the possibility of a powerful new feature to be incorporated into data processing, namely the capability of performing logical operations upon quantum mechanical superpositions of numbers. In a conventional digital computer each data register is, throughout any computation, always in a definite state "1" or "0"; however in a quantum computer each qubit will be in an undetermined quantum superposition of two states |1> and |0>. Calculations would then be performed by external interactions with the various two-level systems that constitute the device, in such a way that logic gate operations involving two or more different qubits can be realized. The final result would be obtained by measurement of the quantum mechanical probability amplitudes at the conclusion of the calculation.

Quantum computers represent a revolutionary new computational paradigm that has seen tremendous growth since 1994, following the invention of quantum algorithms with compelling real-world applications, experimental realizations of systems with a few qubits, and the extension of the theory of error correction to quantum systems. The "killer application" for quantum computers is Shor's algorithm after its inventor, Peter Shor of AT&T Bell Labs. This algorithm allows the determination of the prime factors of large composite numbers efficiently, which has tremendous potential implications.

A number of promising technologies have been proposed for building quantum computers. I work on aspects of two programs here at Los Alamos: trapped ion quantum computers and nuclear-spin based solid-state quantum computers.

Trapped ion quantum computers

One of the most promising quantum computer hardware proposals is the cold-trapped ion system devised by Ignacio Cirac and Peter Zoller of the University of Innsbruck, Austria. Their design consists of a string of ions stored in a linear radio-frequency trap and cooled sufficiently that their motion, which is coupled together due to the Coulomb force between them, is quantum mechanical in nature. Each qubit would be formed by two internal levels of each ion, a laser being used to perform manipulations of the quantum mechanical probability amplitudes of the states; conditional two-qubit logic gates being realized with aid of the excitation or de-excitation of quanta of the ions' collective motion.

External view of the vacuum chamber used for trapped ion quantum computing experiments at Los Alamos during 1995-2001. Various windows are used for laser access to the ion trap (not visible in this photo); a red alignment laser beam is visible. Half way up on the left hand side the source of neutral calcium ions can be seen; these were excited thermally and then ionized by electron beam (whose housing can be seen at roughly `2 o'clock' on the far side of the cahmber). At the bottom left is a multi channel plate used for imaging the electron beam, while at the far right is the CCD camera used for imaging the trapped ions.

The engineering problems associated with making such a device work are formidable. Firstly an ion trap had to be designed and built; Next the ions have to be cooled down to their ground state; Once the ions are cooled, the computation will be performed by a series of laser pulses directed at one or other of the ions; each pulse must transfer population from one level of the ion to a different level, without exciting any third level, or affecting any of the adjacent ions. Sometimes the laser will be used to excite a quantum of the ions' oscillations. Chosing the best combination of lasers and energy level of the ion, and then inventing ways in which these operations can be performed reliably with the available technology is a complicated problem of atomic and optical physics.

Simplified energy level diagram for singly ionized strontium, typical of the atomic structure of alkali-like ions which are being used for the quibits of trapped-ion quantum computers. The two qubit levels could be, for example, the two Zeeman sub-levels of the doublet-S ground state; alternatively one of the S sublevels and one of the sublevels of the metastable D states could be used. The current experimental effort in trapped-ion quantum computing at Los Alamos, based on strontium, is headed by Dr. Dana Berkeland of group P-21.

Daniel James's papers on trapped ions

Quantum Dynamics of Trapped Ions

D. F. V. James. "Quantum dynamics of cold trapped ions, with application to quantum computation," Applied Physics B 66, 181-190 (1998). PDF
T. P. Meyrath and D. F. V. James, "Theoretical and Numerical studies of the positions of cold trapped ions," Physics Letters A 240, 37-42 (1998). PDF
D. F. V. James, "The theory of heating of the quantum ground state of trapped ions," Physical Review Letters 81, 317-320 (1998). PDF
C. Marquet, F. Schmidt-Kaler and D. F. V. James, "Phonon-phonon interactions due to non-linear effects in a linear ion trap," submitted to Applied Physics B (2002); quant-ph/0211079.

Techniques for Quantum Information Processing with Trapped Ions

D. F. V. James, S. Schneider and G. J. Milburn, "Quantum Computation with "Hot" Trapped Ions," Quantum Communication, Computing, and Measurement 2 (Prem Kumar, G. Mauro D'Ariano and Osamu Hirota, eds., Kluwer Academic/Plenum Publishers, 2000), p.289. PDF
S. Schneider, D. F. V. James and G. J. Milburn, "Quantum computation with `hot' trapped ions," Journal of Modern Optics 7, 499-505 (1999). PDF
G.J. Milburn, S. Schneider and D. F. V. James, "Ion trap quantum computing with warm ions," Fortschritte der Physik 48, 801-810 (2000). PDF
D. F. V. James, "Quantum Computation with hot and cold ions: An assessment of proposed schemes," Fortschritte der Physik 48, 823-837 (2000). PDF

Decoherence Processes in Trapped Ion Quantum Computers

R. J. Hughes, D. F. V. James, E. H. Knill, R Laflamme and A. G. Petschek, "Decoherence bounds on quantum computation with trapped ions," Physical Review Letters 77, 3240-3243 (1996). PDF
D. F. V. James, R. J. Hughes, E. H. Knill, R. Laflamme and A. G. Petschek, "Decoherence bounds on the capabilities of cold trapped ion quantum computers" in Photonic Quantum Computing (S. P. Hotaling and A. P. Pirich, eds.) Proccedings of the SPIE 3076, 42-50 (1997). PDF
R. J. Hughes and D. F. V. James, "Prospects for quantum computation with Trapped ions," Fortschritte der Physik 46, 759-769 (1998). PDF
D. F. V. James, "Quantum Computation with Trapped Ions and the `Heating Problem'," Quantum Computing III (E. Donkor and A. R. Pirich, eds.) Proceedings of the SPIE 4047. PDF

Experiments with Trapped Ions

R. J. Hughes, D. F. V. James, J. J. Gomez, M. S. Gulley, M. H. Holzscheiter, P. G. Kwiat, S. K. Lamoreaux, C. G. Peterson, V. D. Sandberg, M. M. Schauer, C. M. Simmons, C. E. Thorburn, D. Tupa, P. Z. Wang and A. G. White, "The Los Alamos Trapped Ion Quantum Computer Experiment," Fortschritte der Physik 46, 329-361 (1998). PDF
D. F. V. James, M. S. Gulley, M. H. Holzscheiter, R. J. Hughes, P. G. Kwiat, S. K. Lamoreaux, C. G. Peterson, V. D. Sandberg, M. M. Schauer, C. M. Simmons, D. Tupa, P. Z. Wang and A. G. White, "Trapped Ion Quantum Computer Research at Los Alamos," Quantum Computing and Quantum Communications, (C. P. Williams, ed., Lecture Notes in Computer Science 1509, Springer, Heidelburg, 1999) pp 426-437. PDF
M. S. Gulley, J. J. Gomez, M. H. Holzscheiter, D. F. V. James, P. G. Kwiat, S. K. Lamoreaux, C. G. Peterson, V. Sandberg, M. M. Schauer, C. Simmons, D. Tupa, P. Wang, A. G. White, R. J. Hughes, "Progress towards using a calcium ion trap to perform quantum logic operations," Quantum Communication, Computing, and Measurement 2 (Prem Kumar, G. Mauro D'Ariano and Osamu Hirota, eds., Kluwer Academic/Plenum Publishers, 2000), p.283. PDF
D. Enzer, M. M. Schauer, J. J. Gomez, M. S. Gulley, M. H. Holzscheiter, P. G. Kwiat, S. K. Lamoreaux, C. G. Peterson, V. D. Sandberg, D. Tupa, A. G. White, R. J. Hughes and D. F. V. James, "Observation of Power-Law Scaling for Phase Transitions in Linear Trapped Ion Crystals," Physical Review Letters 85, 2466-2469 (2000). PDF

Quantum Chaos of trapped ions

G. P. Berman, D. F. V. James, R. J. Hughes, M. S. Gulley, M. H. Holzscheiter and G. V. López, "Dynamical Stability and Quantum Chaos of Ions in a Linear Trap," Physical Review A 61, 023403 (2000). PDF
G. P. Berman, D. F. V. James, D. I. Kamenev, "Stability of the ground state of a harmonic oscillator perturbed by a monochromatic wave," CHAOS11, 449-463 (2001). PDF
G. P. Berman, D.F.V. James, D. I. Kamenev, "Quantum chaos of an ion confined in a linear ion trap interacting with laser fields," CHAOS 10, 371-382 (2000). PDF
G. P. Berman, A. R. Bishop, D. F. V. James, R. J. Hughes and D. I. Kamenev "Dynamical Stability of an Ion in a Linear Trap as a Solid State Problem of Electron Localization," Physical Review A 64, 053406 (2001). PDF

Nuclear-spin based solid-state quantum computers
The long-term goal of quantum computing research is a device with the following features: a scaleable architecture (allowing large numbers of qubits); a high clock speed; the capability to perform quantum operations in parallel; and an ``industrial" fabrication method. Solid state systems are the most promising candidates for meeting these demanding requirements. One solid-state quantum computer design has been suggested by Dr. Bruce Kane, formerly at the University of New South Wales, now at the University of Maryland [see: ``A Silicon-based Nuclear Spin Quantum Computer,'' Nature 393, 133 (1998)]. The key elements of his proposed architecture are an array of spin-1/2 phosphorus nuclei embedded in silicon and a series of surface gate electrodes. The spins of the phosphorus nuclei, which constitute the qubits, will be addressed using a static electric and manipulated using NMR techniques. Single spin interactions are achieved by changing the voltage on a metallic gate electrode (the "A'' gate) positioned above each nucleus; spin-flips are then carried out by a pulse of RF field tuned to the appropriate Stark-shifted resonance frequency. The electron-mediated interaction between two nuclear spins can be turned on and off by applying a voltage to the electrode placed between them (the ``J'' gate); conditional spin flips can then be achieved again using the RF field. It is possible to show that any desired quantum state can be reached with these two types of interactions.

Basic architecture of the Kane spin-based solid state quantum computer. The nuclear spins constitute the qubits which store the quantum information; these are aligned in a strong static magnetic field and can be controlled by a series of electrodes, as described below.


Single qubit operations: by placing a voltage on the electrode imediately above the target qubit, the bound electron is distorted, thereby shifting the nuclear magnetic resonance frequency. Applying a radio-frequency field at this shifted resonance frequency allows the spin of the target qubit to be flipped, while the other qubits (which off-resonance) are left alone.	Two qubit logic gates can be performed by similarly applying a voltage to an electrode which distorts two electrons to the extent that an exchange interaction is induced by their overlap. Since the electrons are interacting with the nuclear spin, and effective qubit-qubit interaction is induced.

Los Alamos is currently engaged on a project to construct a prototype two-qubit device capable of investigating the principles of Kane's design. The program, headed by Marilyn Hawley of MST Division, will be in close collaboration with the University of New South Wales, where the design originated and which has a state-of-the-art semiconductor fabrication facility. Other institutions taking part in the collaboration are CalTech, the University of Maryland, Ohio State University and the University of Queensland.

Research Areas

Quantum Computing Technology