A Trapped ion quantum computer is a type of quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be processed and transferred through the collective quantized motion of the ions in the trap (interacting through the Coulomb force). Lasers are applied to induce coupling between the qubit states (for single qubit operations) or coupling between the internal qubit states and the external motional states (for entanglement between qubits). The fundamental operations of a quantum computer have been demonstrated experimentally with high accuracy (or "high fidelity" in quantum computing language) in trapped ion systems and a strategy has been developed for scaling the system to arbitrarily large numbers of qubits by shuttling ions in an array of ion traps. This makes the trapped ion quantum computer system one of the most promising architectures for a scalable, universal quantum computer.

As of June 2008, the largest number of entangled particles ever achieved in any quantum computer is eight calcium ions by way of the trapped ion method first achieved in 2005.¹²³

History of the Paul trap

The electrodynamic trap currently used in trapped ion quantum computing research was invented in the 1950s by Wolfgang Paul (who received the Nobel Prize in 1989 for his work). Charged particles cannot be trapped in 3D just by electrostatic forces, since Laplace's equation for electrostatics does not allow confining potentials in all three orthogonal directions. Instead, an electric field oscillating at radio frequency (RF) is applied, forming a potential with the shape of a saddle spinning at the RF frequency. If the RF field has the right parameters (oscillation frequency and field strength), the charged particle cannot leave the central region of this saddle potential because of inertia, and become effectively trapped at the saddle point. The particle's motion is described by a set of Mathieu equations in this situation.

History of trapped ion quantum computing

The first implementation scheme for a controlled-NOT quantum gate was proposed by Ignacio Cirac and Peter Zoller in 1995, specifically for the trapped ion system. The same year, a key step in the controlled-NOT gate was experimentally realized at NIST Ion Storage Group, and research in quantum computing began to take off worldwide. Many traditional ion trapping research groups have made the transition to quantum computing research, while, more recently, many other new research groups have joined the effort. An enormous amount of progress in this field has been made in the past decade and trapped ions remain a leading candidate for quantum computation.

Components of a quantum computer

• Qubits Any two-level quantum system can form a qubit, and there are two ways to form a qubit using the electronic states of an ion:

1) Two ground state hyperfine levels (these are called "hyperfine qubits")

2) A ground state level and an excited level (these are called the "optical qubits")

Hyperfine qubits are extremely long-lived (decay time of the order of thousands to millions of years) and phase/frequency stable (traditionally used for atomic frequency standards). Optical qubits are also relatively long-lived (with a decay time of the order of a second), compared to the logic gate operation time (which is of the order of microseconds). The use of each type of qubit poses its own distinct challenges in the laboratory.

• Initialization Ions can be prepared in a specific qubit state using a process called optical pumping. In this process, a laser couples the ion to some excited states which eventually decay to one state which is not coupled to by the laser. Once the ion reaches that state, it has no excited levels to couple to in the presence of that laser and, therefore, remains in that state. If the ion decays to one of the other states, the laser will continue to excite the ion until it decays to the state that does not interact with the laser. This initialization process is standard in many physics experiments and can be performed with extremely high fidelity (>99.9%).

• Measurement Measuring the state of the qubit stored in an ion is quite simple. Typically, a laser is applied to the ion that couples only one of the qubit states. When the ion collapses into this state during the measurement process, the laser will excite it, resulting in a photon being released when the ion decays from the excited state. After decay, the ion is continually excited by the laser and repeatedly emits photons. These photons can be collected by a photomultiplier tube (PMT) or a charge-coupled device (CCD) camera. If the ion collapses into the other qubit state, then it does not interact with the laser and no photon is emitted. By counting the number of collected photons, the state of the ion may be determined with a very high accuracy (>99.9%).

• Arbitrary Single Qubit Rotation One of the requirements of universal quantum computing is to coherently change the state of a single qubit. For example, this can transform a qubit starting out in 0 into any arbitrary superposition of 0 and 1 defined by the user. In a trapped ion system, this is often done using magnetic dipole transitions or stimulated Raman transitions for hyperfine qubits and electric quadrupole transitions for optical qubits. Gate fidelity can be greater than 99%.

• Two Qubit Entangling Gates Besides the controlled-NOT gate proposed by Cirac and Zoller in 1995, many equivalent, but more robust, schemes have been proposed and implemented experimentally since. Recent theoretical work by Garcia-Ripoll, Cirac, and Zoller have shown that there are no fundamental limitations to the speed of entangling gates, but gates in this impulsive regime (faster than 1 microsecond) have not yet been demonstrated experimentally (current gate operation time is of the order of microseconds). The fidelity of these implementations has been greater than 97%.

• Scalable Trap Designs Several groups have successfully fabricated ion traps with multiple trap regions and have shuttled ions between different trap zones. Ions can be separated from the same interaction region to individual storage regions and brought back together without losing the quantum information stored in their internal states. Ions can also be made to turn corners at a "T" junction, allowing a two dimensional trap array design. Semiconductor fabrication techniques have also been employed to manufacture the new generation of traps, making the 'ion trap on a chip' a reality. These developments bring great promise to making a 'quantum charged-coupled device' (QCCD) for quantum computation using a large number of qubits.

Experimental research groups

Here is a (possibly not exhaustive) list of experimental groups researching trapped ion quantum computing:

• University of Innsbruck, Innsbruck, Austria
• NIST Ion Storage Group, Boulder, Colorado, USA
• University of Maryland, Department of Physics and Joint Quantum Institute, College Park, Maryland, USA
• Oxford University, Oxford, UK
• University of Siegen, Siegen, Germany
• Max Planck Institute, Garching, Germany
• McMaster University, Hamilton, Ontario, Canada
• IBM, San Jose, California, USA
• Imperial College, London, UK
• Griffith University, Brisbane, Australia
• University of Washington, Seattle, Washington, USA
• MIT, Cambridge, MA, USA
• University of Sussex, Brighton, UK
• Georgia Institute of Technology, Atlanta, Georgia, USA
• Quanteninformationsverarbeitung, Ulm, Germany
• Quantum Optics Group, The Institute of Photonic Sciences, Barcelona, Spain

Recent developments

• D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan, and C. Monroe," Entanglement of single-atom quantum bits at a distance" Nature 449, 68 (2007).
• D. Stick, W. K. Hensinger, S. Olmschenk, M. J. Madsen, K. Schwab and C. Monroe, "Ion trap in a semiconductor chip" Nature Physics 2, 36-39 (2006).

• D. Leibfried, E. Knill, S. Seidelin, J. Britton, R. B. Blakestad, J. Chiaverini, D. B. Hume, W. M. Itano, J. D. Jost, C. Langer, R. Ozeri, R. Reichle and D. J. Wineland, "Creation of a six-atom 'Schrödinger cat' state" Nature 438, 639 (2005).

• H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür and R. Blatt, "Scalable multiparticle entanglement of trapped ions" Nature 438, 643 (2005).

• J. Chiaverini, J. Britton, D. Leibfried, E. Knill, M. D. Barrett, R. B. Blakestad, W.M. Itano, J.D. Jost, C. Langer, R. Ozeri, T. Schaetz, and D.J. Wineland, "Implementation of the semiclassical quantum Fourier transform in a scalable system" Science 308, 997-1000 (2005).

• B. B. Blinov, D. L. Moehring, L.- M. Duan and C. Monroe, "Observation of entanglement between a single trapped atom and a single photon" Nature 428, 153-157 (2004).

• J. Chiaverini, D. Leibried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W.M. Itano, J.D. Jost, E. Knill, C. Langer, R. Ozeri, and D.J. Wineland, "Realization of quantum error correction" Nature 432, 602-605 (2004).

• M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, J. Benhelm, G. P. T. Lancaster, T. W. Körber, C. Becher, F. Schmidt-Kaler, D. F. V. James, R. Blatt. "Deterministic quantum teleportation with atoms" Nature 429, 734 (2004).

• M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W.M. Itano, J.D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D.J. Wineland, "Deterministic quantum teleportation of atomic qubits" Nature 429, 737-739 (2004).

• C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, R. Blatt."Control and measurement of three-qubit entangled state" Science 304, 1478 (2004).

References

• "Electromagnetic traps for charged and neutral particles", W. Paul, Rev. Mod. Phys, 62, 531,(1990).

• "Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions", D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, Journal of Research of the National Institute of Standards and Technology 103, 259 (1998).

• "Quantum dynamics of single trapped ions" D Leibfried, R Blatt, C Monroe, D Wineland. Review of Modern Physics, volume 75, 281 (2003).

• "The ion trap quantum information processor", A. Steane, Appl. Phys. B. 64, 623 (1997).

• Cirac, J. I. and Zoller, P. Phys. Rev. Lett. 74 4091 (1995).

• Monroe, C. et al. Phys Rev. Lett. 75 4714 (1995).
• Trapped ion computer on arxiv.org