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 number of qubits by shuttling ions in an array of ion traps. This makes trapped ion system one of the most promising architectures for a scalable, universal quantum information processor.

History of ion trap

Ion traps were first invented in the 1960's by Wolfgang Paul and Hans Dehmelt (who received the Nobel Prize in 1989 for their work). The idea is that since a charged particle can not be confined in three dimensional space using static electric fields, an electric field oscillating at radio frequency (RF) is applied instead, forming a potential with the shape of a saddle spinning at the RF frequency. The ions, interacting with this oscillating potential over time, end up trapped in the middle of the saddle potential.

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 many other new research groups have joined the effort more recently. An enormous amount of progress have been made in the past decade, and trapped ions still remain to be the leading candidate for quantum computation.

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

Monroe, C. et al. Phys Rev. Lett. 75 4714 (1995)

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 on the order of thousands to millions of years!) and phase/frequency stable (traditionally been used for atomic frequency standards). Optical qubits are also relatively long-lived (decay time on the order of a second) compared to the logic gate operation time (on the order of microseconds). Each type of qubits poses its own challenges in the laboratory, so choose your poison wisely!

Initialization Ions can be prepared in a specific qubit state using a process called optical pumping. A laser couples the ion to some excited states which eventually decays 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 somehow 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 initiallization process is standard in many physics experiments and can be performed with extremely high fidelity (>99%).

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 state. When the ion is collapsed 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 emitting photons. These photons can be collected by a photomultiplier tube (PMT) or a charge-coupled device (CCD) camera. If the ion is collapsed into the other qubit state, then it does not interact with the laser and no photon will be emitted. By counting the collected photons, it is easy to determine which state the ion is in with very high accuracy (>99.7%).

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 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 as high as >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 ultrafast regime (picoseconds or faster) have not yet been demonstrated experimentally (current gate time is on the order of microseconds). The fidelity of these implementations have been as high as >97%.

Scalable Trap Designs Many groups have successfully fabricated ion traps with multiple trap regions 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 "ion trap on a chip" a reality. These developments bring great promise to making a "quantum charged-coupled device" (QCCD) for quantum computation on a large number of qubits.

References

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

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

• D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys., 75, 281 (2003).

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

• K.-A. Brickman, P. C. Haljan, P. J. Lee, M. Acton, L. Deslauriers, C. Monroe, Implementation of Grover's Quantum Search Algorithm in a Scalable System, Phys. rev. A, 72, 050306 (2005).

Category:Physical Realisations Category:Introductory Tutorials Category:Handbook of Quantum Information