From Wikipedia, the free encyclopedia
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
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.
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 because of Earnshaw's theorem, 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
- 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
- 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.
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,
- University of Maryland, Department of Physics and
Joint Quantum Institute, College Park, Maryland, USA
- Oxford University, Oxford,
- University of Siegen,
- Max Planck Institute, Garching, Germany
- McMaster University,
Hamilton, Ontario, Canada
- IBM, San Jose, California,
- Imperial College, London,
- Griffith University,
- University of Washington,
Seattle, Washington, USA
- MIT, Cambridge, MA,
- University of Sussex,
- Georgia Institute of
Technology, Atlanta, Georgia, USA
- Georgia Tech Quantum
Institute, Atlanta, Georgia, USA
- Quanteninformationsverarbeitung, Ulm,
- Quantum Optics Group, The
Institute of Photonic Sciences, Barcelona, Spain
- University of Cambridge, Cambridge, UK
- Cavity QED Group, Sussex, UK
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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