**Vol.1 Special Issue **Dec.
8, 2001 (in print: Dec 28, 2001)
**
Implementation of Quantum Computation **
Editorial** **
**
(ppi-ii)**
** R. Clark**
Dogma and heresy in
quantum computing** **
**
(pp1-6)**
D.P. DiVincenzo
Important new ideas for the physical
implementation of quantum computers are reviewed.
**
Quantum networks based
on cavity QED** **(pp7-12)**
** H. Mabuchi, M.
Armen, B. Lev, M. Loncar, J. Vuckovic, H.J. Kimble, J.Preskill,
M. Roukes, A. Scherer, and S.J. van Enk**
We review an ongoing program of interdisciplinary
research aimed at developing hardware and protocols for quantum
communication networks. Our primary experimental goals are to
demonstrate *quantum state
mapping* from storage/processing media (internal states of trapped
atoms) to transmission media (optical photons), and to investigate a
nanotechnology paradigm for cavity QED that would involve the
integration of magnetic microtraps with photonic bandgap structures.
Efficient
linear optics quantum computation
**
(pp13-19)**
** G.J. Milburn, T.
Ralph, A. White, E. Knill, and R. Laflamme**
Two qubit gates for photons are generally thought to require exotic
materials with huge optical nonlinearities. We show here that, if we
accept two qubit gates that only work conditionally, single photon
sources, passive linear optics and particle detectors are sufficient for
implementing reliable quantum algorithms. The conditional nature of the
gates requires feed-forward from the detectors to the optical elements.
Without feed forward, non-deterministic quantum computation is possible.
We discuss one proposed single photon source based on the surface
acoustic wave guiding of single electrons.
Quantum
control and information processing in optical lattices
**
(pp20-32)**
** P.S. Jessen, D.L.
Haycock, G. Klose and G.A. Smith***, *I.H. Deutsch, and G.K. Brennen
Neutral
atoms offer a promising platform for single- and many-body quantum
control, as required for quantum information processing. This includes
excellent isolation from the decohering influence of the environment,
and the existence of well developed techniques for atom trapping and
coherent manipulation. We present a review of our work to implement
quantum control and measurement for ultra-cold atoms in
far-off-resonance optical lattice traps. In recent experiments we have
demonstrated coherent behavior of mesoscopic atomic spinor wavepackets
in optical double-well potentials, and carried out quantum state
tomography to reconstruct the full density matrix for the atomic spin
degrees of freedom. This model system shares a number of important
features with proposals to implement quantum logic and quantum computing
in optical lattices. We present a theoretical analysis of a protocol
for universal quantum logic via single qubit operations and an
entangling gate based on electric dipole-dipole interactions. Detailed
calculations including the full atomic hyperfine structure suggests that
high-fidelity quantum gates are possible under realistic experimental
conditions.
Encoded
universality from a single physical interaction
**
(pp33-55)**
** J. Kempe, D.
Bacon, D.P. DiVincenzo, and K.B. Whaley **
We present a
theoretical analysis of the paradigm of encoded universality, using a
Lie algebraic analysis to derive specific conditions under which
physical interactions can provide universality. We discuss the
significance of the tensor product structure in the quantum circuit
model and use this to define the conjoining of encoded qudits. The
construction of encoded gates between conjoined qudits is discussed in
detail. We illustrate the general procedures with several examples from
exchange-only quantum computation. In particular, we extend our earlier
results showing universality with the isotropic exchange interaction to
the derivation of encoded universality with the anisotropic exchange
interaction, i.e., to the XY model. In this case the minimal encoding
for universality is into qutrits rather than into qubits as was the case
for isotropic (Heisenberg) exchange. We also address issues of
fault-tolerance, leakage and correction of encoded qudits.
Solid-state
crystal lattice NMR quantum computation
**
(pp56-81)**
** T.D. Ladd, Y.
Yamamoto, J.R. Goldman, and F. Yamaguchi **
**Construction of a silicon-based solid state quantum
computer **
**(pp82-95)**
**
A.S. Dzurak, M.Y. Simmons, A.R. Hamilton, R.G. Clark, R. Brenner,
T.M. Buehler, N.J. Curson, E. Gauja, R.P. McKinnon, L.D. Macks, M. Mitic, J.L. O’brien,
L. Oberbeck, D.J. Reilly, S.R. Schofield, and F.E. Stanley **
We discuss progress towards the fabrication and
demonstration of a prototype silicon-based quantum computer. The devices
are based on a precise array of ^{31}P dopants embedded in ^{
28}Si. Fabrication is being pursued via two complementary pathways
– a ‘top-down’ approach for near-term production of few-qubit
demonstration devices and a ‘bottom-up’ approach for large-scale qubit
arrays. The ‘top-down’ approach employs ion implantation through a
multi-layer resist structure which serves to accurately register the
donors to metal control gates and single-electron transistor (SET)
read-out devices. In contrast the ‘bottom-up’ approach uses STM
lithography and epitaxial silicon overgrowth to construct devices at an
atomic scale. Techniques for qubit read-out, which utilise coincidence
measurements on novel twin-SET devices, are also presented.
Quantum
computation using electrons trapped by surface acoustic waves** ****(pp96-101)**
**
C.H. W. Barnes,
J.M. Shilton and A.M. Robinson ** We outline a set of ideas for implementing a quantum processor based on
technology used in surface acoustic wave (SAW) single-electron transport
devices. These devices allow single electrons to be captured from a
two-dimensional electron gas by a SAW. We discuss how these devices can
be adapted to capture electrons in pure spin states and how both single
and two-qubit gates can be constructed. We give designs for readout
gates and
discuss possible sources of error and decoherence.
Quantum
computing with electrons floating on liquid helium **
(pp102-107)**
**
M.I. Dykman and
P.M. Platzman **
Electrons on a helium surface form a quasi two-dimensional system which
displays the highest mobility reached in condensed matter physics. We
propose to use this system as a set of interacting quantum bits. We will
briefly describe the system and discuss how the qubits can be addressed
and manipulated. The working frequency of the proposed quantum computer
is ~ 1GHz. Careful analysis shows that the relaxation rate can be
at least 5 orders of magnitude smaller, for low temperatures.
Fabrication of the structure for qubits using electrons on liquid helium **
(pp108-112)**
**
J. Goodkind and S. Pilla **
In the previous papers,
the system of qubits using electrons on a liquid helium film was
described. In this paper we describe the physical realization of the
system that we have begun to fabricate. We will not in this brief
discussion describe how we intend to operate the system. We will show
that we are nano- and micro-fabricating a new type of electronic device
that differs from other microelectronic devices in that the final step
of the fabrication deposits a layer of helium rather than some other
dielectric. The operation of the device will differ in that it
manipulates single electrons and it must operate at low temperatures.
**
Recent results in trapped-ion quantum
computing at NIST **
** ** **
(pp113-123)**
**
D. Kielpinski, A.
Ben-Kish, J. Britton, V. Meyer, M.A. Rowe, W.M. Itano, D.J. Wineland, C.
Sackett, and C. Monroe **
We review recent experiments on entanglement, Bell's inequality, and
decoherence-free subspaces in a quantum register of trapped {9Be+} ions.
We have demonstrated entanglement of up to four ions using the technique
of Molmer and Sorensen. This
method produces the state ({|\uparrow\uparrow\rangle}+{|\downarrow\downarrow\rangle})/\sqrt{2}
for two ions and the state ({\downarrow}{\downarrow}{\downarrow}{\downarrow}
\rangle + | {\uparrow}{\uparrow}{\uparrow}{\uparrow} \rangle)/\sqrt{2} for four
ions. We generate the entanglement deterministically in each shot of the
experiment. Measurements on the two-ion entangled state violates Bell's
inequality at the 8\sigma level. Because of the high
detector efficiency of our
apparatus, this experiment closes the detector loophole for Bell's
inequality measurements for the first time. This measurement is also the
first violation of Bell's inequality by massive particles that does not
implicitly assume results from quantum mechanics. Finally, we have
demonstrated reversible encoding of an arbitrary qubit, originally
contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing
noise and retains coherence under ambient conditions 3.6 times longer
than does an unencoded qubit. The encoding method, which uses single-ion
gates and the two-ion entangling gate, demonstrates all the elements
required
for two-qubit universal quantum logic.
**
Qubit
utilizing charge-number state in
super conducting nanostructure** **(pp124-128)**** **
**
J.S. Tsai, Y.
Nakamura, and YU. Pashkin **
In single-Cooper-pair box, the number of electrons in
the box is quantized and they form a single macroscopic quantum
charge-number state, corresponding to the number of excess electrons in
the box. By making all the electrodes superconducting, we can couple two
neighboring charge-number states coherently. In this way one can create
an artificial two-level system. Qubit operations were demonstrated in
two different control techniques, dc electric-field gate bias and ac
field bias. The dc method was unique compared with the commonly used
Rabi-oscillation-type operation. Here the system was biased at the
degenerate point of the two states so that the dynamical phase does not
develop during the operation. This was the first time that the quantum
coherent oscillation was observed in a solid-state device whose quantum
states involved a macroscopic number of quantum particles.
Multiple-pulse experiments were also carried out and phase control was
also demonstrated.
**
Fabricating an all-epitaxial silicon quantum computer** **
(pp129-133)**
**
J.R. Tucker and T.-C. Shen
**
Scalable silicon quantum computers
will require a material perfection that has never been
attempted. Ground state wavefunctions for conduction
electrons orbiting individual phosphorous donors must be polarized
electronically and coupled to nearest neighbors with great precision.
Elimination of all randomizing influences can be achieved only with a
fully epitaxial structure; and we believe that output circuitry must
also be integrated into the qubit arrays in order to achieve the
uniformity needed for large-scale integration. A process that could
potentially accomplish this will be outlined, based on scanning
tunneling microscope (STM) removal of individual hydrogen atoms from the
H-terminated silicon surface followed by phosphine dosing and
ultra-low-temperature overgrowth. Self-ordering of PH_{3}
molecules onto extended areas of bare silicon should permit patterning
of planar single-electron transistors along with P-donor qubits in the
same lithographic step. Initial plans for an experiment to characterize
exchange coupling under gate control will be described.
NMR
quantum computing - lessons for the future **(pp134-142)**
L. Vandersypen
and I. Chuang
Future physical implementations of large-scale quantum computers will
face significant practical challenges. Many useful lessons can be drawn
from present results with Nuclear Magnetic Resonance realizations of
controllable two, three, five, and seven qubit quantum systems. We
summarize various experimental methods and theoretical procedures
learned in this work which will be of considerable value in building and
testing quantum processors with a wide variety of physical systems.
**
Universal
quantum gates for single cooper pair box based quantum computing
****
(pp143-150)**
**
P. Echternach, C.P. Williams, S.C. Dultz, S.
Braunstein, and J.P. Dowling**
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