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computer. By conditional displacements and rotations we can implement Hamil-
tonians which are trigonometric functions of qubit operators. With such operators
we can effectively implement higher order gates such as Toffoli gates and Cn-NOT
gates, and we show that the entire Grover search algorithm can be implemented
in a direct way.
Comment: This paper shows how, through operations which are compositions of
primitives acting on single and collective degrees of freedom in an harmonic quan-
tum oscillator, non-trivial gates (like multiply controlled NOTs) can be obtained
directly, provided that the Hamiltonian can be continuously modulated in time.
This approach is geometric (connected to the Berry phase) and does not require
freezing of the collective degrees of freedom at the beginning.
3.2.2 Non-dissipative decoherence bounds on quantum computation
author(s): S.Mancini, R.Bonifacio
where: quant-ph/0012057, Phys. Rev. A accepted
We investigate the capabilities of a quantum computer based on cold trapped ions
in presence of non-dissipative decoherence. The latter is accounted by using the
evolution time as a random variable and then averaging on a properly defined
probability distribution. Severe bounds on computational performances are found.
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3.2.3 Prospects for a Quantum Dynamic Random Access Memory (Q-
DRAM)
author(s): S.Bandyopadhyay
where: quant-ph/0101058
Compared to quantum logic gates, quantum memory has received far less attention.
Here, we explore the prognosis for a solid-state, scalable quantum dynamic random
access memory (Q-DRAM), where the qubits are encoded by the spin orientations
of single quantons in exchange-decoupled quantum dots. We address, in particular,
various possibilities for implementing refresh cycles.
3.2.4 Robust quantum memory via quantum control
author(s): A.D.Greentree, S.G.Schirmer, A.I.Solomon
where: quant-ph/0103118, ICQI01
A general scheme for building a quantum memory by transferring quantum infor-
mation to an essentially decoherence-free memory transition using quantum control
is presented and illustrated by computer simulations.
3.2.5 Towards the fabrication of phosphorus qubits for a silicon quantum
computer
author(s): J.L.O Brien, S.R.Schofield, M.Y.Simmons, R.G.Clark, A.S.Dzurak, N.
J. Curson, B.E.Kane, N.S.McAlpine, M.E.Hawley, G.W.Brown
where: cond-mat/0104569, to appear in Phys. Rev. B Rapid Comm.
The quest to build a quantum computer has been inspired by the recognition
of the formidable computational power such a device could offer. In particular
silicon-based proposals, using the nuclear or electron spin of dopants as qubits,
are attractive due to the long spin relaxation times involved, their scalability, and
the ease of integration with existing silicon technology. Fabrication of such devices
however requires atomic scale manipulation - an immense technological challenge.
We demonstrate that it is possible to fabricate an atomically-precise linear array
of single phosphorus bearing molecules on a silicon surface with the required di-
mensions for the fabrication of a silicon-based quantum computer. We also discuss
strategies for the encapsulation of these phosphorus atoms by subsequent silicon
crystal growth.
3.3 Holonomic quantum computation
3.3.1 Geometric quantum computation with NMR
author(s): J.A.Jones, V.Vedral, A.Ekert, G.Castagnoli
where: quant-ph/9910052, JAJQP-99-02, Nature, 403, 869-871 (2000)
The experimental realisation of the basic constituents of quantum information
processing devices, namely fault-tolerant quantum logic gates, requires conditional
quantum dynamics, in which one subsystem undergoes a coherent evolution that
depends on the quantum state of another subsystem. In particular, the subsys-
tem may acquire a conditional phase shift. Here we consider a novel scenario in
which this phase is of geometric rather than dynamical origin. As the conditional
geometric (Berry) phase depends only on the geometry of the path executed it is
resilient to certain types of errors, and offers the potential of an intrinsically fault-
tolerant way of performing quantum gates. Nuclear Magnetic Resonance (NMR)
has already been used to demonstrate both simple quantum information process-
ing and Berry s phase. Here we report an NMR experiment which implements a
conditional Berry phase, and thus a controlled phase shift gate. This constitutes
the first elementary geometric quantum computation.
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3.3.2 Mathematical Foundations of Holonomic Quantum Computer II
author(s): K.Fujii
where: quant-ph/0101102
This is a sequel to the papers (quant-ph/9910063) and (quant-ph/0004102). The
aim of this paper is to give mathematical foundations to Holonomic Quantum
Computation (Computer) proposed by Zanardi and Rasetti (quant-ph/9904011)
and Pachos and Chountasis (quant-ph/9912093). In 2-qubit case we give an ex-
plicit form to non-abelian Berry connection of quantum computational bundle
which is associated with Holonomic Quantum Computation, on some parameter
space. We also suggest a possibility that not only usual holonomy but also higher-
dimensional holonomies must be used to prove a universality of our Holonomic
Quantum Computation.
3.3.3 On the nonadiabatic geometric quantum gates
author(s): W.Xiang-Bin, M.Keiji
where: quant-ph/0108111
Motivated for the fault tolerant quantum computation, quantum gate by adiabatic
geometric phase shift is extensively investigated. In this paper, we demonstrate
the nonadiabatic scheme for the geometric phase shift and conditional geometric
phase shift. Essentially, the new scheme is simply to add an appropriate additional
field. With this additional field, the state evolution can be controlled exactly on
a dynamical phase free path. Geometric quantum gates for single qubit and the
controlled NOT gate for two qubits are given.
3.4 Experiments on error correction codes
3.4.1 Experimental Quantum Error Correction
author(s): D.G.Cory, M.D.Price, W.Maas, E.Knill, R.Laflamme, W. H. Zurek,
T.F.Havel, S.S.Somaroo
where: Physical Review Letters, 81, 2152-2155 (1998)
Quantum error correction is required to compensate for the fragility of the state of a
quantum computer. We report the first experimental implementations of quantum
error correction and confirm the expected state stabilization. A precise analysis of
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