19 research outputs found
Approximate Quantum Fourier Transform and Decoherence
We discuss the advantages of using the approximate quantum Fourier transform
(AQFT) in algorithms which involve periodicity estimations. We analyse quantum
networks performing AQFT in the presence of decoherence and show that extensive
approximations can be made before the accuracy of AQFT (as compared with
regular quantum Fourier transform) is compromised. We show that for some
computations an approximation may imply a better performance.Comment: 14 pages, 10 fig. (8 *.eps files). More information on
http://eve.physics.ox.ac.uk/QChome.html
http://www.physics.helsinki.fi/~kasuomin
http://www.physics.helsinki.fi/~kira/group.htm
Quantum Physics and Computers
Recent theoretical results confirm that quantum theory provides the
possibility of new ways of performing efficient calculations. The most striking
example is the factoring problem. It has recently been shown that computers
that exploit quantum features could factor large composite integers. This task
is believed to be out of reach of classical computers as soon as the number of
digits in the number to factor exceeds a certain limit. The additional power of
quantum computers comes from the possibility of employing a superposition of
states, of following many distinct computation paths and of producing a final
output that depends on the interference of all of them. This ``quantum
parallelism'' outstrips by far any parallelism that can be thought of in
classical computation and is responsible for the ``exponential'' speed-up of
computation.
This is a non-technical (or at least not too technical) introduction to the
field of quantum computation. It does not cover very recent topics, such as
error-correction.Comment: 27 pages, LaTeX, 8 PostScript figures embedded. A bug in one of the
postscript files has been fixed. Reprints available from the author. The
files are also available from
http://eve.physics.ox.ac.uk/Articles/QC.Articles.htm
Effects of noise on quantum error correction algorithms
It has recently been shown that there are efficient algorithms for quantum
computers to solve certain problems, such as prime factorization, which are
intractable to date on classical computers. The chances for practical
implementation, however, are limited by decoherence, in which the effect of an
external environment causes random errors in the quantum calculation. To combat
this problem, quantum error correction schemes have been proposed, in which a
single quantum bit (qubit) is ``encoded'' as a state of some larger number of
qubits, chosen to resist particular types of errors. Most such schemes are
vulnerable, however, to errors in the encoding and decoding itself. We examine
two such schemes, in which a single qubit is encoded in a state of qubits
while subject to dephasing or to arbitrary isotropic noise. Using both
analytical and numerical calculations, we argue that error correction remains
beneficial in the presence of weak noise, and that there is an optimal time
between error correction steps, determined by the strength of the interaction
with the environment and the parameters set by the encoding.Comment: 26 pages, LaTeX, 4 PS figures embedded. Reprints available from the
authors or http://eve.physics.ox.ac.uk/QChome.htm
Conditional Quantum Dynamics and Logic Gates
Quantum logic gates provide fundamental examples of conditional quantum
dynamics. They could form the building blocks of general quantum information
processing systems which have recently been shown to have many interesting
non--classical properties. We describe a simple quantum logic gate, the quantum
controlled--NOT, and analyse some of its applications. We discuss two possible
physical realisations of the gate; one based on Ramsey atomic interferometry
and the other on the selective driving of optical resonances of two subsystems
undergoing a dipole--dipole interaction.Comment: 5 pages, RevTeX, two figures in a uuencoded, compressed fil
Non-invasive detection of the evolution of the charge states of a double dot system
Coupled quantum dots are potential candidates for qubit systems in quantum
computing. We use a non-invasive voltage probe to study the evolution of a
coupled dot system from a situation where the dots are coupled to the leads to
a situation where they are isolated from the leads. Our measurements allow us
to identify the movement of electrons between the dots and we can also identify
the presence of a charge trap in our system by detecting the movement of
electrons between the dots and the charge trap. The data also reveals evidence
of electrons moving between the dots via excited states of either the single
dots or the double dot molecule.Comment: Accepted for publication in Phys. Rev. B. 4 pages, 4 figure
Quantum entanglement using trapped atomic spins
We propose an implementation for quantum logic and computing using trapped
atomic spins of two different species, interacting via direct magnetic
spin-spin interaction. In this scheme, the spins (electronic or nuclear) of
distantly spaced trapped neutral atoms serve as the qubit arrays for quantum
information processing and storage, and the controlled interaction between two
spins, as required for universal quantum computing, is implemented in a three
step process that involves state swapping with a movable auxiliary spin.Comment: minor revisions with an updated discussion on adibatic tranportation
of trapped qubit, 5 pages, 3 figs, resubmitted to PR
Elementary gates for quantum computation
We show that a set of gates that consists of all one-bit quantum gates (U(2))
and the two-bit exclusive-or gate (that maps Boolean values to ) is universal in the sense that all unitary operations on
arbitrarily many bits (U()) can be expressed as compositions of these
gates. We investigate the number of the above gates required to implement other
gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2)
transformation to one input bit if and only if the logical AND of all remaining
input bits is satisfied. These gates play a central role in many proposed
constructions of quantum computational networks. We derive upper and lower
bounds on the exact number of elementary gates required to build up a variety
of two-and three-bit quantum gates, the asymptotic number required for -bit
Deutsch-Toffoli gates, and make some observations about the number required for
arbitrary -bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev.
A. Related information on http://vesta.physics.ucla.edu:7777
Silicon-based spin and charge quantum computation
Silicon-based quantum-computer architectures have attracted attention because
of their promise for scalability and their potential for synergetically
utilizing the available resources associated with the existing Si technology
infrastructure. Electronic and nuclear spins of shallow donors (e.g.
phosphorus) in Si are ideal candidates for qubits in such proposals due to the
relatively long spin coherence times. For these spin qubits, donor electron
charge manipulation by external gates is a key ingredient for control and
read-out of single-qubit operations, while shallow donor exchange gates are
frequently invoked to perform two-qubit operations. More recently, charge
qubits based on tunnel coupling in P substitutional molecular ions in Si
have also been proposed. We discuss the feasibility of the building blocks
involved in shallow donor quantum computation in silicon, taking into account
the peculiarities of silicon electronic structure, in particular the six
degenerate states at the conduction band edge. We show that quantum
interference among these states does not significantly affect operations
involving a single donor, but leads to fast oscillations in electron exchange
coupling and on tunnel-coupling strength when the donor pair relative position
is changed on a lattice-parameter scale. These studies illustrate the
considerable potential as well as the tremendous challenges posed by donor spin
and charge as candidates for qubits in silicon.Comment: Review paper (invited) - to appear in Annals of the Brazilian Academy
of Science