The following is a nontechnical summary of research that I carried out
with Yuval Gefen at the Weizmann Institute, it was written in 2001.
Quantum Computers and Berry Phase
A computer which uses quantum mechanics to do its calculations.
Presentday computers do calculations using logic states (bits) which are
either zero or one (off or on). A quantum computer would use
quantum logic states (qubits) which are in a quantum superposition of
zero and one. This paradigm shift from conventional to quantum logic
will completely change the way computers are programmed and used.
Speciallydesigned software for such a computer
could enable it to do a huge number of calculations at the same time.
This means that a quantum computer could run extremely complex programs in a
tiny fraction of the time presentday computers can.
Truly incredible increases in speed have been predicted,
for example calculations which would take hundreds of years on conventional
computers could be done in a fraction of a second.
Can a quantum computer be built?
Each qubit in the quantum computer has to be a quantum state
which can be easily controlled. Thousands of these qubits then have
to be coupled together to make the computer.
However quantum computers are much more sensitive to errors
than conventional computers.
It is crucial that the qubits of the quantum computer do not interact
with anything surrounding them except for other qubits.
If they do interact with their surroundings then errors occur
and the computer stops working.
These requirements present a huge challenge to our understanding of
interactions between quantum systems.
What should a quantum computer be made out of?
Conventional computers which use ordinary bits (not qubits),
have been built in various very different ways over the years.
Turing's original design (1936) for such a computer was mechanical,
made of cogs and gears. The first working computers were built
from valves which were made of vacuum tubes, while the modern
computer era of computer was made possible by the invention of
microchips made of silicon. Despite this all these computers
work on the same principles.
Quantum computers work on very different principles from
the presentday computers, but there are still many possible ways to
implement these principles.
Candidates for qubits include electronic states of atoms,
spin states of nuclei, quantum dots, or superconducting circuits.
A huge experimental and theoretical effort is being directed towards
understanding the advantages of and problems with the various possibilities.
At present it is much
too early to tell which will be the building blocks of future quantum
computers.
The stateoftheart at the moment has only 34 qubits, rather
than the thousands necessary for a simple computer.
Quantum computing using Berry phase.
Berry phase, so called because it was discovered by Michael Berry in 1984,
is a concept crucial to our understanding of many quantum
mechanical effects. For example it affects the way in which chemical
reactions occur, it modifies the motion of vortices in superconductors,
and the motion of electrons in nanoscale electronic devices.
It has recently been suggested
that it could be used to make a quantum
computer.
Phase is a basic property of all waves, for example the difference in phase
between two waves determines whether they interfere constructively or
destructively.
All quantum particles have wavelike properties, such as phase,
because of waveparticle duality.
Berry phase is a special phase that the particle acquires if it is
forced to slowly rotate.
It appearsn that one way of controlling a qubit is to control
its Berry phase.
However to do this we require a quantum computer with
qubits made from robust quantum systems with Berry phases.
These qubits must be coupled to each other and yet be isolated from everything
else.
Our present work.
We are concentrating on what happens to the Berry phase if the qubits
are not perfectly isolated.
We have studied the errors caused by the qubits interaction with its
surroundings. If the system is not sufficiently well
isolated from its surroundings we have found the Berry phase can be destroyed.
However even if it is not destroyed, it can be modified by the surroundings.
This modification of the Berry phase was unexpected and has surprised a
number of experts in the field.
Our work has enabled us to develop a criterion for a Berry phase qubit
to work. It is now our intention to study the possible implementations
of the Berry phase qubits to find out if they fulfill this criterion.
If they do not, our work will give an excellent indication what
improvements are needed.

Geometric quantum computation using nuclear magnetci resonances
J.A.Jones, Vlatko Vedral, Artur Ekert, Giuseppe Castagnoli
Nature Vol. 403, 869 (2000)

Detection of Geometric Phases in Superconducting Nanocircuits
Giuseppe Falci, Rosario Fazio, G. Massimo Palma, Jens Siewert, Vlatko Vedral Nature Vol. 407, 355 (2000) or
condmat/0011040
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