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The following is a non-technical 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.
Present-day 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. Specially-designed 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 present-day 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 present-day 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 state-of-the-art at the moment has only 3-4 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 wave-particle 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 cond-mat/0011040
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