Advertisement

Abstract

Quantum computation is a fascinating new area that touches upon the foundations of both quantum physics and computer science. Quantum computers can perform certain tasks, such as factoring, exponentially faster than classical computers. This talk will describe the principles underlying the fundamental quantum algorithms.

The power of quantum computation lies in the exponentially many hidden degrees of freedom in the state of an n quantum bit system – whereas 2 n – 1 complex numbers are necessary to specify the state, Holevo’s theorem states that n quantum bits cannot be used to communicate any more than n classical bits. Nevertheless, there are communication tasks in which these hidden degrees of freedom can be tapped into.

Finally, the state of a quantum system is particularly fragile to noise and decoherence. However, there are beautiful techniques – quantum error-correcting codes – for protecting a given quantum state (with its exponentially many degrees of freedom) against noise and decoherence. These codes can be used to create fault-tolerant quantum circuits – which are immune to a constant rate of decoherence.

References

  1. 1.
    Aharanov, D., Ben-Or, M.: Fault tolerant quantum computation with constant error. quant-ph/9611025Google Scholar
  2. 2.
    Ambainis, A., Schulman, L., Ta-Shma, A., Vazirani, U., Wigderson, A.: The Quantum Communication Complexity of Sampling. In: Proceedings of Symposium on the Foundations of Computer Science (1998)Google Scholar
  3. 3.
    Bernstein, E., Vazirani, U.: Quantum complexity theory. Siam Journal of Computing 26 (October 1997) (special issue on quantum computation)Google Scholar
  4. 4.
    Calderbank, A., Shor, P.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1106 (1996)Google Scholar
  5. 5.
    Shor, P.: Algorithms for quantum computation: Discrete logarithms and factoring. Siam Journal of Computing 26, 1484–1509 (1997) (special issue on quantum computatio n)Google Scholar
  6. 6.
    Vazirani, U.: Course Notes on Quantum Computation, http://www.cs.berkeley.edu/vazirani/qc.html

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Umesh Vazirani
    • 1
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

Personalised recommendations