Quantum Computing

1
Quantum Computing

• The next big thing?
• Mike Taylor, Jan 2002

2
Origins

• Richard Feynman observed that quantum systems
  could not be modelled using conventional
  computers and in 1982 proposed a model for
  quantum computation
• In 1985, David Deutsch (Oxford) showed that, in
  principle, any physical process could be modelled
  by a quantum computer

3
What is a quantum computer?

• A computer that processes quantum information
  (represented as qubits) instead of bits
• A qubit is a two-state quantum system and may
  contain a superposition of classical values
• Quantum computing is reducible to one- and
  two-qubit gate operations

4
Why is a QC interesting?

• A system of (say) 500 qubits can represent 2500
  states
• Any operation on the system would act
  simultaneously on all 2500 states
• This is equivalent to a system with 10150
  conventional processors
• QC performs an exponential amount of processing
  in polynomial space and time

5
Main obstacles

• Decoherence. The tendency for the quantum states
  to be disrupted by interaction with the
  environment
• Hardware architecture. How to physically build
  systems of large numbers of qubits

6
Decoherence

• Sophisticated error correction schemes (such as
  spreading out a logical qubit over three
  physical nuclear spins) show the most promise
• But this is a huge issue. Many critics believe
  this problem cannot be overcome for sufficiently
  large numbers of qubits to be interesting

7
Hardware architecture

• Most successful experiment to date is based on a
  specially constructed molecule and NMR. But this
  is likely not scalable.
• Other approaches
• Quantum dots (electrons confined in semiconductor
  nanostructures)
• Single-atom impurities in a semiconductor
• Electronic or magnetic flux in superconductors

8
State of the art

• IBM Research successfully demonstrated Shors
  algorithm (factorization) in December 2001.
  153x5.
• Seven-qubit system based on a molecule with 7
  spins (5 fluorine, 2 carbon)
• Programmed by RF excitation and result read-out
  by NMR

9
Applications

• First interesting algorithm published by Peter
  Shor (ATT) in 1994 - factorization
• Followed by database search (Grover) and Fourier
  transform
• Quantum communication provides unbreakable
  security
• Key challenge/question for research - can QCs
  compute NP-complete or NP-hard problems in
  polynomial time?

10
Some philosophical questions

• Will QCs provide artificial consciousness? (If
  you believe that consciousness is a quantum
  phenomenon)
• How will QCs affect the nature of proof when a
  result can be shown but not the steps to achieve
  it?