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Lecture 16

Lecture 16. Quantum computing Ubiquitous Internet Services The client server paradigm DNS Electronic Mail World Wide Web. Quantum Computing. In a quantum system the amount of parallelism increases exponentially with the size of the system.

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Lecture 16

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  1. Lecture 16 • Quantum computing • Ubiquitous Internet Services • The client server paradigm • DNS • Electronic Mail • World Wide Web

  2. Quantum Computing • In a quantum system the amount of parallelism increases exponentially with the size of the system. • Access to the results disturbs the quantum state through a process called decoherence. • Qubit – a unit vector in a 2-dimensional complex space where a complex base has been chosen.

  3. Classical mechanics • The individual states of particles combine through the cartesian product. • If X and Y are vectors the vector product has dimension dim(X) + dim(Y). • Given a system of n particles the states of the system form a vector space with 2 x n dimensions. • Given n bits we can construct 2n n-tuples and describe a system with 2n states.

  4. Quantum mechanics • The individual states of particles combine through the tensor product. • If X and Y are vectors the vector product has dimension dim(X) x dim(Y). • Given a system of n particles the states of the system form a vector space with 2n dimensions. • The extra states that do not have a classical analogy are called entangled states.

  5. Quantum mechanics (cond’t) • A quantum bit can be in infinitely many superposition states. • When the qubit is measured the measurement changes the state of the particle to one of the two basic states, thus from a qubit we can only extract a clasical bit of information. • Example – the use of polarized light to transmit information.

  6. Polarized light • A photon’s polarized state can be modeled as a unit vector and expresses as a combination of two basis vectors. • There are infinitely many possible orientations of the unit vector  a qubit can be in infinitely many superposition states. • Measuring the polarization is equivalent with projecting the random vector onto one of the two bases.

  7. Quantum algorithms • 1994 Peter Shor found a polynomial time algorithm for factoring n-bit numbers on quantum computers. • The algorithm reduces the factoring problem to finding the period of a function and uses quantum parallelism to find the superposition of all values of the function in one step. • Then the algorithm calculates the quantum Fourier transform of the function in one step.

  8. Ubiquitous Internet Services • The client-server paradigm. • Asynchrounous RPCs • Servers are reactive programs. • Stateless versus statefull servers.

  9. DNS • DNS – Domain Name System, RFC 1034-5 • Distributed database consisting of a hierarchy of name servers. • Each organization has one or more local or authoritative name servers. • Maps host names to IP addresses.

  10. Electronic Mail • Asynchronous communication model • SMTP based upon TCP.

  11. The World Wide Web • Developed at CERN in late 80s. • Stateless servers. • URLs  identify a host and the path to a resource (file) on that host. • HTTP  Hypertext Transfer Protocol • HTML  Hypertext Markup Language

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