Classical Computer

1
Classical Computer

• Turing Machines
• Churchs Thesis
• Complexity Classes
• Limitations

2
Turing Machines

• Deterministic Turing Machine
• Probabilistic Turing Machine
• Quantum Turing Machine

3
Churchs Thesis

• Any physical computing device (which functions in
  a purely classical manner) can be simulated by a
  Turing machine in a number of steps polynomial in
  the resources used by the computing device

4
Compexity Classes

• P polynomial Time
• NP Nondeterministic Polynomial Time
• NP-complete P NP
• Tractable Can be solved in Polynomial Time or
  Less
• Intractable of Operations GrowsExponentially
  with the Input Size

5
Limitations of Classical Computers

• Classical Physics Breaks Down at Sufficiently
  Small Scales
• At the Current rate, Memory Storage Will Reach
  Atomic Scale Around 2020

6
Quantum Computer

• Quantum Physics
• State Vectors and Dirac Notation
• Superposition and Eigenstates
• Quantum Bit
• Quantum Memory Register
• Power of Quantum Computer

7
Quantum Entanglement

• An entangled system consists of two or more
  quantum objects (atoms, photons, etc.) each of
  which carries information about the other
• A single wavefunction characterizes the state of
  the system and is not a product of wave functions
  for each element of the system
• The entire system cannot be analyzed as separate
  subsystems
• In quantum mechanics there is no reality to the
  separate subsystems or objects
• The entanglement persists no matter how far apart
  the atoms become, as long as the quantum state is
  unchanged

8
Experiments With Entangled States

• Verified non-local quantum mechanical
  correlations in polarization of photons over
  distances up to 10 km
• Verified continuous correlations in components of
  entangled electric fields
• The measurement on one entangled object affects
  the outcome of the measurement on the other
  distant object (no know violation of relativity)
  
• Very small possibility that experimental errors
  are the source of the measured non-locality