Quantum Processing Simulation

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Quantum Processing Simulation
Dalibor Hrg
Vienna, June 18, 2004.
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Moores law, classical computers
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Technology and computation
NANOTECHNOLOGY
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(No Transcript)
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Development

• Impact on big mathematical questions (PPSPACE,
  PNP), theoretical research!
• We still dont know if quantum computers are
  stronger than classical computers!
• von Neumann architecture? Quantum memory is
  needed! (in progress)
• Quantum cryptography is demonstrated! (problem
  with error corection codes and speed)
• Quantum teleportation, Quantum communication
  methods (demonstrated, in progress)

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Classical and Quantum computer
State
of classical computer
of quantum computer
bits
qubits
in 2 bits
in 2 qubits
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Classical and Quantum algorithms
Algorithms
EASY
HARD
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Quantum algorithms

• Grovers algorithm (1997.)
• - searching unsorted database of N elements
  in steps
• - on classical computer, steps are
  needed
• - if sorted, there exist classical algorithm
  with steps
• Deutsch-Jozsa problem (1992.)
• - finding global property of some Boolean
  function with N
• variables (function is constant or
  balanced)
• - complexity of quantum algorithm
• - complexity of classical algorithm

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Grovers algorithm
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Deutsch-Jozsa problem
For state
amplitude is
Function constant if
Function balanced if
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QPS Application
All states of register are seen here!
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Characteristics of the QPS

• Windows application, C, .NET Framework 1.1
• Grovers and Deutsch-Jozsa algorithm simulation
  (up to 8 qubits).
• Implementation of the most useful operators (H,
  Pauli X, Pauli Z, Oracle, WH, Grover).
• Easy to use interface (selecting qubits and
  operators)
• For education and further research on
  quantumalgorithms (handy tool).

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Simulation problems?

• Number of qubits N
• Number of states in register
• Needed memory for all states
• Needed memory for Walsh-Hadamard (interference)
  operation

Number of qubits Number of states Memory for all states Memory for Walsh-Hadamard operation
4 16 0.18 KB 2 KB
8 256 4 KB 0.5 MB
12 1024 80 KB 128 MB
16 65536 1.5 MB 32 GB
32 4294967296 160 GB 13.7 10 GB
64 1.84 10 1.23 10 GB 31.2 10 GB
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Conclusion

• Quantum algorithms can be simulated, but
  inefficiantly (memory used and time needed) on
  classical computers.
• Impossibility to implement quantum parallelism is
  a main reason for inefficient simulation ( gt 10
  qubits on classical PC, 256-512 MB RAM).
• QPS is useful in education and research (handy
  tool).