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Quantum Processing Simulation

Quantum Processing Simulation. Dalibor Hrg. Vienna, June 18, 2004. Moore’s law, classical computers. Technology and computation. NANOTECHNOLOGY. Development. Impact on big mathematical questions (P=PSPACE, P=NP), theoretical research!

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Quantum Processing Simulation

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  1. Quantum Processing Simulation Dalibor Hrg Vienna, June 18, 2004.

  2. Moore’s law, classical computers

  3. Technology and computation NANOTECHNOLOGY

  4. Development • Impact on big mathematical questions (P=PSPACE, P=NP), theoretical research! • We still don’t 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)

  5. Transformation of states classical computer quantum computer Boolean circuits: Unitary operators: (Quantum circuits) Classical and Quantum computer State of classical computer of quantum computer bits qubits in 2 bits: in 2 qubits:

  6. classical quantum A problem Grover, Shor Deutsch-Jozsa, Simon Pseudo code (C,C++,C#,… ) Mathematicalmodel ? Asembler Machine code Boolean circuits Quantum circuits (?) Classical and Quantum algorithms Algorithms EASY HARD

  7. Quantum algorithms • Grover’s algorithm (1997.) - searching unsorteddatabaseofNelementsin steps - on classical computer, steps are needed - if sorted, there existclassical 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

  8. Grover’s algorithm

  9. Deutsch-Jozsa problem For state amplitude is Function constant if: Function balanced if:

  10. Quantum gates (unitary operators). Act on selected qubits of quantum register. Quantum register.State of a qubit is colored: (blue, state is 0), (red, state is 1), (green, superposition of 0 and 1). QPS Application All states of register are seen here!

  11. Characteristics of the QPS • Windows application, C#, .NET Framework 1.1 • Grover’sand 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).

  12. Simulation problems? Number of qubits: N Number of states in register: Needed memory for all states: Needed memory for Walsh-Hadamard (interference) operation:

  13. 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 ( > 10 qubits onclassical PC, 256-512 MB RAM). • QPS is useful in education and research (handy tool).

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