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

2. Moore’s law, classical computers

3. Technology and computation
NANOTECHNOLOGY

5. 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)

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

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

8. Quantum algorithms Grover’s 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

9. Grover’s algorithm

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

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

12. Characteristics of the QPS
Windows application, C#, .NET Framework 1.1
Grover’s 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 quantum algorithms (handy tool).

13. Memory for Walsh-Hadamard operation
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
65536
1.5 MB
32 GB 32
160 GB GB 64 GB GB

14. 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 on classical PC, MB RAM).
QPS is useful in education and research (handy tool).