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Mika Hirvensalo: On Quantum Computation, Licentiate's Thesis, University of Turku, 1997.

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Copying quantum computer makes NP-complete problems tractable - Hirvensalo   Self-citation (Hirvensalo)   (Correct)

....qubits represent the value j. We also assume that f will respect linear nature of quantum physics, that is, a single call of f on superposition will produce j ji j f(j)i: 11) If, on the other hand, we assume that f is computable in polynomial time, then there is a matrix U (see [7] or [13] that is a product of polynomially many unitary matrices that operate on subspaces of bounded dimension and performs the computation U j ji j 0i =jji j f(j)i: 12) Moreover, U can be efficiently found. Let al..so H = 1 1 1 Gamma1 (13) be the Hadamard transformation and D = B ....

Mika Hirvensalo: On Quantum Computation, Licentiate's Thesis, University of Turku, 1997.


Copying quantum computer makes NP-complete problems tractable - Hirvensalo   Self-citation (Hirvensalo)   (Correct)

.... nature of quantum physics, that is, a single call of f on superposition 1 p 2 n 2 n Gamma1 X j=0 j ji j 0i (10) will produce 1 p 2 n 2 n Gamma1 X j=0 j ji j f(j)i: 11) If, on the other hand, we assume that f is computable in polynomial time, then there is a matrix U (see [7] or [13] that is a product of polynomially many unitary matrices that operate on subspaces of bounded dimension and performs the computation U j ji j 0i =jji j f(j)i: 12) Moreover, U can be efficiently found. Let al..so H = 1 p 2 1 1 1 Gamma1 (13) be the Hadamard transformation and D ....

Mika Hirvensalo: On Quantum Computation, Licentiate's Thesis, University of Turku, 1997.

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