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Complexity of product preparations |
| contact: |
E. Knill |
date: |
31 Jan 2003 |
last progress: |
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solved by: |
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What can be said about the algorithmic complexity of preparing
\ket \psi \ket \psi ... (n times), asymptotically, as a function
of n and the algorithmic complexity of preparing \ket \psi ? Take
\ket \psi to be a state of m qubits. By algorithmc complexity I
mean the number of gates required to prepare the state from
\ket 0 . This depends on the gate set used so the question concerns
asymptotics. For the present purposes, one can take as a
gate set all roations ei\phi\sigmau where \sigmau is a
product of Pauli matrices. The complexity of this gate is |\phi|.
It might be useful to consider a version of this question involving an
approximation parameter also.
It may be possible to clone \ket \psi more efficiently
than to prepare it, given that one knows \ket \psi .
E. K., Gerardo Ortiz, Rolando Somma.
| [] | The literature on optimal cloning is relevant. |
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