|
|
| Line 21: |
Line 21: |
|
| |
|
| ==Pseudo Code== | | ==Pseudo Code== |
| '''Input:''' j qubits where <math>R_{j}</math> are ancillary and internal states of the QCM.
| |
|
| |
| <u>'''Stage 1'''</u> State preparation
| |
| #Prepare N initial states: <math>|\psi\rangle^{\otimes N}</math> and <math>M - N</math> blank states: <math>|0\rangle^{\otimes M - N}</math>
| |
| <u>'''Stage 2'''</u> Unitary transformation
| |
| # Perform the following unitary transformation on input state <math>|N\psi\rangle = |\psi\rangle^{\otimes N} |0\rangle^{\otimes M - N} |R\rangle</math>
| |
| <math>U_{N,M} |N\psi\rangle = \sum_{j=0}^{M-N} \alpha_{j} |(M - j)\psi, j\psi^{\perp}\rangle \otimes R_{j}(\psi)</math></br>
| |
| where <math>\alpha_{j} = \sqrt{\frac{N + 1}{M + 1}} \sqrt{\frac{(M - N)!(M - j)!}{(M - N - j)! M!}}</math></br>
| |
| <u>'''Stage 3:'''</u> Trace out the QCM state
| |
| #Trace out the state of the QCM in <math>R_{j}</math> states.
| |
|
| |
|
| ==Further Information== | | ==Further Information== |