File:The effect of unitary transforms on registers with pairwise entangled qubits.png
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![File:The effect of unitary transforms on registers with pairwise entangled qubits.png](https://upload.wikimedia.org/wikipedia/commons/thumb/8/85/The_effect_of_unitary_transforms_on_registers_with_pairwise_entangled_qubits.png/800px-The_effect_of_unitary_transforms_on_registers_with_pairwise_entangled_qubits.png?20200901165701)
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[edit]DescriptionThe effect of unitary transforms on registers with pairwise entangled qubits.png |
English: This picture shows the effect of applying a unitary transform (F) on a quantum register A that is in a superposition and that have each one of its qubits pairwise entangled with with a second register B. In particular, it shows the effect of inversion of the transform. |
Date | |
Source | This picture was created by qcircuit, a LaTeX package for making quantum circuit diagrams |
Author | Omnissiahs hierophant |
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% This is the source code of the picture, and can be put in a .tex-file, and compiled by e.g. pdflatex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass{amsart} \usepackage[matrix,frame,arrow]{xypic} \usepackage[braket]{qcircuit} \vfuzz2pt % Don't report over-full v-boxes if over-edge is small %%% ---------------------------------------------------------------------- \begin{document} \[ \Qcircuit @C=0.5em @R=.5em { \lstick{\ket{0}} & \qw & \gate{H} & \ctrl{3} & \qw & \qw & \multigate{2}{F} & \qw & \\ \lstick{\ket{0}} & \qw & \gate{H} & \qw & \ctrl{3} & \qw & \ghost{F} & \qw & \rstick{\Bigg\}A = F\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F|B\rangle} \\ \lstick{\ket{0}} & \qw & \gate{H} & \qw & \qw & \ctrl{3} & \ghost{F} & \qw & \\ \lstick{\ket{0}} & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \\ \lstick{\ket{0}} & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \rstick{\Bigg\}B = \frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F^{\dagger}|A\rangle} \\ \lstick{\ket{0}} & \qw & \qw & \qw & \qw & \targ & \qw & \qw & }\] The equivalences are the same \[ \Qcircuit @C=0.5em @R=.5em { \lstick{\ket{0}} & \qw & \gate{H} & \ctrl{3} & \qw & \qw & \qw & \qw & \\ \lstick{\ket{0}} & \qw & \gate{H} & \qw & \ctrl{3} & \qw & \qw & \qw & \rstick{\Bigg\}A = \frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F^{\dagger\dagger}|B\rangle = F|B\rangle} \\ \lstick{\ket{0}} & \qw & \gate{H} & \qw & \qw & \ctrl{3} & \qw & \qw & \\ \lstick{\ket{0}} & \qw & \qw & \targ & \qw & \qw & \multigate{2}{F^\dag} & \qw & \\ \lstick{\ket{0}} & \qw & \qw & \qw & \targ & \qw & \ghost{F^\dag} & \qw & \rstick{\Bigg\}B = F^{\dagger}\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F^{\dagger}|A\rangle} \\ \lstick{\ket{0}} & \qw & \qw & \qw & \qw & \targ & \ghost{F^\dag} & \qw & }\] \end{document} %
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 16:57, 1 September 2020 | ![]() | 1,050 × 732 (91 KB) | Omnissiahs hierophant (talk | contribs) | Fix: Previous image was generated with the old LaTeX code, that had errors. |
16:45, 1 September 2020 | ![]() | 927 × 723 (90 KB) | Omnissiahs hierophant (talk | contribs) | Index variable "i" changed to "k", to avoid confusion with the imaginary unit. Also updated the text to be more clear about what is meant | |
16:47, 22 December 2019 | ![]() | 573 × 419 (45 KB) | Omnissiahs hierophant (talk | contribs) | Correction of the formulas | |
14:42, 22 December 2019 | ![]() | 524 × 408 (45 KB) | Omnissiahs hierophant (talk | contribs) | Uploading a self-made file using File Upload Wizard |
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File change date and time | 16:53, 1 September 2020 |