Realization of the three-qubit quantum controlled gate based on matching Hermitian generators View Full Text


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Article Info

DATE

2017-03-15

AUTHORS

Kumar Gautam, Tarun Kumar Rawat, Harish Parthasarathy, Navneet Sharma, Varun Upadhyaya

ABSTRACT

This paper deals with the design of quantum unitary gate by matching the Hermitian generators. A given complicated quantum controlled gate is approximated by perturbing a simple quantum system with a small time-varying potential. The basic idea is to evaluate the generator Hφ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\varphi $$\end{document} of the perturbed system approximately using first-order perturbation theory in the interaction picture. Hφ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\varphi $$\end{document} depends on a modulating signal φ(t):0≤t≤T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi (t){:}\; 0\le t\le T$$\end{document} which modulates a known potential V. The generator Hφ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\varphi $$\end{document} of the given gate Ug\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_\mathrm{g}$$\end{document} is evaluated using Hg=ιlogUg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\mathrm{g}=\iota \log U_g$$\end{document}. The optimal modulating signal φ(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi (t)$$\end{document} is chosen so that ‖Hg-Hφ‖\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert H_g - H_\varphi \Vert $$\end{document} is a minimum. The simple quantum system chosen for our simulation is harmonic oscillator with charge perturbed by an electric field that is a constant in space but time varying and is controlled externally. This is used to approximate the controlled unitary gate obtained by perturbing the oscillator with an anharmonic term proportional to q3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q^3$$\end{document}. Simulations results show significantly small noise-to-signal ratio. Finally, we discuss how the proposed method is particularly suitable for designing some commonly used unitary gates. Another example was chosen to illustrate this method of gate design is the ion-trap model. More... »

PAGES

113

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11128-017-1564-4

DOI

http://dx.doi.org/10.1007/s11128-017-1564-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1084029758


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39 idea
40 interaction picture
41 ion-trapping model
42 method
43 minimum
44 model
45 modulating signal
46 noise
47 oscillator
48 paper
49 perturbation theory
50 perturbed system
51 picture
52 potential
53 potential V.
54 quantum
55 quantum systems
56 ratio
57 realization
58 results
59 signal ratio
60 signals
61 simple quantum systems
62 simulation results
63 simulations
64 small noise
65 space
66 system
67 terms
68 theory
69 time
70 time-varying potential
71 unitary gates
72 v.
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