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

  • Kumar Gautam
  • Tarun Kumar Rawat
  • Harish Parthasarathy
  • Navneet Sharma
  • Varun Upadhyaya
Article

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 \(H_\varphi \) of the perturbed system approximately using first-order perturbation theory in the interaction picture. \(H_\varphi \) depends on a modulating signal \(\varphi (t){:}\; 0\le t\le T\) which modulates a known potential V. The generator \(H_\varphi \) of the given gate \(U_\mathrm{g}\) is evaluated using \(H_\mathrm{g}=\iota \log U_g\). The optimal modulating signal \(\varphi (t)\) is chosen so that \(\Vert H_g - H_\varphi \Vert \) 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 \(q^3\). 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.

Keywords

Schrödinger equation Perturbation theory Dyson series Frobenius norm Anharmonic oscillator Controlled unitary gate 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Kumar Gautam
    • 1
  • Tarun Kumar Rawat
    • 2
  • Harish Parthasarathy
    • 2
  • Navneet Sharma
    • 3
  • Varun Upadhyaya
    • 2
  1. 1.Digital Signal Processing LaboratoryElectronics and Communication DivisionGreater NoidaIndia
  2. 2.Digital Signal Processing Laboratory, Room No. 135ECE Division, Netaji Subhas Institute of TechnologyDwarkaIndia
  3. 3.Department of Electronics and Communication Engineering Thapar University PatialaPunjabIndia

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