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

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


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.


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



The author is deeply indebted to Professors Harish Parthasarathy and Dr. Tarun Kumar Rawat for offering invaluable comments and suggestions. He is very grateful to Navneet sharama and Varun for their stimulating discussions and invaluable suggestions. The author would like to express special thanks to his wife Archana Singh for her support and understanding right throughout of his research work. The author is also grateful acknowledged to Dr. R. K. Sharma and Prof. Jitender Kumar Pathak for their support and encouraging in Delhi Technical Campus, Greater Noida.


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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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