Power operator as witness of the decoherence in the execution of the Toffoli gate in a diamond quantum computer


The diamond quantum computer has been employed successfully for several quantum information protocols. A Hamiltonian (), 3-qubits typical diamond quantum computer is used, consisting of diagonal terms and Rabi pulses that generate the spin flit of the Toffoli gate. From such a Hamiltonian, the respective power operator dH/dt is derived and its average behavior as a function of time is calculated. To solve numerically the Schroedinger equation, it is shown both that the Toffoli gate is not executed and that the power operator is witness of the decoherence of the execution of the Toffoli gate. When the Hamiltonian depends on time, there is exchange of energy of the 3-qubit system with the environment. The latter induces decoherence of the system. It is also concluded that the Rabi pulses technology has limitations.

PDF (Español (España))


Nielsen M. & Chuang I. A. (2000) Quantum Information and Quantum Computation, Cambridge University Press.

Toffoli T. (1980) Technical report, MIT/LCS/TM-15.

De Bakker J. W. & van Leeuwen J., ed. (1980) Reversible computing (PDF). Automata, Languages and Programming, Seventh Colloquium. Noordwijkerhout, Netherlands: Springer Verlag. pp. 632–644. doi:10.1007/3-540-10003-2_104

Barenco A., Bennett C. H., Cleve R., DiVincenzo D. P., Margolus N., Shor P., Sleator T., Smolin J. A. & Weinfurter H. (1995). "Elementary gates for quantum computation". Physical Review A. 52 (5): 3457–3467. doi:10.1103/PhysRevA.52.3457

Shi, Xiao-Feng (2018). "Deutsch, Toffoli, and CNOT Gates via Rydberg Blockade of Neutral Atoms". Physical Review Applied 9 (5): 051001. doi:10.1103/PhysRevApplied.9.051001

Monz T., Kim K., Hänse, W., Riebe M., Villar A. S., Schindler P., Chwalla M., Hennrich M., Blatt R. (2009). "Realization of the Quantum Toffoli Gate with Trapped Ions". Physical Review Letters 102 (4): 040501 doi:10.1103/PhysRevLett.102.040501

Dynes J., Takesue H., Yuan Z., Sharpe A., Harada K., Honjo T., Kamada H., Tadanaga O., Nishida Y., Asobe M. & Shields A. (2009). “Efficient entanglement distribution over 200 kilometers”. Optics Express 17. doi:10.1364/OE.17.011440

Gaebel T., Domhan M., Popa I., Wittmann C., Neumann P., Jelezko F., Rabeau J.R., Stavrias N., Greentree A.D., Prawer S., Meijer J., Twamley J., Hemmer P.R., Wrachtrup J. (2006). “Room-temperature coherent coupling of single spins in diamond”. Nature Physics 2: 408-413, doi: 10.1038/nphys318.

Gurudev M.V., Childress L., Jiang L., Togan E., Maze J., Jelezko F., Zibrov A.S., Hemmer P.R., & Lukin M.D. (2007). “Quantum register based on individual electronic and nuclear spin qubits in diamond»”. Science 316: 1312-1316, doi.org/10.1126/science.1139831.