Abstract
In this paper, we derive the work and heat for two kinds of quantum bipartite systems: a closed one and an open one according to the scheme suggested in Ref. (Weimer et al. in EPL 83:30008, 2008). Then the results are used to investigate the evolution of the work and heat in a quantum CNOT gate operations. It is shown that the heat and work conversion cannot be performed in the closed quantum CNOT gate operations. However, the open quantum CNOT gate can be used to perform the conversion of heat and work. If at the beginning, a spin with a large energy-level difference has a greater probability of being in a highly excited state than the other, then the CNOT gate will work as a quantum engine, and if it is initially in highly excited states with a smaller probability than the other, the gate will work as a quantum refrigerator.
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References
P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in In Proceedings of 35th Annual Symposium on the Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, 1994), pp. 124–134
L.K. Grover, Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)
D.P. Divincenzo, Two-bit gates are universal for quantum computation. Phys. Rev. A 51(2), 1015–1022 (1995)
A. Brodutch, D.R. Terno, Entanglement, discord and the power of quantum computation. Phys. Rev. A 83(1), 237–241 (2011)
A. Barenco, A universal two-bit gate for quantum computation. Proc. Math. Phys. Sci. 449(1937), 679–683 (1995)
H. Weimer, M.J. Henrich, F. Rempp, H. Schroder, G. Mahler, Local effective dynamics of quantum systems: a generalized approach to work and heat. EPL 83, 30008 (2008)
A. Barenco, C.H. Bennett, R. Cleve, D.P. Divincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, H. Weinfurter, Elementary gates for quantum computation. Phys. Rev. A 52, 5 (1995)
A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.M. Raimond, S. Haroche, Coherent operation of a tunable quantum phase gate in cavity qed. Phys. Rev. Lett. 83(24), 5166–5169 (1999)
A. Imamoglu, D.D. Awschalom, G. Burkard, D.P. Divincenzo, A.R. Small, Quantum information processing using quantum dot spins and cavity qed. Phys. Rev. Lett. 83(20), 4204–4207 (1999)
H.T. Quan, Y.X. Liu, C.P. Sun, F. Nori, Quantum thermodynamic cycles and quantum heat engines. Phys. Rev. E 76, 031105 (2007)
R. Dann, R. Kosloff, P. Salamon, Quantum finite-time thermodynamics: insight from a single qubit engine. Entropy 1255, 09 (2020)
K. Ono, S. Shevchenko, T. Mori, S. Moriyama, F. Nori, Analog of a quantum heat engine using a single-spin qubit. Phys. Rev. Lett. 08, 166802 (2020)
A.O.-C.H. Hossein-Nejad, E.J. O’Reilly, Work, heat and entropy production in bipartite quantum systems. N. J. Phys. 17, 7 (2015)
D. Valente, F. Brito, R. Ferreira, T. Werlang, Work on a quantum dipole by a single-photon pulse. Opt. Lett. 43(11), 2644 (2018)
A.M. Tsirlin, V. Kazakov, A.A. Ahremenkov, N.A. Alimova, Thermodynamic constraints on temperature distribution in a stationary system with heat engine or refrigerator. J. Phys. D Appl. Phys. 39(19), 4269–4277 (2006)
W. Dai, E. Luo, Y. Zhang, H. Ling, Detailed study of a traveling wave thermoacoustic refrigerator driven by a traveling wave thermoacoustic engine. J. Acoust. Soc. Am. 119(5), 2686–2692 (2006)
M. Silaev, T.T. Heikkil, P. Virtanen, Lindblad-equation approach for the full counting statistics of work and heat in driven quantum systems. Phys. Rev. E 90(2), 22103–22103 (2014)
S. Mukamel, Principles of Nonlinear Optical Spectroscopy, vol. 29 (Oxford University Press, New York, 1995)
M.O. Scully, Extracting work from a single thermal bath via quantum negentropy. Phys. Rev. Lett. 87(22), 220601 (2001)
Marian Scully, O., Zubairy, M., Suhail, Agarwal, Girish, S, and Walther and. , Extracting work from a single heat bath via vanishing quantum coherence. Science 299, 862–864 (2003)
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This project was sponsored by the National Natural Science Foundation of China (Grant Nos. 21773131, 12074206) and the K.C. Wong Magna Foundation in Ningbo University.
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Liang, XT., Cheng, J., Zhang, WZ. et al. Work and heat in quantum CNOT gate operations. Eur. Phys. J. D 75, 265 (2021). https://doi.org/10.1140/epjd/s10053-021-00270-w
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DOI: https://doi.org/10.1140/epjd/s10053-021-00270-w