Abstract
We propose a scheme to realize Controlled-NOT, Controlled-V, Controlled-\(V^{\dag }\) gate based on the indirect coupling of two qubits which are coupled to a common resonator. Based on the state-of-the-art controllability of longitudinal and transverse coupling between a qubit and a resonator, we let the control qubit couple to the resonator longitudinally and the target qubit couple to the resonator transversely. One can get the fidelity of these gates (as well as the synthesized Toffoli gate) over 99% within effective gate timescales. The proposed gate scheme is possible for the experimental setups where the effective qubit–resonator coupling strength is far bigger than the cavity decay rate and the dephasing rate of the qubits and applicable to quantum circuit synthesizing and long-distance qubit interaction.
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References
Benioff, P.: The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J. Stat. Phys. 22(5), 563–591 (1980)
Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6), 467–488 (1982)
Deutsch, D.: Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A Math. Phys. Sci. 400(1818), 97–117 (1985)
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE, pp. 124–134 (1994)
Peng, X., Liao, Z., Xu, N., et al.: Quantum adiabatic algorithm for factorization and its experimental implementation. Phys. Rev. Lett. 101(22), 220405 (2008)
Boneh, D., Lipton, R.J.: Quantum cryptanalysis of hidden linear functions. In: Annual International Cryptology Conference, pp. 424–437. Springer, Berlin (1995)
Biamonte, J., Wittek, P., Pancotti, N., et al.: Quantum machine learning. Nature 549(7671), 195 (2017)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Neill, C., Roushan, P., Kechedzhi, K., et al.: A blueprint for demonstrating quantum supremacy with superconducting qubits. Science 360(6385), 195–199 (2018)
Ballance, C.J., Harty, T.P., Linke, N.M., et al.: High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117(6), 060504 (2016)
Schäfer, V.M., Ballance, C.J., Thirumalai, K., et al.: Fast quantum logic gates with trapped-ion qubits. Nature 555(7694), 75 (2018)
Li, X., Wu, Y., Steel, D., et al.: An all-optical quantum gate in a semiconductor quantum dot. Science 301(5634), 809–811 (2003)
Nichol, J.M., Orona, L.A., Harvey, S.P., et al.: High-fidelity entangling gate for double-quantum-dot spin qubits. npj Quantum Inf. 3(1), 3 (2017)
Petrosyan, D., Motzoi, F., Saffman, M., et al.: High-fidelity Rydberg quantum gate via a two-atom dark state. Phys. Rev. A 96(4), 042306 (2017)
Tiarks, D., Schmidt-Eberle, S., Stolz, T., et al.: A photon-photon quantum gate based on Rydberg interactions. Nat. Phys. 15(2), 124 (2019)
Burkard, G., Shkolnikov, V.O., Awschalom, D.D.: Designing a cavity-mediated quantum CPHASE gate between NV spin qubits in diamond. Phys. Rev. B 95(20), 205420 (2017)
Duan, L.M., Kimble, H.J.: Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92(12), 127902 (2004)
Hacker, B., Welte, S., Rempe, G., et al.: A photon–photon quantum gate based on a single atom in an optical resonator. Nature 536(7615), 193 (2016)
Borregaard, J., Komar, P., Kessler, E.M., et al.: Heralded quantum gates with integrated error detection in optical cavities. Phys. Rev. Lett. 114(11), 110502 (2015)
Borges, H.S., Rossatto, D.Z., Luiz, F.S., et al.: Heralded entangling quantum gate via cavity-assisted photon scattering. Phys. Rev. A 97(1), 013828 (2018)
Lahad, O., Firstenberg, O.: Induced cavities for photonic quantum gates. Phys. Rev. Lett. 119(11), 113601 (2017)
Alqahtani, M.M.: Multiphoton process in cavity QED photons for implementing a three-qubit quantum gate operation. Quantum Inf. Process. 19(1), 12 (2020)
Brecht, T., Pfaff, W., Wang, C., et al.: Multilayer microwave integrated quantum circuits for scalable quantum computing. Npj Quantum Inf. 2, 16002 (2016)
Welte, S., Hacker, B., Daiss, S., et al.: Photon-mediated quantum gate between two neutral atoms in an optical cavity. Phys. Rev. X 8(1), 011018 (2018)
Lekitsch, B., Weidt, S., Fowler, A.G., et al.: Blueprint for a microwave trapped ion quantum computer. Sci. Adv. 3(2), e1601540 (2017)
Chou, K.S., Blumoff, J.Z., Wang, C.S., et al.: Deterministic teleportation of a quantum gate between two logical qubits. Nature 561(7723), 368 (2018)
Wan, Y., Kienzler, D., Erickson, S.D., et al.: Quantum gate teleportation between separated qubits in a trapped-ion processor. Science 364(6443), 875–878 (2019)
Beaudoin, F., Lachance-Quirion, D., Coish, W.A., et al.: Coupling a single electron spin to a microwave resonator: controlling transverse and longitudinal couplings. Nanotechnology 27(46), 464003 (2016)
Richer, S., Maleeva, N., Skacel, S.T., et al.: Inductively shunted transmon qubit with tunable transverse and longitudinal coupling. Phys. Rev. B 96(17), 174520 (2017)
Lambert, N., Cirio, M., Delbecq, M., et al.: Amplified and tunable transverse and longitudinal spin-photon coupling in hybrid circuit-QED. Phys. Rev. B 97(12), 125429 (2018)
Schuetz, M.J.A., Giedke, G., Vandersypen, L.M.K., et al.: High-fidelity hot gates for generic spin-resonator systems. Phys. Rev. A 95(5), 052335 (2017)
Warren, A., Barnes, E., Economou, S.E.: Long-distance entangling gates between quantum dot spins mediated by a superconducting resonator. Phys. Rev. B 100(16), 161303 (2019)
Chen, X.Y., Yin, Z.: Universal quantum gates between nitrogen-vacancy centers in a levitated nanodiamond. Phys. Rev. A 99(2), 022319 (2019)
Maslov, D., Miller, D.M.: Comparison of the cost metrics through investigation of the relation between optimal NCV and optimal NCT three-qubit reversible circuits. IET Comput. Digit. Tech. 1(2), 98–104 (2007)
Maslov, D., Young, C., Miller, D.M., et al.: Quantum circuit simplification using templates. In: Proceedings of the Conference on Design, Automation and Test in Europe, Vol. 2, pp. 1208–1213. IEEE Computer Society (2005)
Tan, Y., Cheng, X., Guan, Z., et al.: Multi-strategy based quantum cost reduction of linear nearest-neighbor quantum circuit. Quantum Inf. Process. 17(3), 61 (2018)
Miller, D.M., Wille, R., Sasanian, Z.: Elementary quantum gate realizations for multiple-control Toffoli gates. In: 2011 41st IEEE International Symposium on Multiple-Valued Logic, pp. 288–293. IEEE (2011)
Frey, T., Leek, P.J., Beck, M., et al.: Dipole coupling of a double quantum dot to a microwave resonator. Phys. Rev. Lett. 108(4), 046807 (2012)
Gullans, M.J., Liu, Y.Y., Stehlik, J., et al.: Phonon-assisted gain in a semiconductor double quantum dot maser. Phys. Rev. Lett. 114(19), 196802 (2015)
Childress, L., Sørensen, A.S., Lukin, M.D.: Mesoscopic cavity quantum electrodynamics with quantum dots. Phys. Rev. A 69(4), 042302 (2004)
Wang, X., Miranowicz, A., Li, H.R., et al.: Multiple-output microwave single-photon source using superconducting circuits with longitudinal and transverse couplings. Phys. Rev. A 94(5), 053858 (2016)
Wang, R., Deacon, R.S., Sun, J., et al.: Gate tunable hole charge qubit formed in a Ge/Si nanowire double quantum dot coupled to microwave photons. Nano Lett. 19, 1052–1060 (2019)
Xu, G., Li, Y., Gao F., et al.: Dipole coupling of a tunable hole double quantum dot in germanium hut wire to a microwave resonator. arXiv:1905.01586 (2019)
Ibberson, D.J., Lundberg, T., Haigh, J.A., et al.: Large dispersive interaction between a CMOS double quantum dot and microwave photons. arXiv:2004.00334 (2020)
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This work is supported by the project of National Natural Science Foundation of China (Grant No. 11775190) and Zhejiang Provincial Natural Science Foundation of China (Grant No. LZ20A040002).
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Li, MC., Chen, AX. Elementary quantum gates between long-distance qubits mediated by a resonator. Quantum Inf Process 19, 365 (2020). https://doi.org/10.1007/s11128-020-02858-4
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DOI: https://doi.org/10.1007/s11128-020-02858-4