- Open Access
Phonon-induced frequency shift in semiconductor spin qubits
Phys. Rev. B 114, 045304 – Published 10 July, 2026
DOI: https://doi.org/10.1103/7wp1-zgs7
Abstract
Spin qubits are a promising platform for quantum computation and can operate at temperatures ranging from tens of millikelvin to a few kelvin. Some recent experiments have revealed a nontrivial, often nonmonotonic dependence of the qubit frequency on temperature, including regions of reduced temperature sensitivity. Motivated by these observations, we investigate whether the interaction of a spin qubit with phonons of the host material can contribute to such frequency shifts in the low-temperature regime. While the resulting shifts are too small to quantitatively account for the experimentally observed magnitudes, our analysis reproduces several qualitative features, including nonmonotonic temperature dependencies and sign changes of the frequency shift. More generally, we demonstrate that phonons can induce a temperature-dependent renormalization of the qubit frequency and provide insight into the interaction between spin qubits and their host material. Understanding and quantifying such individual contributions is an important step toward identifying the microscopic mechanisms underlying the experimentally observed temperature dependence of spin-qubit frequencies.
Physics Subject Headings (PhySH)
Article Text
References (45)
- N. P. De Leon, K. M. Itoh, D. Kim, K. K. Mehta, T. E. Northup, H. Paik, B. Palmer, N. Samarth, S. Sangtawesin, and D. W. Steuerman, Materials challenges and opportunities for quantum computing hardware, Science 372, eabb2823 (2021).
- W. Ha, S. D. Ha, M. D. Choi, Y. Tang, A. E. Schmitz, M. P. Levendorf, K. Lee, J. M. Chappell, T. S. Adams, D. R. Hulbert, E. Acuna, R. S. Noah, J. W. Matten, M. P. Jura, J. A. Wright, M. T. Rakher, and M. G. Borselli, A flexible design platform for Si/SiGe exchange-only qubits with low disorder, Nano Lett. 22, 1443 (2022).
- M. Künne, A. Willmes, M. Oberländer, C. Gorjaew, J. D. Teske, H. Bhardwaj, M. Beer, E. Kammerloher, R. Otten, I. Seidler, R. Xue, L. R. Schreiber, and H. Bluhm, The spinbus architecture for scaling spin qubits with electron shuttling, Nat. Commun. 15, 4977 (2024).
- T. Koch, C. Godfrin, V. Adam, J. Ferrero, D. Schroller, N. Glaeser, S. Kubicek, R. Li, R. Loo, S. Massar, G. Simion, D. Wan, K. D. Greve, and W. Wernsdorfer, Industrial wafer processed spin qubits in natural silicon/silicon-germanium, npj Quantum Inf. 11, 59 (2025).
- H. C. George, M. T. Mądzik, E. M. Henry, A. J. Wagner, M. M. Islam, F. Borjans, E. J. Connors, J. Corrigan, M. Curry, M. K. Harper, D. Keith, L. Lampert, F. Luthi, F. A. Mohiyaddin, S. Murcia, R. Nair, R. Nahm, A. Nethwewala, S. Neyens, B. Patra, et al., 12-spin-qubit arrays fabricated on a 300 mm semiconductor manufacturing line, Nano Lett. 25, 793 (2025).
- P. Steinacker, N. Dumoulin Stuyck, W. H. Lim, T. Tanttu, M. Feng, S. Serrano, A. Nickl, M. Candido, J. D. Cifuentes, E. Vahapoglu, S. K. Bartee, F. E. Hudson, K. W. Chan, S. Kubicek, J. Jussot, Y. Canvel, S. Beyne, Y. Shimura, R. Loo, C. Godfrin, et al., Industry-compatible silicon spin-qubit unit cells exceeding 99% fidelity, Nature (London) 646, 81 (2025).
- G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
- A. R. Mills, C. R. Guinn, M. J. Gullans, A. J. Sigillito, M. M. Feldman, E. Nielsen, and J. R. Petta, Two-qubit silicon quantum processor with operation fidelity exceeding 99%, Sci. Adv. 8, eabn5130 (2022).
- A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sammak, G. Scappucci, and S. Tarucha, Fast universal quantum gate above the fault-tolerance threshold in silicon, Nature (London) 601, 338 (2022).
- B. Undseth, O. Pietx-Casas, E. Raymenants, M. Mehmandoost, M. T. Mądzik, S. G. J. Philips, S. L. de Snoo, D. J. Michalak, S. V. Amitonov, L. Tryputen, B. P. Wuetz, V. Fezzi, D. D. Esposti, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Hotter is easier: Unexpected temperature dependence of spin qubit frequencies, Phys. Rev. X 13, 041015 (2023).
- L. C. Camenzind, S. Geyer, A. Fuhrer, R. J. Warburton, D. M. Zumbühl, and A. V. Kuhlmann, A hole spin qubit in a fin field-effect transistor above 4 kelvin, Nat. Electron. 5, 178 (2022).
- J. Y. Huang, R. Y. Su, W. H. Lim, M. Feng, B. van Straaten, B. Severin, W. Gilbert, N. Dumoulin Stuyck, T. Tanttu, S. Serrano, J. D. Cifuentes, I. Hansen, A. E. Seedhouse, E. Vahapoglu, R. C. C. Leon, N. V. Abrosimov, H.-J. Pohl, M. L. W. Thewalt, F. E. Hudson, C. C. Escott, et al., High-fidelity spin qubit operation and algorithmic initialization above 1 , Nature (London) 627, 772 (2024).
- K. Capannelli, B. Undseth, I. Fernández de Fuentes, E. Raymenants, F. K. Unseld, O. Pietx-Casas, S. G. J. Philips, M. T. Mądzik, S. V. Amitonov, L. Tryputen, G. Scappucci, and L. M. K. Vandersypen, Tracking spin qubit frequency variations over 912 days, npj Quantum Inf. 11, 192 (2025).
- S. Freer, S. Simmons, A. Laucht, J. T. Muhonen, J. P. Dehollain, R. Kalra, F. A. Mohiyaddin, F. E. Hudson, K. M. Itoh, J. C. McCallum, D. N. Jamieson, A. S. Dzurak, and A. Morello, A single-atom quantum memory in silicon, Quantum Sci. Technol. 2, 015009 (2017).
- K. Takeda, J. Yoneda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, Y. Hoshi, N. Usami, K. M. Itoh, S. Oda, T. Kodera, and S. Tarucha, Optimized electrical control of a spin qubit in the presence of an induced frequency shift, npj Quantum Inf. 4, 54 (2018).
- N. Hendrickx, D. Franke, A. Sammak, G. Scappucci, and M. Veldhorst, Fast two-qubit logic with holes in germanium, Nature (London) 577, 487 (2020).
- A. M. J. Zwerver, T. Krähenmann, T. F. Watson, L. Lampert, H. C. George, R. Pillarisetty, S. A. Bojarski, P. Amin, S. V. Amitonov, J. M. Boter, R. Caudillo, D. Correas-Serrano, J. P. Dehollain, G. Droulers, E. M. Henry, R. Kotlyar, M. Lodari, F. Lüthi, D. J. Michalak, B. K. Mueller, et al., Qubits made by advanced semiconductor manufacturing, Nat. Electron. 5, 184 (2022).
- S. G. J. Philips, M. T. Mądzik, S. V. Amitonov, S. L. de Snoo, M. Russ, N. Kalhor, C. Volk, W. I. L. Lawrie, D. Brousse, L. Tryputen, B. P. Wuetz, A. Sammak, M. Veldhorst, G. Scappucci, and L. M. K. Vandersypen, Universal control of a six-qubit quantum processor in silicon, Nature (London) 609, 919 (2022).
- R. Savytskyy, T. Botzem, I. F. de Fuentes, B. Joecker, J. J. Pla, F. E. Hudson, K. M. Itoh, A. M. Jakob, B. C. Johnson, D. N. Jamieson, A. S. Dzurak, and A. Morello, An electrically driven single-atom “flip-flop” qubit, Sci. Adv. 9, eadd9408 (2023).
- F. Ye, L. S. Dhami, and J. M. Nichol, Measuring pulse heating in Si quantum dots with individual two-level fluctuators Phys. Rev. Appl. 25, 024045 (2026).
- T. M. Janda, H. M. Yoo, C. Nasseraddin, A. R. Mills, Z. J. Zheng, and J. R. Petta, Microwave response of electrically driven spins in a three-qubit quantum processor, arXiv:2603.08577.
- Y. Choi and R. Joynt, Interacting random-field dipole defect model for heating in semiconductor-based qubit devices, Phys. Rev. Res. 6, 013168 (2024).
- Y. Sato and T. Kawahara, Simulation of temperature-dependent quantum gates in silicon quantum dots with frequency shifts, arXiv:2407.05295.
- A. V. Khaetskii and Y. V. Nazarov, Spin-flip transitions between sublevels in semiconductor quantum dots, Phys. Rev. B 64, 125316 (2001).
- V. N. Golovach, A. Khaetskii, and D. Loss, Phonon-induced decay of the electron spin in quantum dots, Phys. Rev. Lett. 93, 016601 (2004).
- X. Hu, Two-spin dephasing by electron-phonon interaction in semiconductor double quantum dots, Phys. Rev. B 83, 165322 (2011).
- C. Tahan and R. Joynt, Relaxation of excited spin, orbital, and valley qubit states in ideal silicon quantum dots, Phys. Rev. B 89, 075302 (2014).
- J. Li, B. Venitucci, and Y.-M. Niquet, Hole-phonon interactions in quantum dots: Effects of phonon confinement and encapsulation materials on spin-orbit qubits, Phys. Rev. B 102, 075415 (2020).
- A. Hosseinkhani and G. Burkard, Relaxation of single-electron spin qubits in silicon in the presence of interface steps, Phys. Rev. B 104, 085309 (2021).
- M. Brooks, R. Lundgren, and C. Tahan, Phonon-induced exchange gate infidelities in semiconducting Si-SiGe spin qubits, Phys. Rev. B 110, 235204 (2024).
- H. Hasegawa, Spin-lattice relaxation of shallow donor states in and through a direct phonon process, Phys. Rev. 118, 1523 (1960).
- C. Herring and E. Vogt, Transport and deformation-potential theory for many-valley semiconductors with anisotropic scattering, Phys. Rev. 101, 944 (1956).
- M. Friesen and S. N. Coppersmith, Theory of valley-orbit coupling in a Si/SiGe quantum dot, Phys. Rev. B 81, 115324 (2010).
- M. O. Nestoklon, L. E. Golub, and E. L. Ivchenko, Spin and valley-orbit splittings in heterostructures, Phys. Rev. B 73, 235334 (2006).
- J. R. F. Lima and G. Burkard, Interface and electromagnetic effects in the valley splitting of Si quantum dots, Mater. Quantum Technol. 3, 025004 (2023).
- R. Rahman, J. Verduijn, N. Kharche, G. P. Lansbergen, G. Klimeck, L. C. L. Hollenberg, and S. Rogge, Engineered valley-orbit splittings in quantum-confined nanostructures in silicon, Phys. Rev. B 83, 195323 (2011).
- V. N. Golovach, M. Borhani, and D. Loss, Electric-dipole-induced spin resonance in quantum dots, Phys. Rev. B 74, 165319 (2006).
- C. Kittel and P. McEuen, Introduction to Solid State Physics (John Wiley & Sons, Hoboken, NJ, 2005).
- P. Y. Yu and M. Cardona, Fundamentals of Semiconductors: Physics and Materials Properties, Graduate Texts in Physics (Springer Berlin, Heidelberg, 2010).
- The energies of phonons with are , depending on the polarization of the phonon, for nm.
- In our calculations we used . The actual value of should play no role, and we indeed found that our results are independent of the volume, as long as we set , above which numerical artifacts emerge.
- R. Qi, R. Shi, Y. Li, Y. Sun, M. Wu, N. Li, J. Du, K. Liu, C. Chen, J. Chen, F. Wang, D. Yu, E.-G. Wang, and P. Gao, Measuring phonon dispersion at an interface, Nature (London) 599, 399 (2021).
- Z. Cheng, R. Li, X. Yan, G. Jernigan, J. Shi, M. E. Liao, N. J. Hines, C. A. Gadre, J. C. Idrobo, E. Lee, K. D. Hobart, M. S. Goorsky, X. Pan, T. Luo, and S. Graham, Experimental observation of localized interfacial phonon modes, Nat. Commun. 12, 6901 (2021).
- R. Shi, Q. Li, X. Xu, B. Han, R. Zhu, F. Liu, R. Qi, X. Zhang, J. Du, J. Chen, D. Yu, X. Zhu, J. Guo, and P. Gao, Atomic-scale observation of localized phonons at interface, Nat. Commun. 15, 3418 (2024).
- V. Champain, G. Boschetto, H. Niebojewski, B. Bertrand, L. Mauro, M. Bassi, V. Schmitt, X. Jehl, S. Zihlmann, R. Maurand, Y. M. Niquet, C. B. Winkelmann, S. D. Franceschi, B. Martinez, and B. Brun, A heat-resilient hole spin qubit in silicon, arXiv:2509.15823.