Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Longitudinal (curvature) couplings of an $N$-level qudit to a superconducting resonator at the adiabatic limit and beyond (2312.03118v1)

Published 5 Dec 2023 in cond-mat.mes-hall and quant-ph

Abstract: Understanding how and to what magnitude solid-state qubits couple to metallic wires is crucial to the design of quantum systems such as quantum computers. Here, we investigate the coupling between a multi-level system, or qudit, and a superconducting (SC) resonator's electromagnetic field, focusing on the interaction involving both the transition and diagonal dipole moments of the qudit. Specifically, we explore the effective dynamical (time-dependent) longitudinal coupling that arises when a solid-state qudit is adiabatically modulated at small gate frequencies and amplitudes, in addition to a static dispersive interaction with the SC resonator. For the first time, we derive Hamiltonians describing the longitudinal multi-level interactions in a general dispersive regime, encompassing both dynamical longitudinal and dispersive interactions. These Hamiltonians smoothly transition between their adiabatic values, where the couplings of the n-th level are proportional to the level's energy curvature concerning a qudit gate voltage, and the substantially larger dispersive values, which occur due to a resonant form factor. We provide several examples illustrating the transition from adiabatic to dispersive coupling in different qubit systems, including the charge (1e DQD) qubit, the transmon, the double quantum dot singlet-triplet qubit, and the triple quantum dot exchange-only qubit. In some of these qubits, higher energy levels play a critical role, particularly when their qubit's dipole moment is minimal or zero. For an experimentally relevant scenario involving a spin-charge qubit with magnetic field gradient coupled capacitively to a SC resonator, we showcase the potential of these interactions. They enable close-to-quantum-limited quantum non-demolition (QND) measurements and remote geometric phase gates, demonstrating their practical utility in quantum information processing.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (34)
  1. R. Ruskov and C. Tahan, Quantum-limited measurement of spin qubits via curvature coupling to a cavity (2017), arXiv:1704.05876 .
  2. R. Ruskov and C. Tahan, Quantum-limited measurement of spin qubits via curvature couplings to a cavity, Phys. Rev. B 99, 245306 (2019).
  3. A. J. Kerman, Quantum information processing using quasiclassical electromagnetic interaction between qubits and electrical resonators, New Journal of Physics 15, 123011 (2013).
  4. P. M. Billangeon, J. S. Tsai, and Y. Nakamura, Circuit-QED-based scalable architectures for quantum information processing with superconducting qubits, Phys. Rev. B 91, 094517 (2015).
  5. N. Didier, J. Bourassa, and A. Blais, Fast quantum nondemolition readout by parametric modulation of longitudinal qubit-oscillator interaction, Phys. Rev. Lett. 115, 203601 (2015).
  6. S. Richer and D. P. DiVincenzo, Circuit design implementing longitudinal coupling: A scalable scheme for superconducting qubits, Phys. Rev. B 93, 134501 (2016).
  7. L. Childress, A. S. Sørensen, and M. D. Lukin, Mesoscopic cavity quantum electrodynamics with quantum dots, Phys. Rev. A 69, 042302 (2004).
  8. R. Ruskov and C. Tahan, Modulated longitudinal gates on encoded spin-qubits via curvature couplings to a superconducting cavity, Phys. Rev. B 103, 035301 (2021).
  9. X. Hu, Y.-x. Liu, and F. Nori, Strong coupling of a spin qubit to a superconducting stripline cavity, Phys. Rev. B 86, 035314(R) (2012).
  10. D. F. Walls and G. J. Milburn, Quantum optics (Berlin Heidelberg, DE: Springer-Verlag, 2008).
  11. In an early work [70] a Taylor expansion in light Higgs fields allowed to obtain effective interactions to light hadrons without calculating Feynman diagrams.
  12. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Elsevier Science Ltd., 2003).
  13. E. Magesan and J. M. Gambetta, Effective Hamiltonian models of the cross-resonance gate, Phys. Rev. A 101, 052308 (2020).
  14. A. Groshev, Coulomb blockade of resonant tunneling, Phys. Rev. B 42, 5895 (1990).
  15. D. V. Averin, A. N. Korotkov, and K. K. Likharev, Theory of single electron charging of quantum wells and quantum dots, Phys. Rev. B 44, 6199 (1991).
  16. C. W. J. Beenakker, Theory of Coulomb-blockade oscillations in the conductance of a quantum dot, Phys. Rev. B 44, 1646 (1991).
  17. M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Circuit-QED: How strong can the coupling between a Josephson junction atom and a transmission line resonator be?, Ann. Phys. (Leipzig) 16, 767 (2007).
  18. Similar expansion was provided in Ref. [43].
  19. Y.-P. Shim and C. Tahan, Charge-noise-insensitive gate operations for always-on, exchange-only qubits, Phys. Rev. B 93, 121410(R) (2016).
  20. A. N. Korotkov, Quantum Bayesian approach to circuit QED measurement with moderate bandwidth, Phys. Rev. A 94, 042326 (2016).
  21. E. A. Sete, J. M. Gambetta, and A. N. Korotkov, Purcell effect with microwave drive: Suppression of qubit relaxation rate, Phys. Rev. B 89, 104516 (2014).
  22. M. Russ and G. Burkard, Long distance coupling of resonant exchange qubits, Phys. Rev. B 92, 205412 (2015).
  23. M. Russ, F. Ginzel, and G. Burkard, Coupling of three-spin qubits to their electric environment, Phys. Rev. B 94, 165411 (2016).
  24. V. Srinivasa, J. M. Taylor, and J. R. Petta, Cavity-mediated entanglement of parametrically driven spin qubits via sidebands (2023), arXiv:2307.06067v1 .
  25. C. Rigetti and M. Devoret, Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition, Phys. Rev. B 81, 134507 (2010).
  26. V. Tripathi, M. Khezri, and A. N. Korotkov, Operation and intrinsic error budget of a two-qubit cross-resonance gate, Phys. Rev. A 100, 012301 (2019).
  27. M. H. Devoret, A. Wallraff, and J. M. Martinis, Superconducting qubits: A short review (2004), arXiv:cond-mat/0411174 .
  28. A. B. Zorin, Josephson Charge-Phase Qubit with Radio Frequency Readout: Coupling and Decoherence, Sov. Phys. JETP 98, 1250 (2004).
  29. R. Ruskov and A. N. Korotkov, Quantum feedback control of a solid-state qubit, Phys. Rev. B 66, 041401(R) (2002).
  30. R. Ruskov and A. N. Korotkov, Entanglement of solid-state qubits by measurement, Phys. Rev. B 67, 241305(R) (2003).
  31. G. L. Bir and G. E. Pikus, Symmetry and Strain-induced Effects in Semiconductors (Keter Publishing House, Jerusalem, 1974).
  32. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  33. V. Srinivasa, J. M. Taylor, and C. Tahan, Entangling distant resonant exchange qubits via circuit quantum electrodynamics, Phys. Rev. B 94, 205421 (2016).
  34. R. Ruskov, The Gluonic Mechanism in the Interaction of a Light Higgs boson with Light Hadrons in the Decays: K+→π+⁢H→superscript𝐾superscript𝜋𝐻{K}^{+}\to\pi^{+}\,{H}italic_K start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT → italic_π start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_H, η′→η⁢H→superscript𝜂′𝜂𝐻\eta^{\prime}\to\eta\,{H}italic_η start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT → italic_η italic_H, Physics Letters B 187, 165 (1987).
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets