Optimizing edge state transfer in a Su-Schrieffer-Heeger chain via hybrid analog-digital strategies (2310.12179v2)
Abstract: The Su-Schrieffer-Heeger (SSH) chain, which serves as a paradigmatic model for comprehending topological phases and their associated edge states, plays an essential role in advancing our understanding of quantum materials and quantum information processing and technology. In this paper, we introduce a hybrid analog-digital protocol designed for the nonadiabatic yet high-fidelity transfer of edge states in an SSH chain, featuring two sublattices, A and B. The core of our approach lies in harnessing the approximate time-dependent counterdiabatic (CD) interaction, derived from adiabatic gauge potentials. However, to enhance transfer fidelity, particularly in long-distance chains, higher-order nested commutators become crucial. To simplify the experimental implementation and navigate computational complexities, we identify the next-to-nearest-neighbor hopping terms between sublattice A sites as dominant CD driving and further optimize them by using variational quantum circuits. Through digital quantum simulation, our protocol showcases the capability to achieve rapid and robust solutions, even in the presence of disorder. This analog-digital transfer protocol, an extension of quantum control methodology, establishes a robust framework for edge-state transfer. Importantly, the optimal CD driving identified can be seamlessly implemented across various quantum registers, highlighting the versatility of our approach.
- R. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467–488 (1982).
- B. Field and T. Simula, Introduction to topological quantum computation with non-abelian anyons, Quantum Science and Technology 3, 045004 (2018).
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, Soliton excitations in polyacetylene, Phys. Rev. B 22, 2099 (1980).
- H. Takayama, Y. R. Lin-Liu, and K. Maki, Continuum model for solitons in polyacetylene, Phys. Rev. B 21, 2388 (1980).
- S. Kivelson and D. E. Heim, Hubbard versus peierls and the su-schrieffer-heeger model of polyacetylene, Phys. Rev. B 26, 4278 (1982).
- H.-C. Chang and H.-C. Hsu, Digital quantum simulation of dynamical topological invariants on near-term quantum computers, Quantum Information Processing 21, 41 (2022).
- J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018).
- P. J. Ollitrault, G. Mazzola, and I. Tavernelli, Nonadiabatic molecular quantum dynamics with quantum computers, Phys. Rev. Lett. 125, 260511 (2020).
- S. Longhi, Topological pumping of edge states via adiabatic passage, Phys. Rev. B 99, 155150 (2019).
- D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27, 6083 (1983).
- J. Zurita, C. E. Creffield, and G. Platero, Fast quantum transfer mediated by topological domain walls, Quantum 7, 1043 (2023).
- D. Sels and A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, Proceedings of the National Academy of Sciences 114, E3909 (2017).
- M. V. Berry, Transitionless quantum driving, Journal of Physics A: Mathematical and Theoretical 42, 365303 (2009).
- Q. Xie, K. Seki, and S. Yunoki, Variational counterdiabatic driving of the hubbard model for ground-state preparation, Phys. Rev. B 106, 155153 (2022).
- Y. Ban, X. Chen, and G. Platero, Fast long-range charge transfer in quantum dot arrays, Nanotechnology 29, 505201 (2018).
- Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023).
- IBM Quantum, https://quantum-computing.ibm.com/ (2023).
- S. V. Romero and J. Santos-Suárez, Paulicomposer: compute tensor products of pauli matrices efficiently, Quantum Information Processing 22, 449 (2023).
- H. F. Trotter, On the product of semi-groups of operators, Proceedings of the American Mathematical Society 10, 545 (1959).
- N. Hatano and M. Suzuki, Finding exponential product formulas of higher orders, in Quantum Annealing and Other Optimization Methods (Springer Berlin Heidelberg, Berlin, Heidelberg, 2005) pp. 37–68.
- J. C. Garcia-Escartin and P. Chamorro-Posada, swap test and hong-ou-mandel effect are equivalent, Phys. Rev. A 87, 052330 (2013).
- E. Knill, G. Ortiz, and R. D. Somma, Optimal quantum measurements of expectation values of observables, Phys. Rev. A 75, 012328 (2007).
- E. Hellinger, Neue begründung der theorie quadratischer formen von unendlichvielen veränderlichen, Journal für die reine und angewandte Mathematik 1909, 210–271 (1909).
- H. Jeffreys, An invariant form for the prior probability in estimation problems, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 186, 453 (1946).
- E. J. Meier, F. A. An, and B. Gadway, Observation of the topological soliton state in the su–schrieffer–heeger model, Nature Communications 7, 13986 (2016).
- J. Polo, J. Mompart, and V. Ahufinger, Geometrically induced complex tunnelings for ultracold atoms carrying orbital angular momentum, Phys. Rev. A 93, 033613 (2016).
- A. Vepsäläinen, S. Danilin, and G. Sorin Paraoanu, Superadiabatic population transfer in a three-level superconducting circuit, Sci. Adv. 5, eaau5999 (2019).
- I. Reshodko, A. Benseny, and T. Busch, Robust boson dispenser: Quantum state preparation in interacting many-particle systems, Phys. Rev. A 96, 023606 (2017).
- S. Kumar, H. Zhang, and Y.-P. Huang, Large-scale ising emulation with four body interaction and all-to-all connections, Communications Physics 3, 108 (2020).
Sponsored by Paperpile, the PDF & BibTeX manager trusted by top AI labs.
Get 30 days freePaper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.