Virtual mitigation of coherent non-adiabatic transitions by echo verification

Benjamin F. Schiffer1, Dyon van Vreumingen2,3, Jordi Tura4, and Stefano Polla4,5

1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
2Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
3QuSoft, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands
4Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
5Google Quantum AI, 80636 München, Germany

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Transitions out of the ground space limit the performance of quantum adiabatic algorithms, while hardware imperfections impose stringent limitations on the circuit depth. We propose an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. Quasi-adiabatically evolving forward and backward allows for an echo-verified measurement of any observable. In addition to mitigating hardware noise, our method uses positive-time dynamics only. Crucially, the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement.

The adiabatic algorithm is a powerful state preparation technique in quantum computation, and one of the few algorithms successfully implemented on devices with up to hundreds of qubits. However, its performance is limited by non-adiabatic transitions, which arise due to a limited circuit depth. Our work addresses this challenge by adapting error mitigation techniques to the adiabatic algorithm. We introduce an Adiabatic Echo Verification (AEV) scheme, demonstrating up to a quadratic suppression of errors caused by non-adiabatic transitions while also mitigating hardware noise. Notably, our protocol requires the simulation of Hamiltonian evolution for positive times only, making it appealing for analog quantum simulators.

► BibTeX data

► References

[1] R. Barends, A. Shabani, L. Lamata, J. Kelly, A. Mezzacapo, U. Las Heras, R. Babbush, A. G. Fowler, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, and E. Lucero, ``Digitized adiabatic quantum computing with a superconducting circuit'' Nature 534, 222-226 (2016).

[2] S. Ebadi, A. Keesling, M. Cain, T. T. Wang, H. Levine, D. Bluvstein, G. Semeghini, A. Omran, J.-G. Liu, R. Samajdar, X.-Z. Luo, B. Nash, X. Gao, B. Barak, and E. Farhi, ``Quantum optimization of maximum independent set using Rydberg atom arrays'' Science 376, 1209–1215 (2022).

[3] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien, ``Quantum error mitigation'' Reviews of Modern Physics 95, 045005 (2023).

[4] T. E. O’Brien, G. Anselmetti, F. Gkritsis, V. E. Elfving, S. Polla, W. J. Huggins, O. Oumarou, K. Kechedzhi, D. Abanin, R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, K. Anderson, and M. Ansmann, ``Purification-based quantum error mitigation of pair-correlated electron simulations'' Nature Physics 19, 1787–1792 (2023).

[5] Youngseok Kim, Andrew Eddins, Sajant Anand, Ken Xuan Wei, Ewout van den Berg, Sami Rosenblatt, Hasan Nayfeh, Yantao Wu, Michael Zaletel, Kristan Temme, and Abhinav Kandala, ``Evidence for the utility of quantum computing before fault tolerance'' Nature 618, 500–505 (2023).

[6] Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev, ``Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation'' SIAM Journal on Computing 37, 166–194 (2007).

[7] Albert Messiah ``Quantum mechanics: Volume II'' North-Holland Publishing Company Amsterdam (1962).

[8] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser, ``Quantum Computation by Adiabatic Evolution'' (2000).

[9] Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler, ``Bounds for the adiabatic approximation with applications to quantum computation'' Journal of Mathematical Physics 48, 102111 (2007).

[10] M. H. S. Amin ``Consistency of the Adiabatic Theorem'' Physical Review Letters 102, 220401 (2009).

[11] Nathan Wiebeand Nathan S. Babcock ``Improved error-scaling for adiabatic quantum evolutions'' New Journal of Physics 14, 013024 (2012).

[12] Christian Grossand Immanuel Bloch ``Quantum simulations with ultracold atoms in optical lattices'' Science 357, 995–1001 (2017).

[13] Pascal Scholl, Michael Schuler, Hannah J. Williams, Alexander A. Eberharter, Daniel Barredo, Kai-Niklas Schymik, Vincent Lienhard, Louis-Paul Henry, Thomas C. Lang, Thierry Lahaye, Andreas M. Läuchli, and Antoine Browaeys, ``Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms'' Nature 595, 233–238 (2021).

[14] Dolev Bluvstein, Harry Levine, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Marcin Kalinowski, Alexander Keesling, Nishad Maskara, Hannes Pichler, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin, ``A quantum processor based on coherent transport of entangled atom arrays'' Nature 604, 451–456 (2022).

[15] Andrew D. King, Jack Raymond, Trevor Lanting, Richard Harris, Alex Zucca, Fabio Altomare, Andrew J. Berkley, Kelly Boothby, Sara Ejtemaee, Colin Enderud, Emile Hoskinson, Shuiyuan Huang, Eric Ladizinsky, Allison J. R. MacDonald, and Gaelen Marsden, ``Quantum critical dynamics in a 5,000-qubit programmable spin glass'' Nature 617, 61–66 (2023).

[16] William J. Huggins, Sam McArdle, Thomas E. O'Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, and Jarrod R. McClean, ``Virtual Distillation for Quantum Error Mitigation'' Physical Review X 11, 041036 (2021).

[17] Bálint Koczor ``Exponential Error Suppression for Near-Term Quantum Devices'' Physical Review X 11, 031057 (2021).

[18] Zhenyu Cai ``Resource-efficient Purification-based Quantum Error Mitigation'' (2021).

[19] Mingxia Huoand Ying Li ``Dual-state purification for practical quantum error mitigation'' Physical Review A 105, 022427 (2022).

[20] Thomas E. O’Brien, Stefano Polla, Nicholas C. Rubin, William J. Huggins, Sam McArdle, Sergio Boixo, Jarrod R. McClean, and Ryan Babbush, ``Error Mitigation via Verified Phase Estimation'' PRX Quantum 2, 020317 (2021).

[21] Kevin C. Young, Mohan Sarovar, and Robin Blume-Kohout, ``Error Suppression and Error Correction in Adiabatic Quantum Computation: Techniques and Challenges'' Physical Review X 3, 041013 (2013).

[22] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, ``Faster Digital Quantum Simulation by Symmetry Protection'' PRX Quantum 2, 010323 (2021).

[23] Sergio Boixo, Emanuel Knill, and Rolando Somma, ``Eigenpath traversal by phase randomization'' Quantum Info. Comput. 9, 833–855 (2009).

[24] M. Bornand V. Fock ``Beweis des Adiabatensatzes'' Zeitschrift für Physik 51, 165–180 (1928).

[25] Steven G. Johnson ``Saddle-point integration of $C_\infty$ "bump" functions'' (2015).

[26] Subir Sachdev ``Quantum phase transitions'' (1999).

[27] A. T. Rezakhani, A. K. Pimachev, and D. A. Lidar, ``Accuracy versus run time in an adiabatic quantum search'' Physical Review A 82, 052305 (2010).

[28] Stefano Polla ``StefanoPolla/​Adiabatic-Mitigation: V1.0'' Zenodo (2024).

[29] Simon J. Evered, Dolev Bluvstein, Marcin Kalinowski, Sepehr Ebadi, Tom Manovitz, Hengyun Zhou, Sophie H. Li, Alexandra A. Geim, Tout T. Wang, Nishad Maskara, Harry Levine, Giulia Semeghini, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin, ``High-fidelity parallel entangling gates on a neutral-atom quantum computer'' Nature 622, 268–272 (2023).

[30] Jeremie Rolandand Nicolas J. Cerf ``Quantum Search by Local Adiabatic Evolution'' Physical Review A 65, 042308 (2002).

[31] Benjamin F. Schiffer, Jordi Tura, and J. Ignacio Cirac, ``Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm'' PRX Quantum 3, 020347 (2022).

[32] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, ``Variational quantum algorithms'' Nature Reviews Physics 3, 625–644 (2021).

[33] Yilun Yang, Arthur Christianen, Sandra Coll-Vinent, Vadim Smelyanskiy, Mari Carmen Bañuls, Thomas E. O’Brien, Dominik S. Wild, and J. Ignacio Cirac, ``Simulating Prethermalization Using Near-Term Quantum Computers'' PRX Quantum 4, 030320 (2023).

[34] Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandrà, Jeffrey Marshall, Charles Neill, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Rami Barends, Joao Basso, Andreas Bengtsson, and Sergio Boixo, ``Information scrambling in quantum circuits'' Science 374, 1479–1483 (2021).

[35] Yuta Shingu, Tetsuro Nikuni, Shiro Kawabata, and Yuichiro Matsuzaki, ``Quantum annealing with error mitigation'' Physical Review A 109, 042606 (2024).

[36] Stefano Polla, Gian-Luca R. Anselmetti, and Thomas E. O'Brien, ``Optimizing the information extracted by a single qubit measurement'' Physical Review A 108, 012403 (2023).

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2024-05-26 13:23:05). On SAO/NASA ADS no data on citing works was found (last attempt 2024-05-26 13:23:06).