Symmetry-enhanced counterdiabatic quantum algorithm for qudits

Year: 2025

Authors: Bottarelli A., de Andoin MG., Chandarana P., Paul K., Chen X., Sanz M., Hauke P.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR, INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Trento Inst Fundamental Phys & Applicat, INFN TIFPA, Trento, Italy; Basque Res & Technol Alliance BRTA, TECNALIA, Derio 48160, Spain; Univ Basque Country UPV EHU, Dept Phys Chem, Leioa 48940, Spain; Univ Basque Country UPV EHU, EHU Quantum Ctr, Leioa 48940, Spain; Kipu Quantum, Greifswalderstr 226, D-10405 Berlin, Germany; CSIC, Inst Ciencia Mat Madrid, E-28049 Madrid, Spain; Basque Fdn Sci, IKERBASQUE, Bilbao 48009, Spain; Basque Ctr Appl Math BCAM, Bilbao 48009, Spain.

Abstract: Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. Here, we introduce a symmetry-based enhancement to digitized counterdiabatic quantum algorithms, applicable for qudits of any dimension. This approach offers three types of compression compared to conventional variational circuits. First, compression in the circuit depth is achieved by counterdiabatic protocols. Second, information about the problem is compressed by replacing qubits with qudits, allowing for a more efficient representation of the problem. Finally, the number of parameters is reduced by employing the symmetries of the system. We illustrate this approach by tackling a graph-based optimization problem MAX-3-CUT, a highly entangled state preparation, the qutrit W state, and a two-body only antiferromagnetic Ising problem. As our numerical results show, we achieve a better convergence with a lower circuit depth and less measurement overhead, albeit with some identified limitations for which we propose a work-around. This work leads to a better design of shallow variational quantum circuits, improving the feasibility of their implementation on near-term qudit devices.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 7 (4)      Pages from: 43030-1  to: 43030-14

More Information: We thank Julian Ferreiro for insights about counter-diabatic driving and expressivity of the counterdiabatic terms. A.B. acknowledges funding from the Honda Research Institute Europe. P.H. acknowledges funding by the European Union under Horizon Europe Programme, Grant Agreement No. 101080086-NeQST. This project has received funding from the Italian Ministry of University and Research (MUR) through the FARE grant for the project DAVNE (Grant No. R20PEX7Y3A) , was supported by the Provincia Autonoma di Trento, and Q@TN, the joint laboratory between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR-National Research Council. Project funded under the National Recovery and Resilience Plan (NRRP) , Mission 4 Component 2 Investment 1.4-call for Tender No. 1031 of 17/06/2022 of Italian Ministry for University and Research funded by the European Union-NextGenerationEU (Project No. CN_00000013) . Project DYNAMITE QUANTERA2_-00056 WAS funded by the Ministry of University and Research through the ERANET COFUND QuantERA II-2021 call and cofunded by the European Union (H2020, Grant Agreement No. 101017733) . M.G.d.A., P.C., K.P., and M.S. acknowledge funding from OpenSuperQ+100 (Grant No. 101113946) of the EU Flagship on Quantum Technologies, EU FET-Open project EPIQUS (Grant No. 899368) , Spanish Ramon y Cajal Grant No. RYC-2020-030503-I funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe and ERDF Invest in your Future, Spanish Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call-Quantum Spain, EU through the Recovery, Transformation and Resilience Plan-NextGenerationEU within the framework of the Digital Spain 2026 Agenda, Basque Government through Grant No. IT1470-22, and IKUR Strategy under the collaboration agreement between Ikerbasque Foundation and BCAM on behalf of the Department of Education of the Basque Government. M.G.d.A. acknowledges support from the UPV/EHU and TECNA-LIA 2021 PIF contract call, from the Basque Government through the Plan complementario de comunicacion cuantica (EXP.2022/01341) (A/20220551) , from the Basque Government through the ELKARTEK program, project KUBIT-Kuantikaren Berrikuntzarako Ikasketa Teknologikoa (KK-2024/00105) , and from the Spanish Ministry of Science and Innovation under the Recovery, Transformation and Resilience Plan (CUCO, MIG-20211005) , Spanish CDTI through Plan complementario Comunicacion cuantica (EXP. 2022/01341) (A/20220551) . Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Commission, the European Union, or of the Ministry of University and Research. Neither the European Union nor the granting authority can be held responsible for them.
KeyWords: Computational Advantage; Optimization; Approximation; Models
DOI: 10.1103/6ldg-3w1f