Quantum approximate optimization algorithm for qudit systems

Year: 2023

Authors: Deller Y., Schmitt S., Lewenstein M., Lenk S., Federer M., Jendrzejewski F., Hauke P., Kasper V.

Autors Affiliation: Heidelberg Univ, Kirchhoff Inst Phys, Neuenheimer Feld 227, D-69120 Heidelberg, Germany; Honda Res Inst Europe GmbH, Carl Legien Str 30, D-63073 Offenbach, Germany; Barcelona Inst Sci & Technol, ICFO Inst Ciencies Foton, Ave Carl Friedrich Gauss 3, Barcelona 08860, Spain; ICREA, Passeig Lluis Co 23, Barcelona 08010, Spain; Fraunhofer IOSB, Adv Syst Technol IOSB AST, Vogelherd 90, D-98693 Ilmenau, Germany; Univ Trento, INO CNR BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Trento, Italy.

Abstract: A frequent starting point of quantum computation platforms is the two-state quantum system, i.e., the qubit. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, socalled qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudit systems. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these in a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a maximum-k-graph-coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

Journal/Review: PHYSICAL REVIEW A

Volume: 107 (6)      Pages from: 62410-1  to: 62410-14

More Information: We acknowledge fruitful discussions with R. Blatt, A. Bottarelli, A. Garcia-Sala, D. Gonzalez-Cuadra, M. K. Oberthaler, M. Ringbauer, H. Tuereci, T. V. Zache, and P. Zoller. S.L. acknowledges support from the project Quantum Hub Thueringen, 2021 FGI 0047, Free State of Thuringia, Thueringer Aufbaubank. F.J. acknowledges the DFG support through the project FOR 2724, the Emmy-Noether grant (Project No. 377616843) . This work is supported by the DFGCollaborative Research Centre SFB 1225 (ISOQUANT) , by the Bundesministerium fuer Wirtschaft und Energie through the project EnerQuant (Project No. 03EI1025C) , and by the Bundesministerium fuer Bildung und Forschung through the project HFAK (Project No. 13N15632) . P.H. acknowledges support from Provincia Autonoma di Trento, the ERC starting grant StrEnQTh (Project No. 804305) , the Google Research Scholar Award ProGauge, and Q@TN-Quantum Science and Technology in Trento. V.K. and M.L. acknowledge support from ERC AdG NOQIA; Agencia Estatal de Investigacion (R & D Project No. CEX2019-000910-S, funded by MCIN/AEI/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI, QUANTERA MAQS PCI2019-111828-2, Proyectos de I+D+I Retos Colaboracion QUSPIN RTC2019-007196-7) ; Fundacio Cellex; Fundacio Mir-Puig; Generalitat de Catalunya through the CERCA program, AGAUR Grant No. 2017 SGR 134, QuantumCAT U16-011424, cofunded by ERDF Operational Program of Catalonia 2014-2020; EU Horizon 2020 FET-OPEN OPTOLogic (Grant No. 899794) ; National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314) ; Marie Sklodowska-Curie grant STREDCH No. 101029393; La Caixa Junior Leaders fellowships (No. 100010434) ; and EU Horizon 2020 under Marie Sklodowska-Curie Grant Agreement No. 847648 (LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, and LCF/BQ/PR21/11840013) .
KeyWords: Decoherence
DOI: 10.1103/PhysRevA.107.062410

Citations: 7
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