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  4. Quantum approximate optimization algorithm for qudit systems with long-range interactions
 
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01 April 2022
Paper (Preprint, Research Paper, Review Paper, White Paper, etc.)
Titel

Quantum approximate optimization algorithm for qudit systems with long-range interactions

Titel Supplements
Published on arxiv
Abstract
A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. 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, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudits, layout its implementation in platforms with long-range interactions between qudits such as trapped ions, cold atomic mixtures, Rydberg atoms and atoms in cavities. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle (EV) charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these into 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 max-$k$-graph coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.
Author(s)
Deller, Yannick
Schmitt, Sebastian
Lewenstein, Maciej
Lenk, Steve
Fraunhofer-Institut für Optronik, Systemtechnik und Bildauswertung IOSB
Federer, Marika
Fraunhofer-Institut für Optronik, Systemtechnik und Bildauswertung IOSB
Jendrzejewski, Fred
Hauke, Philipp
Kasper, Valentin
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DOI
10.48550/arXiv.2204.00340
Language
English
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Fraunhofer-Institut für Optronik, Systemtechnik und Bildauswertung IOSB
Tags
  • quant-ph

  • cond-mat.quant-gas

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