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1. The quantum-to-classical graph homomorphism game

   https://doi.org/10.1063/5.0072288  

   Brannan, Michael; Ganesan, Priyanga; Harris, Samuel J. (November 2022, Journal of Mathematical Physics)

   Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a “quantum–classical game,” that is, a non-local game of two players involving quantum questions and classical answers. This game generalizes the graph homomorphism game between classical graphs. We show that winning strategies in the various quantum models for the game is an analog of the notion of non-commutative graph homomorphisms due to Stahlke [IEEE Trans. Inf. Theory 62(1), 554–577 (2016)]. Moreover, we present a game algebra in this context that generalizes the game algebra for graph homomorphisms given by Helton et al. [New York J. Math. 25, 328–361 (2019)]. We also demonstrate explicit quantum colorings of all quantum complete graphs, yielding the surprising fact that the algebra of the four coloring game for a quantum graph is always non-trivial, extending a result of Helton et al. [New York J. Math. 25, 328–361 (2019)]. 

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2. Colloquium : Quantum and classical discrete time crystals

   https://doi.org/10.1103/RevModPhys.95.031001  

   Zaletel, Michael P; Lukin, Mikhail; Monroe, Christopher; Nayak, Chetan; Wilczek, Frank; Yao, Norman Y (July 2023, Reviews of Modern Physics)
3. Graph-| Q ⟩⟨ C |: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure

   https://doi.org/10.1021/acs.jpca.3c04261  

   Iyengar, Srinivasan S.; Zhang, Juncheng Harry; Saha, Debadrita; Ricard, Timothy C. (November 2023, The Journal of Physical Chemistry A)
4. Hybrid Quantum-Classical Unit Commitment

   https://doi.org/10.1109/TPEC54980.2022.9750763  

   Mahroo, Reza; Kargarian, Amin (February 2022, 2022 IEEE Texas Power and Energy Conference (TPEC))
5. Hybrid Quantum-Classical Computing Architectures

   Suchara, M.; Alexeev, Y.; Chong, F.; Finkel, H.; Hoffmann, H.; Larson, J.; Osborn, J.; Smith, G. (November 2018, Proceedings of the 3rd International Workshop on Post-Moore's Era Supercomputing)

   —We describe how classical supercomputing can aid unreliable quantum processors of intermediate size to solve large problem instances reliably. We advocate using a hybrid quantum-classical architecture where larger quantum circuits are broken into smaller sub-circuits that are evaluated separately, either using a quantum processor or a quantum simulator running on a classical supercomputer. Circuit compilation techniques that determine which qubits are simulated classically will greatly impact the system performance as well as provide a tradeoff between circuit reliability and runtime. 

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