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1. Hybrid Quantum-Classical Computing Architectures

   Suchara, Martin; Alexeev, Yuri; Chong, Frederic; Finkel, Hal; Hoffmann, Henry; Larson, Jeffrey; Osborn, James; and Smith, Graeme (November 2018, Proceedings of the 3rd International Workshop on Post-Moore Era Supercomputing, 2018.)

   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. 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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2. 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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3. Learning Shallow Quantum Circuits

   https://doi.org/10.1145/3618260.3649722  

   Huang, Hsin-Yuan; Liu, Yunchao; Broughton, Michael; Kim, Isaac; Anshu, Anurag; Landau, Zeph; McClean, Jarrod R (June 2024, ACM)

   Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions that are classically hard to sample from, existing learning algorithms do not apply. In this work, we present a polynomial-time classical algorithm for learning the description of any unknown 𝑛-qubit shallow quantum circuit 𝑈 (with arbitrary unknown architecture) within a small diamond distance using single-qubit measurement data on the output states of 𝑈. We also provide a polynomial-time classical algorithm for learning the description of any unknown 𝑛-qubit state |𝜓⟩ = 𝑈|0^𝑛⟩ prepared by a shallow quantum circuit 𝑈 (on a 2D lattice) within a small trace distance using single-qubit measurements on copies of |𝜓⟩. Our approach uses a quantum circuit representation based on local inversions and a technique to combine these inversions. This circuit representation yields an optimization landscape that can be efficiently navigated and enables efficient learning of quantum circuits that are classically hard to simulate. 

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4. A verified optimizer for Quantum circuits

   https://doi.org/10.1145/3434318  

   Hietala, Kesha; Rand, Robert; Hung, Shih-Han; Wu, Xiaodi; Hicks, Michael (January 2021, Proceedings of the ACM on Programming Languages)

   null (Ed.)

   We present VOQC, the first fully verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a simple quantum intermediate representation, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. SQIR uses a semantics of matrices of complex numbers, which is the standard for quantum computation, but treats matrices symbolically in order to reason about programs that use an arbitrary number of quantum bits. SQIR's careful design and our provided automation make it possible to write and verify a broad range of optimizations in VOQC, including full-circuit transformations from cutting-edge optimizers. 

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5. Constructing Optimal Contraction Trees for Tensor Network Quantum Circuit Simulation

   https://doi.org/10.1109/HPEC55821.2022.9926353  

   Ibrahim, Cameron; Lykov, Danylo; He, Zichang; Alexeev, Yuri; Safro, Ilya (September 2022, 2022 IEEE High Performance Extreme Computing Conference (HPEC))

   One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits. Reproducibility: Our source code and data are available at https://github.com/cameton/HPEC2022_ContractionTrees. 

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