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1. Verified tensor-program optimization via high-level scheduling rewrites

   https://doi.org/10.1145/3498717  

   Liu, Amanda ; Bernstein, Gilbert Louis ; Chlipala, Adam ; Ragan-Kelley, Jonathan ( January 2022 , Proceedings of the ACM on Programming Languages)

   We present a lightweight Coq framework for optimizing tensor kernels written in a pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually for compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within a purely functional language. Our language comprises a set of core constructs for expressing high-level computation detail and a set of what we call reshape operators, which can be derived from core constructs but trigger low-level decisions about storage patterns and ordering. We demonstrate that not only is this system capable of deriving the optimizations ofmore »existing state-of-the-art languages like Halide and generating comparably performant code, it is also able to schedule a family of useful program transformations beyond what is reachable in Halide.« less
2. Optimized Quantum Program Execution Ordering to Mitigate Errors in Simulations of Quantum Systems

   https://doi.org/10.1109/ICRC53822.2021.00013  

   Tomesh, Teague ; Gui, Kaiwen ; Gokhale, Pranav ; Shi, Yunong ; Chong, Frederic T. ; Martonosi, Margaret ; Suchara, Martin ( November 2021 , 2021 International Conference on Rebooting Computing (ICRC))

   Simulating the time evolution of a physical system at quantum mechanical levels of detail - known as Hamiltonian Simulation (HS) - is an important and interesting problem across physics and chemistry. For this task, algorithms that run on quantum computers are known to be exponentially faster than classical algorithms; in fact, this application motivated Feynman to propose the construction of quantum computers. Nonetheless, there are challenges in reaching this performance potential. Prior work has focused on compiling circuits (quantum programs) for HS with the goal of maximizing either accuracy or gate cancellation. Our work proposes a compilation strategy that simultaneouslymore »advances both goals. At a high level, we use classical optimizations such as graph coloring and travelling salesperson to order the execution of quantum programs. Specifically, we group together mutually commuting terms in the Hamiltonian (a matrix characterizing the quantum mechanical system) to improve the accuracy of the simulation. We then rearrange the terms within each group to maximize gate cancellation in the final quantum circuit. These optimizations work together to improve HS performance and result in an average 40% reduction in circuit depth. This work advances the frontier of HS which in turn can advance physical and chemical modeling in both basic and applied sciences.« less
3. Not All SWAPs Have the Same Cost: A Case for Optimization-Aware Qubit Routing

   https://doi.org/10.1109/HPCA53966.2022.00058  

   Liu, Ji ; Li, Peiyi ; Zhou, Huiyang ( April 2022 , 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA))

   Despite rapid advances in quantum computing technologies, the qubit connectivity limitation remains to be a critical challenge. Both near-term NISQ quantum computers and relatively long-term scalable quantum architectures do not offer full connectivity. As a result, quantum circuits may not be directly executed on quantum hardware, and a quantum compiler needs to perform qubit routing to make the circuit compatible with the device layout. During the qubit routing step, the compiler inserts SWAP gates and performs circuit transformations. Given the connectivity topology of the target hardware, there are typically multiple qubit routing candidates. The state-of-the-art compilers use a cost functionmore »to evaluate the number of SWAP gates for different routes and then select the one with the minimum number of SWAP gates. After qubit routing, the quantum compiler performs gate optimizations upon the circuit with the newly inserted SWAP gates. In this paper, we observe that the aforementioned qubit routing is not optimal, and qubit routing should not be independent on subsequent gate optimizations. We find that with the consideration of gate optimizations, not all of the SWAP gates have the same basis-gate cost. These insights lead to the development of our qubit routing algorithm, NASSC (Not All Swaps have the Same Cost). NASSC is the first algorithm that considers the subsequent optimizations during the routing step. Our optimization-aware qubit routing leads to better routing decisions and benefits subsequent optimizations. We also propose a new optimization-aware decomposition for the inserted SWAP gates. Our experiments show that the routing overhead compiled with our routing algorithm is reduced by up to 69.30% (21.30% on average) in the number of CNOT gates and up to 43.50% (7.61% on average) in the circuit depth compared with the state-of-the-art scheme, SABRE.« less
4. Compositional optimizations for CertiCoq

   https://doi.org/10.1145/3473591  

   Paraskevopoulou, Zoe ; Li, John M. ; Appel, Andrew W. ( August 2021 , Proceedings of the ACM on Programming Languages)

   Compositional compiler verification is a difficult problem that focuses on separate compilation of program components with possibly different verified compilers. Logical relations are widely used in proving correctness of program transformations in higher-order languages; however, they do not scale to compositional verification of multi-pass compilers due to their lack of transitivity. The only known technique to apply to compositional verification of multi-pass compilers for higher-order languages is parametric inter-language simulations (PILS), which is however significantly more complicated than traditional proof techniques for compiler correctness. In this paper, we present a novel verification framework for lightweight compositional compiler correctness . Wemore »demonstrate that by imposing the additional restriction that program components are compiled by pipelines that go through the same sequence of intermediate representations , logical relation proofs can be transitively composed in order to derive an end-to-end compositional specification for multi-pass compiler pipelines. Unlike traditional logical-relation frameworks, our framework supports divergence preservation—even when transformations reduce the number of program steps. We achieve this by parameterizing our logical relations with a pair of relational invariants . We apply this technique to verify a multi-pass, optimizing middle-end pipeline for CertiCoq, a compiler from Gallina (Coq’s specification language) to C. The pipeline optimizes and closure-converts an untyped functional intermediate language (ANF or CPS) to a subset of that language without nested functions, which can be easily code-generated to low-level languages. Notably, our pipeline performs more complex closure-allocation optimizations than the state of the art in verified compilation. Using our novel verification framework, we prove an end-to-end theorem for our pipeline that covers both termination and divergence and applies to whole-program and separate compilation, even when different modules are compiled with different optimizations. Our results are mechanized in the Coq proof assistant.« less
5. Automatically Translating Quantum Programs from a Subset of Common Gates to an Adiabatic Representation

   https://doi.org/10.1007/978-3-030-21500-2_9  

   Regan M., Eastwood B. ( May 2019 , nternational Conference on Reversible Computation (RC), Springer LNCS)

   Adiabatic computing with two degrees of freedom of 2-local Hamiltonians has been theoretically shown to be equivalent to the gate model of universal quantum computing. But today’s quantum annealers, namely D-Wave’s 2000Q platform, only provide a 2-local Ising Hamiltonian abstraction with a single degree of freedom. This raises the question what subset of gate programs can be expressed as quadratic unconstrained binary problems (QUBOs) on the D-Wave. The problem is of interest because gate-based quantum platforms are currently limited to 20 qubits while D-Wave provides 2,000 qubits. However, when transforming entire gate circuits into QUBOs, additional qubits will be required.more »The objective of this work is to determine a subset of quantum gates suitable for transformation into single-degree 2-local Ising Hamiltonians under a common qubit base representation such that they comprise a compound circuit suitable for pure quantum computation, i.e., without having to switch between classical and quantum computing for different bases. To this end, this work contributes, for the first time, a fully automated method to translate quantum gate circuits comprised of a subset of common gates expressed as an IBM Qiskit program to single-degree 2-local Ising Hamiltonians, which are subsequently embedded in the D-Wave 2000Q chimera graph. These gate elements are placed in the chimera graph and augmented by constraints that enforce inter-gate logical relationships, resulting in an annealer embedding that completely characterizes the overall gate circuit. Annealer embeddings for several example quantum gate circuits are then evaluated on D-Wave 2000Q hardware.« less