Papers
2024
- publicationRealistic Cost to Execute Practical Quantum Circuits using Direct Clifford+T Lattice Surgery CompilationTyler LeBlond, Christopher Dean, George Watkins, and Ryan BenninkACM Transactions on Quantum Computing, Oct 2024
We report a resource estimation pipeline that explicitly compiles quantum circuits expressed using the Clifford+T gate set into a surface code lattice surgery instruction set. The cadence of magic state requests from the compiled circuit enables the optimization of magic state distillation and storage requirements in a post-hoc analysis. To compile logical circuits into lattice surgery operations, we build upon the open-source Lattice Surgery Compiler. The revised compiler operates in two stages: the first translates logical gates into an abstract, layout-independent instruction set; the second compiles these into local lattice surgery instructions that are allocated to hardware tiles according to a specified resource layout. The second stage retains logical parallelism while avoiding resource contention in the fault-tolerant layer, aiding realism. Additionally, users can specify dedicated tiles at which magic states are replenished, enabling resource costs from the logical computation to be considered independently from magic state distillation and storage. We demonstrate the applicability of our pipeline to large practical quantum circuits by providing resource estimates for the ground state estimation of molecules. We find that variable magic state consumption rates in real circuits can cause the resource costs of magic state storage to dominate unless production is varied to suit.
@article{Leblond-2024-Realistic-Cost-to-Execute, address = {New York, NY, USA}, articleno = {25}, author = {LeBlond, Tyler and Dean, Christopher and Watkins, George and Bennink, Ryan}, doi = {10.1145/3689826}, issue_date = {December 2024}, journal = {ACM Transactions on Quantum Computing}, keywords = {Lattice Surgery Compilation, Surface Code Lattice Surgery, Quantum Resource Estimation, Magic State Management}, month = oct, number = {4}, numpages = {28}, publisher = {Association for Computing Machinery}, title = {Realistic Cost to Execute Practical Quantum Circuits using Direct Clifford+T Lattice Surgery Compilation}, url = {https://doi.org/10.1145/3689826}, volume = {5}, year = {2024}, } - publicationComputads for weak ω-categories as an inductive typeAdvances in Mathematics, Jul 2024
We give a new description of computads for weak globular ω-categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads, and allows a new definition of ω-category that avoids the technology of globular operads. Our framework permits direct proofs of important results via structural induction, and we use this to give new proofs that every ω-category is equivalent to a free one, and that the category of computads with generator-preserving maps is a presheaf topos, giving a direct description of the index category. We prove that our resulting definition of ω-category agrees with that of Batanin and Leinster and that the induced notion of cofibrant replacement for ω-categories coincides with that of Garner.
@article{Dean-2024-Computads-for-weak-o-categories, author = {Dean, Christopher J. and Finster, Eric and Markakis, Ioannis and Reutter, David and Vicary, Jamie}, doi = {https://doi.org/10.1016/j.aim.2024.109739}, issn = {0001-8708}, journal = {Advances in Mathematics}, keywords = {Higher categories, Computads, Inductive types}, month = jul, pages = {109739}, title = {Computads for weak $\omega$-categories as an inductive type}, url = {https://www.sciencedirect.com/science/article/pii/S0001870824002548}, volume = {450}, year = {2024}, }
2022
- thesisGlobular Multicategories with Homomorphism TypesChristopher J. DeanUniversity of Oxford, Oct 2022
We introduce various notions of globular multicategory with homomorphism types. We develop a higher dimensional modules construction that constructs globular multicategories with strict homomorphism types. We illustrate how this construction is related to iterated enrichment. We show how various collections of “higher category-like” objects give rise to globular multicategories with homomorphism types. We show how these structures suggest a new globular approach to the semantics of (directed) homotopy type theory.
@phdthesis{Dean-2022-Thesis, author = {Dean, Christopher J.}, keywords = {Category Theory (math.CT)}, month = oct, school = {University of Oxford}, title = {Globular Multicategories with Homomorphism Types}, year = {2022} }