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Realistic Cost to Execute Practical Quantum Circuits using Direct Clifford+T Lattice Surgery Compilation

Tyler LeBlondChristopher DeanGeorge WatkinsRyan S. Bennink
Nov 2023
In this article, we report the development of a resource estimation pipeline that explicitly compiles quantum circuits expressed using the Clifford+T gate set into a lower level instruction set made out of fault-tolerant operations on the surface code. 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, we build upon the open-source Lattice Surgery Compiler, which is extensible to different surface code compilation strategies within the lattice surgery paradigm. 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. In the second stage, parallelism in the logical circuit is translated into parallelism within the fault-tolerant layer while avoiding resource contention, which allows the compiler to find a realistic number of logical time-steps to execute the circuit. The revised compiler also improves the handling of magic states by allowing users to specify dedicated hardware tiles at which magic states are replenished according to a user-specified rate, which allows resource costs from the logical computation to be considered independently from magic state distillation and storage. We demonstrate the applicability of our resource estimation pipeline to large, practical quantum circuits by providing resource estimates for the ground state estimation of molecules. We find that, unless carefully considered, the resource costs of magic state storage can dominate in real circuits which have variable magic state consumption rates.
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