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arXiv:2112.12160 · PRX Quantum

Logical Blocks for Fault-Tolerant Topological Quantum Computation

Héctor Bombín, Chris Dawson, Ryan V. Mishmash, Naomi Nickerson, Fernando Pastawski, Sam Roberts

Published Apr 7, 2023• 60 citations
arXivHTMLPDF

Abstract

A comprehensive and platform-independent framework for universal fault-tolerant logic is presented, enabling mapping from an abstract description of the logical gate to a precise set of physical instructions.
DOI
10.1103/prxquantum.4.020303

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Abstract This paper presents a physical mapping tool for quantum circuits, which generates the optimal Universal Logic Block (ULB) that can, on average, perform any logical fault-tolerant (FT) quantum operations with the min-imum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations, which in turn determines routing latencies. The proposed flow for the quantum physical mapper captures these dependencies by applying (i) a loose scheduling step, which transforms an initial quantum data flow graph into one that explicitly captures the no-cloning theorem of the quan-tum computing and then performs instruction scheduling based on a modified force-directed scheduling approach to minimize the resource contention and quantum circuit latency, (ii) a placement step, which uses timing-driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force-directed scheduler to correct scheduling levels of quantum operations as needed, and (iii) a routing step that finds dynamic values of routing latencies for the qubits. In addition to the quantum physical mapper, an approach is presented to determine the single best ULB size for a target quantum circuit by examining the latency of different