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Fault-tolerant quantum computation with color codes

Jonas Anderson, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. Concatenated coding is a well-studied route to fault-tolerant quantum computation, but suffers from low accuracy thresholds (on the order of one part in 10,000) or high resource overheads (millions of physical qubits per logical qubit to achieve thresholds on the order of one percent). Kitaev's surface codes offer a new route to fault tolerance with more modest overheads and thresholds approaching 1%. The recently discovered color codes share many properties with surface codes, such as the ability to perform syndrome extraction locally in two dimensions. Some families of color codes admit a transversal implementation of the entire Clifford group. It is expected that color codes have a threshold near that of the surface codes, however the precise value of this threshold is not currently known. In this poster we investigate a particular class of planar color codes on the 4.8.8 lattice known as triangular codes. We develop a fault-tolerant error-correction strategy for these codes in which repeated syndrome measurements on this lattice generate a three-dimensional space-time combinatorial structure. We then develop an integer program (IP) that analyzes this structure and determines the most likely set of errors consistent with the observed syndrome values. We have implemented this IP for simulated noise on small versions of these triangular codes; our goal is to obtain an estimate on the threshold for fault-tolerant quantum memory with the 4.8.8 triangular color codes. Because the threshold for magic state distillation is likely to be higher than this value and because logical CNOT gates can be performed by code deformation in a single block instead of between pairs of blocks, the threshold for fault-tolerant quantum memory for these codes is also the threshold for fault-tolerant quantum computation with them.