Fault-tolerant one-bit addition with the smallest interesting color code
Yang Wang (TU Delft - QCD/Terhal Group, University of Stuttgart, TU Delft - QuTech Advanced Research Centre)
Selwyn Simsek (Quantinuum Terrington House)
Thomas M. Gatterman (Quantinuum)
Justin A. Gerber (Quantinuum)
Kevin Gilmore (Quantinuum)
Dan Gresh (Quantinuum)
Nathan Hewitt (Quantinuum)
Chandler V. Horst (Quantinuum)
Ben Criger (Quantinuum Terrington House, IGDORE Institute)
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Abstract
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are necessary to define a universal gate set. As a result, implementations of these operations must use either error-correcting codes with more complicated error correction procedures or gate teleportation and magic states, which are prepared at the logical level, increasing overhead to a degree that precludes near-term implementation. Here, we implement a small quantum algorithm, one-qubit addition, fault-tolerantly on a trapped-ion quantum computer, using the [[ 8, 3, 2 ]] color code. By removing unnecessary error correction circuits and using low-overhead techniques for fault-tolerant preparation and measurement, we reduce the number of error-prone two-qubit gates and measurements to 36. We observe arithmetic errors with a rate of ∼1.1 × 10−3 for the fault-tolerant circuit and ∼9.5 × 10−3 for the unencoded circuit.
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