Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code

• URL: http://arxiv.org/abs/2309.09893v1
• Date: Mon, 18 Sep 2023 15:56:14 GMT
• Title: Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code
• Authors: Yang Wang, Selwyn Simsek, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Nathan Hewitt, Chandler V. Horst, Mitchell Matheny, Tanner Mengle, Brian Neyenhuis, Ben Criger
• Abstract summary: We implement a small quantum algorithm, one-qubit addition, fault-tolerantly on the Quantinuum H1-1 quantum computer. We observe arithmetic errors with a rate of $sim 1.1 times 10-3$ for the fault-tolerant circuit and $sim 9.5 times 10-3$ for the unencoded circuit.
• Score: 2.5553228515450765
• License: http://creativecommons.org/licenses/by/4.0/
• 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 either use 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. In this work, we implement a small quantum algorithm, one-qubit addition, fault-tolerantly on the Quantinuum H1-1 quantum computer, using the [[8,3,2]] colour 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 $\sim 1.1 \times 10^{-3}$ for the fault-tolerant circuit and $\sim 9.5 \times 10^{-3}$ for the unencoded circuit.

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