Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code
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arXiv
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| Format: | Preprint |
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2023
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| author | Wang, Yang Simsek, Selwyn Gatterman, Thomas M. Gerber, Justin A. Gilmore, Kevin Gresh, Dan Hewitt, Nathan Horst, Chandler V. Matheny, Mitchell Mengle, Tanner Neyenhuis, Brian Criger, Ben |
| author_facet | Wang, Yang Simsek, Selwyn Gatterman, Thomas M. Gerber, Justin A. Gilmore, Kevin Gresh, Dan Hewitt, Nathan Horst, Chandler V. Matheny, Mitchell Mengle, Tanner Neyenhuis, Brian Criger, Ben |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09893 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code Wang, Yang Simsek, Selwyn Gatterman, Thomas M. Gerber, Justin A. Gilmore, Kevin Gresh, Dan Hewitt, Nathan Horst, Chandler V. Matheny, Mitchell Mengle, Tanner Neyenhuis, Brian Criger, Ben Quantum Physics 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. |
| title | Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.09893 |