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Quantum computing companies are moving away from setting qubit records in favor of practical hardware and long-term goals.
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Some companies are taking aim at the classic form of error correction, using some qubits to correct errors in others. Last year, both Google Quantum AI and Quantinuum, a new company formed by Honeywell and Cambridge Quantum Computing, issued <anchor>papers</anchor> demonstrating that qubits can be assembled into error-correcting ensembles that outperform the underlying physical qubits.
[2208.01863] Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code
\[2208.01863\] Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code

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# Quantum Physics

**arXiv:2208.01863** (quant-ph)


\[Submitted on 3 Aug 2022\]

# Title:Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code

Authors: [C. Ryan-Anderson](https://arxiv.org/search/quant-ph?searchtype=author&query=Ryan-Anderson,+C), [N. C. Brown](https://arxiv.org/search/quant-ph?searchtype=author&query=Brown,+N+C), [M. S. Allman](https://arxiv.org/search/quant-ph?searchtype=author&query=Allman,+M+S), [B. Arkin](https://arxiv.org/search/quant-ph?searchtype=author&query=Arkin,+B), [G. Asa-Attuah](https://arxiv.org/search/quant-ph?searchtype=author&query=Asa-Attuah,+G), [C. Baldwin](https://arxiv.org/search/quant-ph?searchtype=author&query=Baldwin,+C), [J. Berg](https://arxiv.org/search/quant-ph?searchtype=author&query=Berg,+J), [J. G. Bohnet](https://arxiv.org/search/quant-ph?searchtype=author&query=Bohnet,+J+G), [S. Braxton](https://arxiv.org/search/quant-ph?searchtype=author&query=Braxton,+S), [N. Burdick](https://arxiv.org/search/quant-ph?searchtype=author&query=Burdick,+N), [J. P. Campora](https://arxiv.org/search/quant-ph?searchtype=author&query=Campora,+J+P), [A. Chernoguzov](https://arxiv.org/search/quant-ph?searchtype=author&query=Chernoguzov,+A), [J. Esposito](https://arxiv.org/search/quant-ph?searchtype=author&query=Esposito,+J), [B. Evans](https://arxiv.org/search/quant-ph?searchtype=author&query=Evans,+B), [D. Francois](https://arxiv.org/search/quant-ph?searchtype=author&query=Francois,+D), [J. P. Gaebler](https://arxiv.org/search/quant-ph?searchtype=author&query=Gaebler,+J+P), [T. M. Gatterman](https://arxiv.org/search/quant-ph?searchtype=author&query=Gatterman,+T+M), [J. Gerber](https://arxiv.org/search/quant-ph?searchtype=author&query=Gerber,+J), [K. Gilmore](https://arxiv.org/search/quant-ph?searchtype=author&query=Gilmore,+K), [D. Gresh](https://arxiv.org/search/quant-ph?searchtype=author&query=Gresh,+D), [A. Hall](https://arxiv.org/search/quant-ph?searchtype=author&query=Hall,+A), [A. Hankin](https://arxiv.org/search/quant-ph?searchtype=author&query=Hankin,+A), [J. Hostetter](https://arxiv.org/search/quant-ph?searchtype=author&query=Hostetter,+J), [D. Lucchetti](https://arxiv.org/search/quant-ph?searchtype=author&query=Lucchetti,+D), [K. Mayer](https://arxiv.org/search/quant-ph?searchtype=author&query=Mayer,+K), [J. Myers](https://arxiv.org/search/quant-ph?searchtype=author&query=Myers,+J), [B. Neyenhuis](https://arxiv.org/search/quant-ph?searchtype=author&query=Neyenhuis,+B), [J. Santiago](https://arxiv.org/search/quant-ph?searchtype=author&query=Santiago,+J), [J. Sedlacek](https://arxiv.org/search/quant-ph?searchtype=author&query=Sedlacek,+J), [T. Skripka](https://arxiv.org/search/quant-ph?searchtype=author&query=Skripka,+T), [A. Slattery](https://arxiv.org/search/quant-ph?searchtype=author&query=Slattery,+A), [R. P. Stutz](https://arxiv.org/search/quant-ph?searchtype=author&query=Stutz,+R+P), [J. Tait](https://arxiv.org/search/quant-ph?searchtype=author&query=Tait,+J), [R. Tobey](https://arxiv.org/search/quant-ph?searchtype=author&query=Tobey,+R), [G. Vittorini](https://arxiv.org/search/quant-ph?searchtype=author&query=Vittorini,+G), [J. Walker](https://arxiv.org/search/quant-ph?searchtype=author&query=Walker,+J), [D. Hayes](https://arxiv.org/search/quant-ph?searchtype=author&query=Hayes,+D)

View a PDF of the paper titled Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code, by C. Ryan-Anderson and 36 other authors

[View PDF](/pdf/2208.01863)

> Abstract:We compare two different implementations of fault-tolerant entangling gates on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit codes. The operation is evaluated with varying degrees of fault tolerance, which are provided by including quantum error correction circuit primitives known as flagging and pieceable fault tolerance. In the second instance, a twenty-qubit trapped-ion quantum computer is used to implement a transversal logical CNOT gate on two \[\[7,1,3\]\] color codes. The two codes were implemented on different but similar devices, and in both instances, all of the quantum error correction primitives, including the determination of corrections via decoding, are implemented during runtime using a classical compute environment that is tightly integrated with the quantum processor. For different combinations of the primitives, logical state fidelity measurements are made after applying the gate to different input states, providing bounds on the process fidelity. We find the highest fidelity operations with the color code, with the fault-tolerant SPAM operation achieving fidelities of 0.99939(15) and 0.99959(13) when preparing eigenstates of the logical X and Z operators, which is higher than the average physical qubit SPAM fidelities of 0.9968(2) and 0.9970(1) for the physical X and Z bases, respectively. When combined with a logical transversal CNOT gate, we find the color code to perform the sequence--state preparation, CNOT, measure out--with an average fidelity bounded by \[0.9957,0.9963\]. The logical fidelity bounds are higher than the analogous physical-level fidelity bounds, which we find to be \[0.9850,0.9903\], reflecting multiple physical noise sources such as SPAM errors for two qubits, several single-qubit gates, a two-qubit gate and some amount of memory error.

Subjects:Quantum Physics (quant-ph)Cite as:[arXiv:2208.01863](https://arxiv.org/abs/2208.01863) \[quant-ph\](or [arXiv:2208.01863v1](https://arxiv.org/abs/2208.01863v1) \[quant-ph\] for this version)
[https://doi.org/10.48550/arXiv.2208.01863](https://doi.org/10.48550/arXiv.2208.01863)

Focus to learn more

arXiv-issued DOI via DataCite

## Submission history

From: Ciarán Ryan-Anderson \[ [view email](/show-email/984caa5d/2208.01863)\]

**\[v1\]**
Wed, 3 Aug 2022 06:20:13 UTC (679 KB)

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