Transversal injection for direct encoding of ancilla states for non-Clifford gates using stabilizer codes

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023-07
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Mcode
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Language
en
Pages
16
1-16
Series
PHYSICAL REVIEW RESEARCH, Volume 5, issue 3
Abstract
Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realization of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal set of quantum gate operations in a fault-tolerant, error-corrected framework suffers from a conservation of unpleasantness. In general, no matter what error-correction technique is employed, there is always one element of a universal gate set that carries a significant resource overhead - either in physical qubits, computational time, or both. Specifically, this is due to the application of non-Clifford gates. A common method for realizing these gates for stabilizer codes such as the surface code is a combination of three protocols: state injection, distillation, and gate teleportation. These protocols contribute to the resource overhead compared with logical operations such as a CNOT gate and contribute to the qubit resources for any error-corrected quantum algorithm. In this paper, we introduce a very simple protocol to potentially reduce this overhead for non-Clifford gates: transversal injection. Transversal injection modifies the initial physical states of all data qubits in a stabilizer code before standard encoding and results in the direct preparation of a large class of single qubit states, including resource states for non-Clifford logic gates. Preliminary results hint at high-quality fidelities at larger distances and motivate further research on this technique.
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Funding Information: Thank you to Austin Fowler for early feedback on the findings of this paper and Sam Elman for help with editing the manuscript. The views, opinions, and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. This research was developed in part with funding from the Defense Advanced Research Projects Agency [under the Quantum Benchmark- ing (QB) program under Award No. HR00112230007 and HR001121S0026 contracts]. M.J.B. acknowledges the support of Google. M.J.B., J.G., and A.S. were supported by the ARC Centre of Excellence for Quantum Computation and Communication Technology (CQC2T), Project No. CE170100012. A.S. was also supported by the Sydney Quantum Academy. Publisher Copyright: © 2023 authors. Published by the American Physical Society.
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Citation
Gavriel , J , Herr , D , Shaw , A , Bremner , M J , Paler , A & Devitt , S J 2023 , ' Transversal injection for direct encoding of ancilla states for non-Clifford gates using stabilizer codes ' , PHYSICAL REVIEW RESEARCH , vol. 5 , no. 3 , 033019 , pp. 1-16 . https://doi.org/10.1103/PhysRevResearch.5.033019