Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes

• URL: http://arxiv.org/abs/2211.10046v2
• Date: Tue, 22 Nov 2022 23:43:29 GMT
• Title: Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes
• Authors: Jason Gavriel, Daniel Herr, Alexis Shaw, Michael J. Bremner, Alexandru Paler and Simon J. Devitt
• Abstract summary: We introduce a protocol to potentially reduce this overhead for non-Clifford gates. Preliminary results hint at high quality fidelities at larger distances.
• Score: 55.90903601048249
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realisation 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 realising these gates for stabiliser 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 to logical operations such as a CNOT gate and contributes 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 stabiliser 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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