Magic State Distillation from Qudit Stabilizer Codes

Sharma, AK and Garani, SS (2024) Magic State Distillation from Qudit Stabilizer Codes. In: 59th Annual IEEE International Conference on Communications, ICC 2024, 9 June 2024through 13 June 2024, Denver, pp. 1795-1800.

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Abstract

Magic state distillation (MSD) is a procedure to purify noisy non-stabilizer states from a quantum code, useful towards fault-tolerant quantum computing. Quantum circuits requiring non-Clifford gates can be realized using special states called magic states that are the eigenstates of both non-Clifford and Clifford gates. The purification of noisy states is realized by projecting these magic states onto the space spanned by the eigenstates of the projection operator of the stabilizer code. Given a noisy non- stabilizer state from a given stabilizer code, not all states can be distilled towards magic states. In this paper, we provide the condition for distillability of magic states specific to the choice of qudit stabilizer codes. We derive the noise threshold for magic state distillation depending on the code parameters. We prove that magic state distillation is a convergent map in the entropic sense. We also give an efficient decoding circuit for the best-known code to distill the |Hi state, which is an eigenstate of the qutrit Hadamard gate. © 2024 IEEE.

Item Type:	Conference Paper
Publication:	IEEE International Conference on Communications
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Decoding; Eigenvalues and eigenfunctions; Fault tolerant computer systems; Quantum electronics; Quantum optics; SPICE, ClIFFORD; Condition; Distillability; Eigenstates; Fault-tolerant quantum computing; Projection Operator; Quantum circuit; Quantum codes; Stabilizer codes; Stabilizer state, Quantum computers
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	25 Sep 2024 10:33
Last Modified:	25 Sep 2024 10:33
URI:	http://eprints.iisc.ac.in/id/eprint/86295

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