Near-threshold qudit stabilizer codes with efficient encoding circuits for magic-state distillation

Sharma, AK and Garani, SS (2024) Near-threshold qudit stabilizer codes with efficient encoding circuits for magic-state distillation. In: Physical Review A, 109 (6).

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Abstract

Magic-state distillation is a protocol to purify noisy quantum states using quantum stabilizer codes. In this paper, we provide conditions for identifying magic states along with analytical expressions for computing the noise threshold. Through quantum entropic results, we prove the convergence of the magic-state distillation procedure. We derive analytical results to show how the noise threshold scales as a function of the minimum distance and the number of physical qudits of the underlying quantum stabilizer code. We distill |T) and |S) states with thresholds 0.498 (theoretical limit is 0.5) and 0.71 (theoretical limit is 0.75) over the depolarizing channel using 31,1,16]]2 quantum Bose-Chaudhuri-Hocquenghem code and 29,1,15]]3 quantum qutrit code, respectively. Finally, encoding algorithms based on quantum Calderbank-Shor-Steane (CSS) and non-CSS qudit stabilizer codes along with circuits are proposed for magic-state distillation. © 2024 American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review A
Publisher:	American Physical Society
Additional Information:	The copyright for this article belongs to American Physical Society.
Keywords:	Computer circuits; Distillation; Encoding (symbols); Quantum theory; Signal encoding, Analytical expressions; Condition; Distillation procedure; Efficient encoding; Near thresholds; Noise thresholds; Quantum stabilizer codes; Quantum state; Stabilizer codes; Theoretical limits, Timing circuits
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	04 Aug 2024 13:14
Last Modified:	04 Aug 2024 13:14
URI:	http://eprints.iisc.ac.in/id/eprint/85711

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