Reducing Postselection Overhead in Magic-State Cultivation by In-Patch Multiplexing

TL;DR

This paper introduces an in-patch multiplexing scheme that significantly reduces postselection overhead in magic-state cultivation for fault-tolerant quantum computing by utilizing early-stage idle resources within a logical patch.

Contribution

It proposes a novel in-patch multiplexing method that decreases discard rates and attempts in magic-state preparation without altering the core acceptance procedures.

Findings

Reduces expected attempts by 45-73% at physical error rate of 2×10^{-3}.

Further reduces attempts by 49-79% when including full-cycle evaluation.

Maintains logical-error behavior while decreasing postselection overhead.

Abstract

Fault-tolerant quantum computing requires high-fidelity logical magic states for implementing non-Clifford operations. Magic-state cultivation provides a lower-overhead route to logical magic-state preparation, but its efficiency is limited by postselection loss during the early injection-and-cultivation stages. In this work, we propose an in-patch multiplexing scheme that uses early-stage idle resources within a single logical patch to create multiple local cultivation opportunities. A candidate that passes the early stages is forwarded to the standard escape pathway, while the escape stage and the decoder-based acceptance procedure are kept identical to those of the single-site baseline. Under a uniform depolarizing noise model with idle noise, the proposed protocol substantially reduces the injection-and-cultivation discard rate and the expected number of attempts required to obtain an accepted early-stage candidate. At a physical error rate of \(p=2\times10^{-3}\), the injection-and-cultivation expected attempts are reduced by \(45.46\%\) for \(d_1=3\) and by \(72.91\%\) for \(d_1=5\), relative to the single-site MSC baseline. In the direct full-cycle evaluation including escape, the expected attempts per kept logical output are further reduced by \(49.04\%\) for \(d_1=3\) and by \(78.69\%\) for \(d_1=5\) at the same physical error rate. The full-cycle cost curves are shifted toward smaller expected attempts, while the final logical-error behavior remains governed by the escape-stage gap threshold. These results show that in-patch multiplexing can reduce postselection overhead while preserving the standard magic-state cultivation framework.