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  • Open Access

Magic State Injection with Erasure Qubits

Shoham Jacoby1,2,*, Yotam Vaknin1,2, Alex Retzker1,2, and Arne L. Grimsmo1

  • *Contact author: shohamjac@gmail.com
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PRX Quantum 6, 040323 – Published 4 November, 2025

DOI: https://doi.org/10.1103/5q1v-ry3y

Abstract

Erasure qubits constitute a promising approach for tackling the daunting resources required for fault-tolerant quantum computing. By heralding of erasure errors, both the error-correction threshold and the sub-threshold scaling of the logical error rate are significantly improved. While previous research has focused primarily on fault-tolerant quantum memories, we extend this investigation to magic state injection—a critical yet resource-intensive component of fault-tolerant quantum computation. We show that, after postselection on erasures, the logical error rate of the injected magic state is set by the residual Pauli error, while the space-time overhead is only marginally increased as compared with the case of non-erasure qubits with a similar noise strength. These conclusions hold both for injection into the surface code and for injection and cultivation on the color code. For the former, we show that most of the gains can be achieved by the use of just three strategically placed erasure qubits in the surface code patch, independent of the patch size. For the latter, in contrast, it is beneficial to have all the qubits in the cultivation patch be erasure qubits. Our results for cultivation suggest that algorithmically relevant logical error rates may be within reach without magic state distillation for erasure rates ≲4×10−3 and residual Pauli error rates of ∼10−4.

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Popular Summary

Quantum error correction is a key ingredient in building large-scale, fault-tolerant quantum computers. A critical step in this process is the generation of special quantum states known as magic states, which enable operations that cannot be performed directly on encoded qubits. Current methods for generating them—such as injection, cultivation, and distillation—are effective but come with significant resource overhead.

In this work, we propose an approach that uses erasure qubits—qubits that can flag when an error has occurred. By post-selecting on these heralded erasure events during magic state generation, we can dramatically suppress the effect of the dominant noise source.

This decouples the logical error rate from the erasure noise itself, leaving only the much smaller residual Pauli error rate. As a result, the fidelity of the produced magic states improves significantly—enough to reduce the number of distillation rounds needed. This, in turn, leads to a substantial reduction in overhead.

We show that most of these advantages are achievable even when just three erasure qubits are used, making this approach compatible with near-term experimental systems. Our results suggest that incorporation of erasure detection into quantum devices could significantly reduce the cost of generating magic states, ultimately reducing the overhead required for fault-tolerant quantum computing.

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Outline

Information

PRX Quantum 6, 040323– Published 4 November, 2025
  • Received 27 April 2025
  • Revised 21 July 2025
  • Accepted 4 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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