In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes

Quantum Physics [Submitted on 6 Apr 2026] In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes Kun Liu, Shifan Xu, Tomas Jochym-O'Connor, Zhiyang He, Shraddha Singh, Yongshan Ding Quantum low-density parity-check (qLDPC) codes can encode many logical qubits within a single code block at low physical qubit overhead, yet magic state injection into such codes remains largely underexplored. Existing state injection proposals for qLDPC codes predominantly follow an external prepare-and-transfer paradigm, in which raw magic states are prepared outside the target code block and subsequently injected via inter-code operations. We propose the first \emph{in-situ} magic state injection: a scheme in which logical magic states are directly prepared within a qLDPC memory block, only using resources required for syndrome extraction. We show that our scheme is generalizable to any CSS qLDPC code, with examples of circuit-level simulations on the [[144,12,12]] Bivariate Bicycle (BB) code and the [[225,9,4]] Hypergraph Product code. We focus on a regime where correlated injection errors are negligible. In the BB code, this corresponds to a configuration that simultaneously injects four logical |Y\rangle states. Under a uniform depolarizing noise model with physical error rate 10^{-3}, this achieves an injection error rate of 1.62 \times 10^{-3} per logical qubit, while the correlated-error contribution is only 2 \times 10^{-5} per logical qubit (about 1\% of the injection error rate). Under a hardware-motivated asymmetric noise model where single-qubit gate errors are 10\% of two-qubit gate errors, the injection error rate per logical qubit falls to 6.7 \times 10^{-4} , below the error rate ( 10^{-3} ) of the two-qubit gates used to encode the magic states. Its simplicity allows our scheme to be applied to arbitrary CSS qLDPC codes using only the ancilla qubits native to syndrome extraction, and yield a reduction in space overhead relative to both prepare-and-transfer approaches and surface-code-based magic state injection schemes. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.05126 [quant-ph]   (or arXiv:2604.05126v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.05126 Focus to learn more Submission history From: Kun Liu [view email] [v1] Mon, 6 Apr 2026 19:40:46 UTC (922 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)