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Paper 1

Simple, Efficient, and Generic Post-Selection Decoding for qLDPC codes

Haipeng Xie, Nobuyuki Yoshioka, Kento Tsubouchi, Ying Li

Year

2026

Journal

arXiv preprint

DOI

arXiv:2601.17757

arXiv

2601.17757

Quantum error correction is indispensable for scalable quantum computation. Although encoding logical qubits substantially enhances noise resilience, achieving logical error rates low enough for practical algorithms remains challenging on existing hardware. Here we introduce argument reweighting, a simple and broadly applicable post-selection decoding strategy that boosts the performance of maximum-likelihood-type decoders, including minimum-weight perfect matching and belief-propagation families. The method suppresses logical errors by performing additional decoding rounds under reweighted error models, enabling acceptance of high-confidence syndrome outcomes. Circuit-level simulations across multiple decoders and qLDPC codes show that argument reweighting substantially suppresses logical errors, requiring a rejection rate of only $1.44\times10^{-5}$ to reduce the logical error rate by almost two orders of magnitude for the $[[144,12,12]]$ bivariate bicycle code. These results establish argument reweighting as a practical and resource-efficient approach for enhancing quantum fault tolerance.

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Paper 2

Proofs of quantum memory

Minki Hhan, Tomoyuki Morimae, Yasuaki Okinaka, Takashi Yamakawa

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.04159

arXiv

2510.04159

With the rapid advances in quantum computer architectures and the emerging prospect of large-scale quantum memory, it is becoming essential to classically verify that remote devices genuinely allocate the promised quantum memory with specified number of qubits and coherence time. In this paper, we introduce a new concept, proofs of quantum memory (PoQM). A PoQM is an interactive protocol between a classical probabilistic polynomial-time (PPT) verifier and a quantum polynomial-time (QPT) prover over a classical channel where the verifier can verify that the prover has possessed a quantum memory with a certain number of qubits during a specified period of time. PoQM generalize the notion of proofs of quantumness (PoQ) [Brakerski, Christiano, Mahadev, Vazirani, and Vidick, JACM 2021]. Our main contributions are a formal definition of PoQM and its constructions based on hardness of LWE. Specifically, we give two constructions of PoQM. The first is of a four-round and has negligible soundness error under subexponential-hardness of LWE. The second is of a polynomial-round and has inverse-polynomial soundness error under polynomial-hardness of LWE. As a lowerbound of PoQM, we also show that PoQM imply one-way puzzles. Moreover, a certain restricted version of PoQM implies quantum computation classical communication (QCCC) key exchange.

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