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Paper 1

Optimal Decoding with the Worm

Zac Tobias, Nikolas P. Breuckmann, Benedikt Placke

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.05428

arXiv

2603.05428

We propose a new decoder for ``matchable'' qLDPC codes that uses a Markov-Chain Monte-Carlo algorithm -- called the \emph{worm algorithm} -- to approximately compute the probabilities of logical error classes given a syndrome. The algorithm hence performs (approximate) \emph{optimal} decoding, and we expect it to be computationally efficient in certain settings. The algorithm is applicable to decoding random errors for the surface code, the honeycomb Floquet code, and hyperbolic surface codes with constant rate, in all cases with and without measurement errors. The efficiency of the decoder hinges on the mixing time of the underlying Markov chain. We give a rigorous mixing time guarantee in terms of a quantity that we call the \emph{defect susceptibility}. We connect this quantity to the notion of disorder operators in statistical mechanics and use this to argue (non-rigorously) that the algorithm is efficient for \emph{typical} errors in the entire decodable phase. We also demonstrate the effectiveness of the worm decoder numerically by applying it to the surface code with measurement errors as well as a family of hyperbolic surface codes. For most codes, the matchability condition restricts direct application of our decoder to noise models with independent bit-flip, phase-flip, and measurement errors. However, our decoder returns \emph{soft information} which makes it useful also in heuristic ``correlated decoding'' schemes which work beyond this simple setting. We demonstrate this by simulating decoding of the surface code under depolarizing noise, and we find that the threshold for ``correlated worm decoding'' is substantially higher than for both minimum-weight perfect matching and for correlated matching.

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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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