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Paper 1

Holstein Primakoff spin codes for local and collective noise

Sivaprasad Omanakuttan, Tyler Thurtell, Andrew K. Forbes, Vikas Buchemmavari, Ben Q. Baragiola

Year
2026
Journal
arXiv preprint
DOI
arXiv:2601.17592
arXiv
2601.17592

Quantum error correction is essential for fault-tolerant quantum computation, yet most existing codes rely on local control and stabilizer measurements that are difficult to implement in systems dominated by collective interactions. Inspired by spin-GKP codes in PhysRevA.108.022428, we develop a general framework for Holstein-Primakoff spin codes, which maps continuous-variable bosonic codes onto permutation-symmetric spin ensembles via the Holstein-Primakoff approximation. We show that HP codes are robust to both collective and local-spin noise and propose an explicit measurement-free local error recovery procedure to map local noise into correctable collective-spin errors.

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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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