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Paper 1
Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
Ryota Nakai, Hayato Goto
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.04526
- arXiv
- 2510.04526
Quantum error-correcting codes (QECCs) require high encoding rate in addition to high threshold unless a sufficiently large number of physical qubits are available. The many-hypercube (MHC) codes defined as the concatenation of the [[6,4,2]] quantum error-detecting code have been proposed as high-performance and high-encoding-rate QECCs. However, the concatenated codes have a disadvantage that the syndrome weight grows exponentially with respect to the concatenation level. To address this issue, here we propose subsystem quantum codes based on the MHC codes. In particular, we study the smallest subsystem MHC codes, namely, subsystem codes derived from the concatenated [[4,2,2]] error-detecting codes. The resulting codes have a constant syndrome-measurement weight of 4, while keeping high encoding rates. We build the block-MAP and neural-network decoders and show that they demonstrate superior performance to the bounded-distance decoder.
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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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