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Paper 1

Towards low overhead magic state distillation

Anirudh Krishna, Jean-Pierre Tillich

Year

2018

Journal

arXiv preprint

DOI

arXiv:1811.08461

arXiv

1811.08461

Magic state distillation is a resource intensive sub-routine for quantum computation. The ratio of noisy input states to output states with error rate at most $ε$ scales as $O(\log^γ(1/ε))$ (Bravyi and Haah, PRA 2012). In a breakthrough paper, Hastings and Haah (PRL 2018) showed that it is possible to construct distillation routines with sub-logarithmic overhead, achieving $γ\approx 0.6779$ and falsifying a conjecture that $γ$ is lower bounded by $1$. They then ask whether $γ$ can be made arbitrarily close to $0$. We answer this question in the affirmative for magic state distillation routines using qudits ($d$ dimensional quantum systems).

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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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