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Paper 1
An Undergraduate Course in Quantum Computing
Peter Young
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2604.10396
- arXiv
- 2604.10396
This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied linear algebra (though a review of this topic is given in the course). No prior knowledge of quantum mechanics is required. The most important topics covered are Shor's algorithm and an introduction to quantum error correction. Most of the text is a build-up to these topics.
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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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