Single-Round Proofs of Quantumness from Knowledge Assumptions
<|reference_start|>Single-Round Proofs of Quantumness from Knowledge Assumptions: A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the certification of quantum devices. Existing single-round protocols (like asking the quantum computer to factor a large number) require large quantum circuits, whereas multi-round ones use smaller circuits but require experimentally challenging mid-circuit measurements. As such, current proofs of quantumness are out of reach for near-term devices.   In this work, we construct efficient single-round proofs of quantumness based on existing knowledge assumptions. While knowledge assumptions have not been previously considered in this context, we show that they provide a natural basis for separating classical and quantum computation. Specifically, we show that multi-round protocols based on Decisional Diffie-Hellman (DDH) or Learning With Errors (LWE) can be "compiled" into single-round protocols using a knowledge-of-exponent assumption or knowledge-of-lattice-point assumption, respectively. We also prove an adaptive hardcore-bit statement for a family of claw-free functions based on DDH, which might be of independent interest.   Previous approaches to constructing single-round protocols relied on the random oracle model and thus incurred the overhead associated with instantiating the oracle with a cryptographic hash function. In contrast, our protocols have the same resource requirements as their multi-round counterparts without necessitating mid-circuit measurements, making them, arguably, the most efficient single-round proofs of quantumness to date. Our work also helps in understanding the interplay between black-box/white-box reductions and cryptographic assumptions in the design of proofs of quantumness.<|reference_end|>
@article{arabadjieva2024single-round,
    title={Single-Round Proofs of Quantumness from Knowledge Assumptions},
    author={Petia Arabadjieva, Alexandru Gheorghiu, Victor Gitton, Tony Metger},
    journal={arXiv preprint arXiv:2405.15736},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.15736},
    primaryClass={quant-ph cs.CR}
}