Additive-error fine-grained quantum supremacy
1Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyoku, Kyoto 606-8502, Japan
2JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
3School of Social Information Science, University of Hyogo, 8-2-1, Gakuennishi-machi, Nishi-ku, Kobe, Hyogo 651-2197, Japan
Published: | 2020-09-24, volume 4, page 329 |
Eprint: | arXiv:1912.06336v3 |
Doi: | https://doi.org/10.22331/q-2020-09-24-329 |
Citation: | Quantum 4, 329 (2020). |
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Abstract
It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain conjectures in classical complexity theory. Recently, these results have been improved to ``fine-grained" versions where even exponential-time classical simulations are excluded assuming certain classical fine-grained complexity conjectures. All these fine-grained results are, however, about the hardness of strong simulations or multiplicative-error sampling. It was open whether any fine-grained quantum supremacy result can be shown for a more realistic setup, namely, additive-error sampling. In this paper, we show the additive-error fine-grained quantum supremacy (under certain complexity assumptions). As examples, we consider the IQP model, a mixture of the IQP model and log-depth Boolean circuits, and Clifford+$T$ circuits. Similar results should hold for other sub-universal models.
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Cited by
[1] Martin Kliesch and Ingo Roth, "Theory of Quantum System Certification", PRX Quantum 2 1, 010201 (2021).
[2] Alexander M. Dalzell, Aram W. Harrow, Dax Enshan Koh, and Rolando L. La Placa, "How many qubits are needed for quantum computational supremacy?", Quantum 4, 264 (2020).
[3] Alexander M. Dalzell, Nicholas Hunter-Jones, and Fernando G. S. L. Brandão, "Random Quantum Circuits Anticoncentrate in Log Depth", PRX Quantum 3 1, 010333 (2022).
[4] Alexander M. Dalzell, Nicholas Hunter-Jones, and Fernando G. S. L. Brandão, "Random quantum circuits anti-concentrate in log depth", arXiv:2011.12277, (2020).
[5] Martin Kliesch and Ingo Roth, "Theory of quantum system certification: a tutorial", arXiv:2010.05925, (2020).
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