The DOI matches its Crossref record; 90 of the 90 references it cites were found in a registry or an index.
Chaos and complexity by design
Open accessAbstract
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
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Cites
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Cited by
Barren plateaus in quantum neural network training landscapes
McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018) · Nature Communications · doi:10.1038/s41467-018-07090-4 · Cited by 2,329
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Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus
Holmes, Z., Sharma, K., Cerezo, M., & Coles, P. J. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010313 · Cited by 570
Black holes and random matrices
Cotler, J. S., Gur-Ari, G., Hanada, M., Polchinski, J., Saad, P., Shenker, S. H., Stanford, D., Streicher, A., & Tezuka, M. (2017) · Journal of High Energy Physics · doi:10.1007/jhep05(2017)118 · Cited by 562
Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
Choi, S., Bao, Y., Qi, X.-L., & Altman, E. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.030505 · Cited by 435
Metadata
- Authors
- Roberts, D. A., & Yoshida, B.
- Venue
- Journal of High Energy Physics
- Published
- 2017-04
- Volume
- 2017
- Issue
- 4
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W2537703961
- Cited by
- 455
- References
- 90
- FWCI
- 16.99
- Type
- journal article
- Language
- en
- Open access
- diamond
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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