The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Exact and approximate unitary 2-designs and their application to fidelity estimation
Open accessAbstract
We develop the concept of a unitary $t$-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group $U({2}^{n})$ on $n$ qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an $O(n)$-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on $n$ qubits with quantum circuits of size $O(n)$ without requiring any ancilla qubits, thereby improving upon previous approaches.
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Citations
Cites
Scalable noise estimation with random unitary operators
Emerson, J., Alicki, R., & Życzkowski, K. (2005) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/7/10/021 · Cited by 502
Self-citationRandomizing Quantum States: Constructions and Applications
Hayden, P., Leung, D., Shor, P. W., & Winter, A. (2004) · Communications in Mathematical Physics · doi:10.1007/s00220-004-1087-6 · Cited by 345
Quantum process tomography of the quantum Fourier transform
Weinstein, Y. S., Havel, T. F., Emerson, J., Boulant, N., Saraceno, M., Lloyd, S., & Cory, D. G. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1785151 · Cited by 178
Self-citation
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
Trapped-ion quantum computing: Progress and challenges
Bruzewicz, C. D., Chiaverini, J., McConnell, R., & Sage, J. M. (2019) · Applied Physics Reviews · doi:10.1063/1.5088164 · Cited by 1,483
Black holes as mirrors: quantum information in random subsystems
Hayden, P., & Preskill, J. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/09/120 · Cited by 1,332
Cost function dependent barren plateaus in shallow parametrized quantum circuits
Cerezo, M., Sone, A., Volkoff, T., Cincio, L., & Coles, P. J. (2021) · Nature Communications · doi:10.1038/s41467-021-21728-w · Cited by 1,047
Shenker, S. H., & Stanford, D. (2015) · Journal of High Energy Physics · doi:10.1007/jhep05(2015)132 · Cited by 604
Metadata
- Authors
- Dankert, C., Cleve, R., Emerson, J., & Livine, E.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2009-07-06
- Volume
- 80
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1848366941
- Cited by
- 685
- References
- 3
- FWCI
- 11.93
- Type
- journal article
- Language
- en
- Open access
- green
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- Dankert, C., Cleve, R., Emerson, J., & Livine, E. (2009). Exact and approximate unitary 2-designs and their application to fidelity estimation. Physical Review A. https://doi.org/10.1103/physreva.80.012304
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