The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
On the Hardness of Distinguishing Mixed-State Quantum Computations
Open accessAbstract
This paper considers the following problem. Two mixed-state quantum circuits Q/sub 0/ and Q/sub 1/ are given, and the goal is to determine which of two possibilities holds: (i) Q/sub 0/ and Q/sub 1/ act nearly identically on all possible quantum state inputs, or (ii) there exists some input state /spl rho/ that Q/sub 0/ and Q/sub 1/ transform into almost perfectly distinguishable outputs. This may be viewed as an abstraction of the problem that asks, given two discrete quantum mechanical processes described by sequences of local interactions, are the processes effectively the same or are they different? We prove that this promise problem is complete for the class QIP of problems having quantum interactive proof systems, and is therefore PSPACE-hard. This is in contrast to the fact that the analogous problem for classical (probabilistic) circuits is in AM, and for unitary quantum circuits is in QMA.
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“This result provides insight into the black hole information paradox as one would need to have a representation of a black hole's scrambling unitary in order to unscramble information from emitted Hawking radiation [185].”
From Variational quantum algorithms (2021) · cites this paper as [185]
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Cites
Completely positive linear maps on complex matrices
Choi, M.-D. (1975) · Linear Algebra and its Applications · doi:10.1016/0024-3795(75)90075-0 · Cited by 2,659
Quantum computations: algorithms and error correction
Kitaev, A. Y. (1997) · Russian Mathematical Surveys · doi:10.1070/rm1997v052n06abeh002155 · Cited by 1,424
Research works printed but not linked: 13
- watrous, 2005, Notes on super-operator norms induced by Schatten norms, Quantum Information and Computation, 5, 58, 10.26421/QIC5.1-6 · DOI
- 10.1109/SFCS.2002.1181970 · DOI
- 10.1016/S0304-3975(01)00375-9 · DOI
- nielsen, 2000, Quantum Computation and Quantum Information
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- 10.1145/1147954.1147962 · DOI
- 10.1145/276698.276708 · DOI
- 10.1016/S0304-3975(98)00191-1 · DOI
- 10.1145/335305.335387 · DOI
- kitaev, 2002, Classical and quantum computation, Graduate Studies in Mathematics, 47, 10.1090/gsm/047/18 · DOI
- janzing, 2003, "Identity Check" Is QMA-complete
- 10.1109/SFCS.1997.646094 · DOI
- 10.1103/PhysRevLett.81.5672 · DOI
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Variational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385
Quantum-assisted quantum compiling
Khatri, S., LaRose, R., Poremba, A., Cincio, L., Sornborger, A. T., & Coles, P. J. (2019) · Quantum · doi:10.22331/q-2019-05-13-140 · Cited by 382
Metadata
- Authors
- Rosgen, B., & Watrous, J.
- Affiliations
- University of Alberta (CA)
- ORCID
- Watrous, J.
- Venue
- 20th Annual IEEE Conference on Computational Complexity (CCC'05)
- Publisher
- IEEE
- Published
- 2005-06-28
- Pages
- 344-354
- ISSN
- 1093-0159 (ISSN-L)
- OpenAlex
- W2266502407
- Cited by
- 70
- References
- 2
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 3 · 2023: 3 · 2021: 2 · 2020: 4 · 2019: 4 · 2018: 1 · 2017: 1 · 2016: 7 · 2015: 3 · 2014: 5 · 2013: 7 · 2012: 3
- FWCI
- 1.88
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Conference on Computational Complexity (CCC) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Canada Research Chairs
- Natural Sciences and Engineering Research Council of Canada
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Keywords
- promise problems, quantum interactive proofs, PSPACE-hardness, QMA
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