Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1141-1170 |
| Seitenumfang | 30 |
| Fachzeitschrift | Quantum Information and Computation |
| Jahrgang | 19 |
| Ausgabenummer | 13-14 |
| Publikationsstatus | Veröffentlicht - Nov. 2019 |
| Extern publiziert | Ja |
Abstract
We describe a cohomological framework for measurement-based quantum computation in which symmetry plays a central role. Therein, the essential information about the computation is contained in either of two topological invariants, namely two cohomology groups. One of them applies only to deterministic quantum computations, and the other to general probabilistic ones. Those invariants characterize the computational output, and at the same time witness quantumness in the form of contextuality. In result, they give rise to fundamental algebraic structures underlying quantum computation.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Physik und Astronomie (insg.)
- Kern- und Hochenergiephysik
- Mathematik (insg.)
- Mathematische Physik
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Informatik (insg.)
- Theoretische Informatik und Mathematik
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in: Quantum Information and Computation, Jahrgang 19, Nr. 13-14, 11.2019, S. 1141-1170.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Cohomological framework for contextual quantum computations
AU - Raussendorf, Robert
N1 - Funding Information: I thank C. Okay and E. Tyhurst for discussions, and acknowledge support from NSERC. Funding Information: I thank C. Okay and E. Tyhurst for discussions, and acknowledge support from NSERC. This paper is dedicated to Dr. Klaus Weidig, my mother Marina Rau?endorf, Dr. Manfred Gubsch, RA Uwe Wunderlich, and Matthias Kluge, and to the memory of Karl Friedrich. They kept a ship afloat, and Klaus Weidig rebuilt it.
PY - 2019/11
Y1 - 2019/11
N2 - We describe a cohomological framework for measurement-based quantum computation in which symmetry plays a central role. Therein, the essential information about the computation is contained in either of two topological invariants, namely two cohomology groups. One of them applies only to deterministic quantum computations, and the other to general probabilistic ones. Those invariants characterize the computational output, and at the same time witness quantumness in the form of contextuality. In result, they give rise to fundamental algebraic structures underlying quantum computation.
AB - We describe a cohomological framework for measurement-based quantum computation in which symmetry plays a central role. Therein, the essential information about the computation is contained in either of two topological invariants, namely two cohomology groups. One of them applies only to deterministic quantum computations, and the other to general probabilistic ones. Those invariants characterize the computational output, and at the same time witness quantumness in the form of contextuality. In result, they give rise to fundamental algebraic structures underlying quantum computation.
KW - Bell inequalities
KW - Cohomology
KW - Measurement-based quantum computation
KW - Symmetry
UR - http://www.scopus.com/inward/record.url?scp=85078847902&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1602.04155
DO - 10.48550/arXiv.1602.04155
M3 - Article
AN - SCOPUS:85078847902
VL - 19
SP - 1141
EP - 1170
JO - Quantum Information and Computation
JF - Quantum Information and Computation
SN - 1533-7146
IS - 13-14
ER -