Details
| Original language | English |
|---|---|
| Pages (from-to) | 1141-1170 |
| Number of pages | 30 |
| Journal | Quantum Information and Computation |
| Volume | 19 |
| Issue number | 13-14 |
| Publication status | Published - Nov 2019 |
| Externally published | Yes |
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.
Keywords
- Bell inequalities, Cohomology, Measurement-based quantum computation, Symmetry
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Computer Science(all)
- Computational Theory and Mathematics
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In: Quantum Information and Computation, Vol. 19, No. 13-14, 11.2019, p. 1141-1170.
Research output: Contribution to journal › Article › Research › 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
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 -