Details
| Original language | English |
|---|---|
| Pages (from-to) | 1091–1110 |
| Number of pages | 20 |
| Journal | Quantum Information and Computation |
| Volume | 21 |
| Issue number | 13-14 |
| Publication status | Published - Nov 2021 |
| Externally published | Yes |
Abstract
We investigate the Λ-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, Λn, for every number n of qubits. We establish two properties of the family {Λn; n ∊ N}, namely (i) Any extremal point (vertex) Aα ∊Λm can be used to construct vertices in Λn, for all n > m. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to the classical simulation based on the preimage Aα. In addition, we describe a new class of vertices in Λ2 which is outside the known classification. While the hardness of classical simulation remains an open problem for most extremal points of Λn, the above results extend efficient classical simulation of quantum computations beyond the presently known range.
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)
- General Physics and Astronomy
- Computer Science(all)
- Computational Theory and Mathematics
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In: Quantum Information and Computation, Vol. 21, No. 13-14, 11.2021, p. 1091–1110.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the extremal points of the Λ-polytopes and classical simulation of quantum computation with magic states
AU - Okay, Cihan
AU - Zurel, Michael
AU - Raussendorf, Robert
N1 - Funding Information: CO is supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0002. RR acknowledges funding from NSERC, in part through the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program. Publisher Copyright:
PY - 2021/11
Y1 - 2021/11
N2 - We investigate the Λ-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, Λn, for every number n of qubits. We establish two properties of the family {Λn; n ∊ N}, namely (i) Any extremal point (vertex) Aα ∊Λm can be used to construct vertices in Λn, for all n > m. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to the classical simulation based on the preimage Aα. In addition, we describe a new class of vertices in Λ2 which is outside the known classification. While the hardness of classical simulation remains an open problem for most extremal points of Λn, the above results extend efficient classical simulation of quantum computations beyond the presently known range.
AB - We investigate the Λ-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, Λn, for every number n of qubits. We establish two properties of the family {Λn; n ∊ N}, namely (i) Any extremal point (vertex) Aα ∊Λm can be used to construct vertices in Λn, for all n > m. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to the classical simulation based on the preimage Aα. In addition, we describe a new class of vertices in Λ2 which is outside the known classification. While the hardness of classical simulation remains an open problem for most extremal points of Λn, the above results extend efficient classical simulation of quantum computations beyond the presently known range.
UR - http://www.scopus.com/inward/record.url?scp=85118703127&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2104.05822
DO - 10.48550/arXiv.2104.05822
M3 - Article
AN - SCOPUS:85118703127
VL - 21
SP - 1091
EP - 1110
JO - Quantum Information and Computation
JF - Quantum Information and Computation
SN - 1533-7146
IS - 13-14
ER -