Details
| Original language | English |
|---|---|
| Article number | 042301 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 86 |
| Issue number | 4 |
| Publication status | Published - 1 Oct 2012 |
| Externally published | Yes |
Abstract
We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum computation. The operational cost of this method is polynomial in the size of the surface-code state, but in the worst case scales as 22g in the genus g of the surface embedding the code. However, there are states in the code space for which the simulation becomes efficient. In general, the simulation cost is exponential in the entanglement contained in a certain effective state, capturing the encoded state, the encoding, and the local postmeasurement states. The same efficiencies hold, with additional assumptions on the temporal order of measurements and on the tessellations of the code surfaces, for the harder task of sampling from the distribution of the computational output.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 86, No. 4, 042301, 01.10.2012.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Classical simulation of measurement-based quantum computation on higher-genus surface-code states
AU - Goff, Leonard
AU - Raussendorf, Robert
PY - 2012/10/1
Y1 - 2012/10/1
N2 - We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum computation. The operational cost of this method is polynomial in the size of the surface-code state, but in the worst case scales as 22g in the genus g of the surface embedding the code. However, there are states in the code space for which the simulation becomes efficient. In general, the simulation cost is exponential in the entanglement contained in a certain effective state, capturing the encoded state, the encoding, and the local postmeasurement states. The same efficiencies hold, with additional assumptions on the temporal order of measurements and on the tessellations of the code surfaces, for the harder task of sampling from the distribution of the computational output.
AB - We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum computation. The operational cost of this method is polynomial in the size of the surface-code state, but in the worst case scales as 22g in the genus g of the surface embedding the code. However, there are states in the code space for which the simulation becomes efficient. In general, the simulation cost is exponential in the entanglement contained in a certain effective state, capturing the encoded state, the encoding, and the local postmeasurement states. The same efficiencies hold, with additional assumptions on the temporal order of measurements and on the tessellations of the code surfaces, for the harder task of sampling from the distribution of the computational output.
UR - http://www.scopus.com/inward/record.url?scp=84866997368&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1201.6319
DO - 10.48550/arXiv.1201.6319
M3 - Article
AN - SCOPUS:84866997368
VL - 86
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 4
M1 - 042301
ER -