Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics

Schmidt, Frank; van Loock, Peter

doi:10.1103/PhysRevA.105.042427

Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics

Frank Schmidt
(
- Mainz U.
)
,
Peter van Loock
(
- Mainz U.
)

Oct 11, 2021

22 pages

e-Print:

2110.05315 [quant-ph]

DOI:

10.1103/PhysRevA.105.042427 (publication)

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Abstract: (arXiv)

We propose two schemes to obtain Gottesman-Kitaev-Preskill (GKP) error syndromes by means of linear optical operations, homodyne measurements and GKP ancillae. This includes showing that for a concatenation of GKP codes with a

[n,k,d]

stabilizer code only

2n

measurements are needed in order to obtain the complete syndrome information, significantly reducing the number of measurements in comparison to the canonical concatenated measurement scheme and at the same time generalizing linear-optics-based syndrome detections to higher GKP codes. Furthermore, we analyze the possibility of building the required ancilla states from single-mode states and linear optics. We find that for simple GKP codes this is possible, whereas for concatenations with qubit Calderbank-Shor-Steane (CSS) codes of distance

d\geq3

it is not. We also consider the canonical concatenated syndrome measurements and propose methods for avoiding crosstalk between ancillae. In addition, we make use of the observation that the concatenation of a GKP code with a stabilizer code forms a lattice in order to see the analog information decoding of such codes from a different perspective allowing for semi-analytic calculations of the logical error rates.

Note:

22 pages, 4 figures. Comments are welcome

optics: linear
stabilizer code
quantum error correction
lattice
optical
qubit

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