To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However, it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code. Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large-scale cluster states for the topologically protected, measurement-based, quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large-scale quantum computation.To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However, it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code. Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large-scale cluster states for the topologically protected, measurement-based, quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large-scale quantum computation.

May 25, 2018152 citations

Generation of flying logical qubits using generalized photon subtraction with adaptive Gaussian operations

Kan Takase, Fumiya Hanamura, H. Nagayoshi +6 more

The generation of a logical qubit called the Gottesman-Kitaev-Preskill (GKP) qubit in an optical traveling wave is a major challenge for realizing large-scale universal fault-tolerant optical quantum computers. Recently, probabilistic generation of elementary GKP qubits has been demonstrated using photon number measurements and homodyne measurements. However, the generation rate is only a few Hz, and it will be difficult to generate fault-tolerant GKP qubits at a practical rate unless success probability is significantly improved. Here, we propose a method to efficiently synthesize GKP qubits from several quantum states by adaptive Gaussian operations. In the initial-state preparation that utilizes photon number measurements, an adaptive operation allows any measurement outcome above a certain threshold to be considered as a success. This threshold is lowered by utilizing the generalized photon subtraction method. The initial states are synthesized into a GKP qubit by homodyne measurements and a subsequent adaptive operation. As a result, the single-shot success probability of generating fault-tolerant GKP qubits in a realistic scale system exceeds $10%$ , which is $1\ifmmode\times\else\texttimes\fi{}{10}^{6}$ times better than previous methods. This proposal will become a powerful tool for advancing optical quantum computers from the proof-of-principle stage to practical application.The generation of a logical qubit called the Gottesman-Kitaev-Preskill (GKP) qubit in an optical traveling wave is a major challenge for realizing large-scale universal fault-tolerant optical quantum computers. Recently, probabilistic generation of elementary GKP qubits has been demonstrated using photon number measurements and homodyne measurements. However, the generation rate is only a few Hz, and it will be difficult to generate fault-tolerant GKP qubits at a practical rate unless success probability is significantly improved. Here, we propose a method to efficiently synthesize GKP qubits from several quantum states by adaptive Gaussian operations. In the initial-state preparation that utilizes photon number measurements, an adaptive operation allows any measurement outcome above a certain threshold to be considered as a success. This threshold is lowered by utilizing the generalized photon subtraction method. The initial states are synthesized into a GKP qubit by homodyne measurements and a subsequent adaptive operation. As a result, the single-shot success probability of generating fault-tolerant GKP qubits in a realistic scale system exceeds $10%$, which is $1\ifmmode\times\else\texttimes\fi{}{10}^{6}$ times better than previous methods. This proposal will become a powerful tool for advancing optical quantum computers from the proof-of-principle stage to practical application.

arXiv:2401.07287Physical Review AJul 12, 202431 citations

Fault-tolerant quantum computation with few qubits

Ben W. Reichardt

Bulletin of the American Physical SocietyMar 5, 20190 citations

Tolerable Noise in Scalable Quantum Computing

Manny Knill

Quantum Electronics and Laser Science ConferenceMay 6, 20070 citations

Photon-loss tolerance of the surface-GKP code with anti-photon-loss decoding

Guan-Ju Yan, Pei-Lin Du, Ke-Min Hu +7 more

Photon loss somewhat limits fault-tolerant photonic quantum computing. We investigate its effect on finite-energy Gottesman--Kitaev--Preskill (GKP) states by modeling the pure-loss channel directly. We obtain photon-loss threshold estimates for the surface-GKP code using nearest-lattice-point inner GKP decoding and minimum-weight perfect matching for the outer surface code. For GKP states with $ε=0.01$ and $ε=0.05$ , corresponding to GKP squeezing of $20$ and $13\,\mathrm{dB}$ , the estimated thresholds are $γ^\ast=5.5\%$ ( $0.24\,\mathrm{dB}$ ) and $γ^\ast=5.9\%$ ( $0.26\,\mathrm{dB}$ ), respectively. We then introduce an anti-photon-loss inner decoder that compensates for the contraction of the measured quadrature. It increases the corresponding threshold estimates to $γ^\ast=9.8\%$ ( $0.45\,\mathrm{dB}$ ) and $γ^\ast=6.3\%$ ( $0.28\,\mathrm{dB}$ ). Our results highlight the importance of accounting for loss-induced lattice contraction in inner decoding and demonstrate that quadrature compensation enhances the photon-loss tolerance of surface-GKP codes for both high- and moderate-quality GKP states, providing a route toward more photon-loss-robust optical quantum computing.Photon loss somewhat limits fault-tolerant photonic quantum computing. We investigate its effect on finite-energy Gottesman--Kitaev--Preskill (GKP) states by modeling the pure-loss channel directly. We obtain photon-loss threshold estimates for the surface-GKP code using nearest-lattice-point inner GKP decoding and minimum-weight perfect matching for the outer surface code. For GKP states with $ε=0.01$ and $ε=0.05$, corresponding to GKP squeezing of $20$ and $13\,\mathrm{dB}$, the estimated thresholds are $γ^\ast=5.5\%$ ($0.24\,\mathrm{dB}$) and $γ^\ast=5.9\%$ ($0.26\,\mathrm{dB}$), respectively. We then introduce an anti-photon-loss inner decoder that compensates for the contraction of the measured quadrature. It increases the corresponding threshold estimates to $γ^\ast=9.8\%$ ($0.45\,\mathrm{dB}$) and $γ^\ast=6.3\%$ ($0.28\,\mathrm{dB}$). Our results highlight the importance of accounting for loss-induced lattice contraction in inner decoding and demonstrate that quadrature compensation enhances the photon-loss tolerance of surface-GKP codes for both high- and moderate-quality GKP states, providing a route toward more photon-loss-robust optical quantum computing.

quant-pharXiv:2611.00694Nov 3, 2026

10%

, which is $1\ifmmode\times\else\texttimes\fi{}{10}^{6}$ times better than previous methods. This proposal will become a powerful tool for advancing optical quantum computers from the proof-of-principle stage to practical application.

ε=0.01

and

ε=0.05

, corresponding to GKP squeezing of

20

and

13\,\mathrm{dB}

, the estimated thresholds are

γ^\ast=5.5\%

(

0.24\,\mathrm{dB}

) and

γ^\ast=5.9\%

(

0.26\,\mathrm{dB}

), respectively. We then introduce an anti-photon-loss inner decoder that compensates for the contraction of the measured quadrature. It increases the corresponding threshold estimates to

γ^\ast=9.8\%

(

0.45\,\mathrm{dB}

) and

γ^\ast=6.3\%

(

0.28\,\mathrm{dB}

). Our results highlight the importance of accounting for loss-induced lattice contraction in inner decoding and demonstrate that quadrature compensation enhances the photon-loss tolerance of surface-GKP codes for both high- and moderate-quality GKP states, providing a route toward more photon-loss-robust optical quantum computing.