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2019

Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes

Wan, Kwok Ho, Neville, Alex, Kolthammer, W. S.

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We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys.

Rev.
A {\bf 73}, 012325 (2006)].
We show that combining multiple rounds of error-syndrome extraction with Bayesian estimation offers enhanced protection of GKP-encoded qubits over comparible single-round approaches.

Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes · Around

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Ben Q. Baragiola, Giacomo Pantaleoni, Rafael N. Alexand er, Angela Karanjai, and Nicolas C. Menicucci, “All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code,” arXiv e-prints , arXiv:1903.00012 (2019), arXiv:1903.00012 [quant-ph]
Original
1903
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P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys-Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf, L. Frunzio, M. Mirrahimi, and M. H. Devoret, “A stabilized logical quantum bit encoded in grid states of a superconducting cavity,” arXiv e-prints , arXiv:1907.12487 (2019), arXiv:1907.12487 [quant-ph]
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1907
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Giacomo Pantaleoni, Ben Q. Baragiola, and Nicolas C. Menicucci, “Modular Bosonic Subsystem Codes,” arXiv e-prints , arXiv:1907.08210 (2019), arXiv:1907.08210 [quant-ph]
Original
1907
Earlier work this paper cites.
Kyungjoo Noh and Christopher Chamberland, “Fault-tolerant bosonic quantum error correction with the surface-GKP code,” arXiv e-prints , arXiv:1908.03579 (2019), arXiv:1908.03579 [quant-ph]
Original
1908
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Ilan Tzitrin, J. Eli Bourassa, Nicolas C. Menicucci, and Krishna Kumar Sabapathy, “Towards practical qubit computation using approximate error-correcting grid states,” arXiv e-prints , arXiv:1910.03673 (2019), arXiv:1910.03673 [quant-ph]
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1910
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A. M. Steane, “Active stabilization, quantum computation, and quantum state synthesis,” Phys. Rev. Lett. 78
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Seth Lloyd and Samuel L. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82
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Daniel Gottesman, Alexei Kitaev, and John Preskill, “Encoding a qubit in an oscillator,” Phys. Rev. A 64
2001
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Samuel L. Braunstein and Peter van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77
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S. Glancy and E. Knill, “Error analysis for encoding a qubit in an oscillator,” Phys. Rev. A 73
2006
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Mile Gu, Christian Weedbrook, Nicolas C. Menicucci, Timothy C. Ralph, and Peter van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79
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2009
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A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement, A Hybrid Approach to Optical Quantum Information Processing (Wiley, 2011)
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Jun-ichi Yoshikawa, Shota Yokoyama, Toshiyuki Kaji, Chanond Sornphiphatphong, Yu Shiozawa, Kenzo Makino, and Akira Furusawa, “Invited Article: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing,” APL Photonics 1
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2017
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Kosuke Fukui, Akihisa Tomita, Atsushi Okamoto, and Keisuke Fujii, “High-threshold fault-tolerant quantum computation with analog quantum error correction,” Phys. Rev. X 8
2018
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C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. P. Home, “Encoding a qubit in a trapped-ion mechanical oscillator,” Nature 566
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