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A. L. Grimsmo, J. Combes, and B. Q. Baragiola, “Quantum computing with rotation-symmetric bosonic codes,” arXiv:1901.08071 [quant-ph] (2019) , arXiv: 1901.08071
Original
1901
Earlier work this paper cites.
B. Q. Baragiola, G. Pantaleoni, R. N. Alexander, A. Karanjai, and N. C. Menicucci, “All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code,” arXiv:1903.00012 [quant-ph] (2019) , arXiv: 1903.00012
Original
1903
Earlier work this paper cites.
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:1907.12487 [quant-ph] (2019) , arXiv: 1907.12487
Original
1907
Earlier work this paper cites.
V. V. Albert, J. P. Covey, and J. Preskill, “Robust encoding of a qubit in a molecule,” arXiv:1911.00099 [cond-mat, physics:physics, physics:quant-ph] (2019) , arXiv: 1911.00099 version: 1
Original
1911
Earlier work this paper cites.
R. L. Stratonovich, “On distributions in representation space,” Soviet Physics JETP-USSR 4
1957
Earlier work this paper cites.
E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A 55
1997
Earlier work this paper cites.
D. Gottesman, “The heisenberg representation of quantum computers,” arXiv:quant-ph/9807006 (1998) , arXiv: quant-ph/9807006
1998
Earlier work this paper cites.

Similar

S. Heiss and S. Weigert, “Discrete Moyal-type representations for a spin,” Physical Review A 63
2000
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D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,” Physical Review A 64
2001
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K. Audenaert and B. De Moor, “Optimizing completely positive maps using semidefinite programming,” Physical Review A 65
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S. Glancy and E. Knill, “Error analysis for encoding a qubit in an oscillator,” Physical Review A 73
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S. Pirandola, S. Mancini, S. L. Braunstein, and D. Vitali, “Minimal qudit code for a qubit in the phase-damping channel,” Physical Review A 77
2008
Cited alongside, same era.

Then

D. H. Sattinger and O. L. Weaver, Lie groups and algebras with applications to physics, geometry, and mechanics , Vol. 61 (Springer Science & Business Media, 2013)
2013
Later among the works it cites.
M. Fallbacher, “Breaking classical Lie groups to finite subgroups - an automated approach,” Nuclear Physics B 898
2015
Later among the works it cites.
D. J. Weigand and B. M. Terhal, “Generating grid states from Schrödinger-cat states without postselection,” Physical Review A 97
2018
Later among the works it cites.
K. Noh, V. V. Albert, and L. Jiang, “Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes,” IEEE Transactions on Information Theory 65
2019
Later among the works it cites.
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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2020

Encoding a qubit in a spin

Gross, Jonathan A.

Understand

I present a new approach for designing quantum error-correcting codes that guarantees a physically natural implementation of Clifford operations.

Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in an oscillator, in which Clifford operations may be performed via Gaussian unitaries, this approach yields new schemes for encoding a qubit in a large spin in which single-qubit Clifford operations may be performed via spatial rotations.
I construct all possible examples of such codes, provide universal-gate-set implementations using Hamiltonians that are at most quadratic in angular-momentum operators, and derive criteria for when these codes exactly correct physically relevant noise channels to lowest order, illustrating their performance numerically for specific low-dimensional examples.

Built on

A. L. Grimsmo, J. Combes, and B. Q. Baragiola, “Quantum computing with rotation-symmetric bosonic codes,” arXiv:1901.08071 [quant-ph] (2019) , arXiv: 1901.08071
Original
1901
Earlier work this paper cites.
B. Q. Baragiola, G. Pantaleoni, R. N. Alexander, A. Karanjai, and N. C. Menicucci, “All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code,” arXiv:1903.00012 [quant-ph] (2019) , arXiv: 1903.00012
Original
1903
Earlier work this paper cites.
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:1907.12487 [quant-ph] (2019) , arXiv: 1907.12487
Original
1907
Earlier work this paper cites.
V. V. Albert, J. P. Covey, and J. Preskill, “Robust encoding of a qubit in a molecule,” arXiv:1911.00099 [cond-mat, physics:physics, physics:quant-ph] (2019) , arXiv: 1911.00099 version: 1
Original
1911
Earlier work this paper cites.
R. L. Stratonovich, “On distributions in representation space,” Soviet Physics JETP-USSR 4
1957
Earlier work this paper cites.
E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A 55
1997
Earlier work this paper cites.
D. Gottesman, “The heisenberg representation of quantum computers,” arXiv:quant-ph/9807006 (1998) , arXiv: quant-ph/9807006
1998
Earlier work this paper cites.

Similar

S. Heiss and S. Weigert, “Discrete Moyal-type representations for a spin,” Physical Review A 63
2000
Cited alongside, same era.
D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,” Physical Review A 64
2001
Cited alongside, same era.
K. Audenaert and B. De Moor, “Optimizing completely positive maps using semidefinite programming,” Physical Review A 65
2002
Cited alongside, same era.
S. Glancy and E. Knill, “Error analysis for encoding a qubit in an oscillator,” Physical Review A 73
2006
Cited alongside, same era.
S. Pirandola, S. Mancini, S. L. Braunstein, and D. Vitali, “Minimal qudit code for a qubit in the phase-damping channel,” Physical Review A 77
2008
Cited alongside, same era.

Then

D. H. Sattinger and O. L. Weaver, Lie groups and algebras with applications to physics, geometry, and mechanics , Vol. 61 (Springer Science & Business Media, 2013)
2013
Later among the works it cites.
M. Fallbacher, “Breaking classical Lie groups to finite subgroups - an automated approach,” Nuclear Physics B 898
2015
Later among the works it cites.
D. J. Weigand and B. M. Terhal, “Generating grid states from Schrödinger-cat states without postselection,” Physical Review A 97
2018
Later among the works it cites.
K. Noh, V. V. Albert, and L. Jiang, “Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes,” IEEE Transactions on Information Theory 65
2019
Later among the works it cites.
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

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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C. Cafaro, F. Maiolini, and S. Mancini, “Quantum stabilizer codes embedding qubits into qudits,” Physical Review A 86

2012

Cited alongside, same era.

See supplemental material

Cited in the paper.

2019

Later among the works it cites.

T. Dokchitser, “GroupNames,” https://people.maths.bris.ac.uk/~matyd/GroupNames/index.html (2020), [Online; accessed 2-April-2020]

2020

Closest in time.