Performance and structure of single-mode bosonic codes

By Victor V. Albert, Kyungjoo Noh, K. Duivenvoorden, Dylan J. Young, R. T. Brierley, P. Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, Steven M. Girvin and 2 more. 2017

275 citations recorded by the source corpus.

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/01c43ab213317e08dd54617d6ce395a602f6b65b

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Citations in the corpus

Fast universal control of an oscillator with weak dispersive coupling to a qubit (2021, background): “This is important in applications where these spurious couplings can cause decoherence and distortion of encoded states, especially during idling periods [39].”
Quantum information processing and quantum optics with circuit quantum electrodynamics (2020, background): “Such brute-force approaches are viable up to around 1,000 qubits — a loose estimate — limited primarily by packaging, signal routing and the size of dilution refrig-a”
Advances in quantum cryptography (2019, unknown): “[627–629] by using the Gottesman-Preskill-Kitaev (GKP) states [630], realizable with various technologies [631–635].”
Robust Encoding of a Qubit in a Molecule (2019, background): “The variance of ̄̀, σ ̄̀ = 〈r̃| L̂ |r̃〉 1/2 − ̄̀2 = O ( ̄̀2 ) , is also similar to GKP states (for the latter, photon number moments satisfy a geometric distribution [3]).”
Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code (2019, background): “Notably, bosonic quantum error correction [5] has recently risen as a hardware-efficient route to implement quantum error correction (QEC) by taking advantage of the infinite-dimensionality of a bosonic Hilbert space.”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, background): “This includes weak levels of photon loss, the dominant error mode for quantum communication [64, 65].”