Encoding a qubit in an oscillator

By Daniel Gottesman, Alexei Y. Kitaev, John Preskill. 2000

1,338 citations recorded by the source corpus.

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.

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

View Paper: https://www.semanticscholar.org/paper/49325b4d95f0fca3500ca1ce60c712a9ddf8fbfd

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum computing and the entanglement frontier (2012, background): “15,16 Here “adaptive” means that subsequent operations can be conditioned on the outcomes of earlier measurements.”
Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. (2013, methodology): “…motivated model of encoded states in which the Wigner function for an ideal GKP-encoded state, which is a regular lattice of ± δ functions [32], is replaced by a corresponding lattice of sharp ± Gaussian spikes, each of which has the same 2 × 2 covariance matrix η , which we call the…”
Deterministic quantum teleportation between distant atomic objects (2012, background): “While probabilistic teleportation, in which entanglement is distributed by photon counting [7, 15], is capable of reaching distances of many km [2, 16], the power of continuous variable (cv) teleportation is that it succeeds deterministically in every attempt [8, 10], that it is capable of teleporti”
The computational complexity of linear optics (2010, methodology): “There have been ingenious proposals for working around these problems, including the schemes of Knill, La.amme, and Milburn [22] and Gottesman, Kitaev, and Preskill [14], both of which require the additional resource of adaptive measurements.”
Superconducting nanocircuits for topologically protected qubits (2008, background): “The effect of this coupling is equivalent to the fault-tolerant R (π/4)= exp ( i π/4 σ z ) unitary operatio”
Fusion-based quantum computation (2021, methodology): “With GKP encoded qubits fusion can be implemented with homodyme measurements [11].”