Finite-energy effects in two GKP qubit operations. (a) Momentum marginal distribution P (p) of both oscillators starting in the state |0 ∆ before (left) and after (right) the CZ gate. The output distributions get broadened as the operation corresponds to a continuous set of displacements that spreads each oscillator's wave function conditioned on the position of the other one. (b) Wigner quasiprobability distribution, showing broadening only in the p quadrature. (c) Peak widths as a function of input width, showing clearly the linear relation. (d) The physical and logical infidelity between the input and output states as a function of the energy parameter ∆.

Contexts in source publication

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... with κ, it is natural to set this parameter as low as possible. In practice, κ = ∆/ √ 2 is sufficient enough. Fig for the parameters ∆ = κ = ∆ sim / √ 2 with the initial naive ones ∆ = κ = ∆ sim used so far. As above the input state is |Φ + ∆sim with ∆ sim ∈ (0.1, 0.4) that has been beforehand stabilized for 15 rounds and subjected to a CZ gate. Fig. S21 presents how this optimization would modify the trajectories of the system's state and their statistics. In these simulations, the first round of stabilization consists of two cycles of 2) . Since the stabilized state has now a larger energy parameter in the momentum space we adiabatically reduce it during the next nine rounds by ...

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... the wrong outcome using R z,(∆/ √ 2,∆/ √ 2) is ∼ 5% lower (for ∆ = 0.3) than with R z,(∆,∆) we reduced by almost 10% the probability of a false positive error in the first cycle in either of the two subsystems. Moreover, in this setting the fidelity with the desired state also increased compared to the naive correction procedure used above. Fig. S21(c) shows that the infidelity for trajectories with 0 or 2 outcomes is in average ∼ 3 − 4 times lower than in the situation depicted in Fig. S19 and the total average infidelity over all the shots is twice as low as ...