Teleportation-based Gottesman-Kitaev-Preskill (GKP) error correction typically assumes a decoherence-free GKP ancilla Bell pair, an idealization that is difficult to reconcile with the ubiquitous environmental decoherence in bosonic systems. Here, we analyze the performance of the GKP protocol subject to pure-dephasing processes, ubiquitous in realistic situations. We show that, under this class of interactions, teleportation, instead of projecting the input onto the GKP subspace, transforms GKP error correction into a correlated Pauli-Gaussian noise process that can accumulate over successive correction rounds. Thus, unlike in previously studied noisy GKP scenarios, the code no longer self-corrects. Moreover, repeated noisy GKP teleportation drives the encoded modes out of the logical subspace, progressively degrading the encoded codewords. We show that the resulting leakage rapidly saturates with the number of correction rounds. Finally, we investigate the implications of our results for motional-oscillator-based GKP error-correction platforms.
In order to solve practical problems on a quantum computer, it is necessary to use fault-tolerant quantum error correction schemes to overcome noise: the errors arising from imperfections in physical components. The Gottesman-Kitaev-Preskill (GKP) code aims at achieving this in a hardware efficient manner by encoding f...
Gottesman-Kitaev-Preskill (GKP) states are widely studied as a bosonic encoding for fault-tolerant quantum computing because small displacement errors can be identified and corrected through syndrome measurements. However, fault-tolerant operation requires substantially greater GKP squeezing than is currently available...
Özlem Erkılıç, Aritra Das, S. Swain et al.· 0 citations
We present the case of a Gottesman-Kitaev-Preskill (GKP) state-enhanced optical interferometry with detailed analysis of the phase sensitivity for both the SU(2) and SU(1,1) interferometers. The conventional quantum-enhanced SU(2) interferometer, employing coherent light at one input port and squeezed light at the othe...
Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories...
Brian Chung Hang Cheung, L. Kristensen, Frederik Nathan et al.· 0 citations
Quantum error-correcting codes require that the environment cannot distinguish relevant error processes acting on different codewords. In practice, residual Zeeman, Stark, or anharmonic interactions shift the underlying states, making errors distinguishable and weakening the conditions for perfect recovery. We study th...
Shubham P. Jain, Eric R. Hudson, Wesley C. Campbell et al.· 1 citation
Leakage, occurring when a qubit undetectably exits the computational subspace, poses a significant challenge for quantum error correction by inducing correlated errors in space and time. These correlations reduce both the code threshold and the effective code distance. To address this challenge, we introduce two zero-o...
Hanna Westerheim, Kaavya Sahay, S. Puri· 1 citation
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