The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve universal quantum computing. However, there is a disconnect between the noise model that GKP qubits are in theory designed to correct—uniform random displacement errors—and the conditions that affect GKP qubits in superconducting devices in practice: realistic noise channels, logical gates, and inefficient measurements. In this work we bridge this gap in three ways. First, we approximate the effect loss and dephasing on approximate GKP codestates using a random displacement channel, and show that this approximation matches well with numerics. Second, we analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder following the implementation of each gate can reduce the gate infidelity by multiple orders of magnitude. Finally, we consider the effect of homodyne measurement inefficiencies on logical state readout and analyze a scheme to improve the measurement efficiency using the theory of quantum trajectories.
Optical quantum memories based on Er, with its telecom-compatible optical transition, could benefit quantum networking and linear optics quantum computing applications, if the requirements for high memory efficiency, fidelity, and storage capacity can be met simultaneously. Here, we demonstrate the first high efficiency memory in Er, with spin-state storage for 25 μs and classical efficiencies up to 81%, using the rephased amplified spontaneous emission protocol. We show quantum storage along with high-fidelity entanglement of an output state and the state stored in memory, and a demonstration of multiplexing, storing 70 modes in the temporal domain. We use the results to discuss how, with modifications to the pulse sequences and experimental geometry only, the performance can be improved to meet the requirements for practical quantum applications.
