Quantum error correction using squeezed Schrödinger cat states

Abstract

Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schrödinger cat codes -based on the superposition of two coherent states with opposite displacements -can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by photon loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e. cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by photon loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both photon loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of stateof-the-art quantum hardware platforms, the squeezed cat code has a resilience to photon-loss errors that significantly outperforms that of the conventional cat code.

Quantum capacity and codes for the bosonic loss-dephasing channel

“…This agrees with the known fact that the performance of two-legged cat codes improves as their mean energy increases [20,[30][31][32]. Squeezed two-legged cat codes have also been found to provide limited protection against photon loss in addition to dephasing [29].…”

Quantum capacity and codes for the bosonic loss-dephasing channel

“…In the case of pure-dephasing noise (Figs. 2(a) and 2(f)), we observe that two-legged cat codes and squeezed two-legged cat codes [29] provide optimal protection. Similarly to the GKP codes in the pure loss case, these codes saturate the energy constraint.…”

All-optical generation of deterministic squeezed Schrödinger-cat states

“…then we can get the expressions of the above squeezed Schrödinger-cat states according to the fitting formulas in Eqs. (38)(39)(40). Specifically, for the SECS, Q ≈ 5.42 + 3.24N ; (43) for the SOCS Q ≈ −4.40N −1 − 3.01N − 1 2 + 1.28 + N ; (44) and for the SYSCS…”

“…However, the particularly promising approach is to squeeze a non-Gaussian state, and the squeezed Schrödinger-cat state is the one that has a large Mandel Q parameter, which can have a threefold improvement over the optimal Gaussian state [38]. Besides, the squeezed Schrödinger-cat states also have been shown to have a significant role in quantum error correction [40]. For quantum technologies with squeezed Schrödinger-cat states, the preparation fidelity is crucial for realizing quantum advantage.…”