Scalable Multimode Entangling Operations for Multimode Grid Codes

Bosonic grid codes can achieve logical error rates below 10⁻⁹ for physical error rates around 10⁻³ under photon loss using near-optimal recovery [1]. Extending grid codes to multiple modes mitigates the impact of errors in auxiliary systems used for logical operations [2]. A first step in this direction was the recent demonstration that the two-mode Tesseract code enables error detection not accessible in single-mode grid codes [3]. Theory further suggests that increasing the number of modes enhances resilience to auxiliary errors.

 

Here, we demonstrate entangling operations between an auxiliary transmon and four bosonic modes of a multimode prototype using multimode echoed conditional displacements (ECD) [4]. Frequency-domain multiplexing allows implementing the gate with no additional hardware overhead. The fidelity, extracted from an error-amplification protocol, remains independent of the number of modes for a fixed Euclidean displacement in phase space. These results establish a foundation for scalable multimode bosonic encodings with enhanced robustness to auxiliary errors.

 

[1] G. Zheng et al., Phys. Rev. Lett. 132, 250602 (2024)

[2] B. Royer, S. Singh, S. M. Girvin, PRX Quantum 3, 010335 (2022)

[3] Nord Quantique, https://www.nordquantique.ca/en/news/suppressing-logical-errors-with-multimode-quantum-error-correction

[4] D. Lachance-Quirion et al., Quantum gate for control and entanglement of multimode systems, US 19067306, patent pending