Nonadiabatic geometric control of bosonic binomial codes

Clemens Gneiting

Dong-Sheng Li, Yang Xiao, Yu Wang +5 more

The binomial code is renowned for its parity-mediated loss immunity and loss-error recoverability, while geometric phases are widely recognized for their intrinsic resilience against noise. Capitalizing on their complementary merits, we propose a noise-resilient protocol to realize Nonadiabatic geometric quantum computation with binomial codes in a superconducting system composed of a microwave cavity %off-resonantly dispersively coupled to a %three-level qutrit. The control field %geometric quantum computation is designed by %combining geometric phases, integrating reverse engineering and optimal control. This design provides a customized control protocol featuring strong error-tolerance and inherent noise-resilience. Using experimentally accessible parameters in superconducting systems, numerical simulations show that the protocol yields relatively high average fidelity for geometric quantum gates based on binomial code, even in the presence of parameter fluctuations and decoherence. Thus, this protocol may provide a practical approach for realizing reliable Nonadiabatic geometric quantum computation with binomial codes in current technology.

Luyan Sun, Ling Hu, Yuwei Ma +10 more

Yifang Xu, Yilong Zhou, Lida Sun +12 more

High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering approach for implementing controlled-phase gates for binomially encoded logical qubits. This method leverages the structural simplicity of geometric drives to reduce the numerical optimization dimensionality while fully incorporating system nonlinearities, enabling fast and high-fidelity logical operations. As an example, we experimentally demonstrate a process fidelity of 97.4$\pm$0.8\% for a controlled-Z gate between two binomial codes, surpassing all previously reported two-logical-qubit gates in bosonic codes. This work demonstrates that geometric phase engineering provides an effective and experimentally feasible route to fast, high-fidelity logical operations in bosonic quantum processors.

Yi‐Hao Kang, Jie Song, Yan Xia

We propose a scheme to realize error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering. A strong Kerr nonlinearity restricts the evolution in a computational subspace of the binomial code and a two-photon squeezing drive provides the connections between the logical states. The effective Hamiltonian possesses SU(2) dynamic structure and is analyzed through reverse engineering based on a dynamic invariant. By combining reverse engineering with the optimal control method, we find the evolution paths for nonadiabatic geometric quantum computation and derive the control field robust against the systematic error. Numerical simulations show that the scheme holds excellent resistance to the systematic error and is still well implemented in the presence of resonator leakage with the current superconducting nonlinear resonator technology. Therefore, the scheme may provide a promising approach for accurate nonadiabatic binomial-code geometric quantum computation.

Zakaria Giunashvili