Noise-resilient nonadiabatic geometric quantum computation for bosonic binomial codes

Abstract

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.

Figures (7)

• Figure 1: (a) Configuration of the superconducting system, which consists of a 3D superconducting microwave cavity $C_0$ capacitively coupled to a superconducting flux qutrit (a three-level system) $Q_0$, where the orange cylinder represents the coaxial cavity of the 3D superconducting microwave cavity, the yellow ellipse indicates the coupling port between the cavity and the right-side superconducting qubit, and the red rectangle denotes the Josephson junction of the superconducting qubit. (b) Energy level structure of the qutrit is shown above. The lowest three energy levels of the qutrit are labeled as $|g\rangle_q$, $|e\rangle_q$, and $|f\rangle_q$, respectively.
• Figure 2: Control fields $\Omega_x(t)$ and $\Omega_y(t)$ versus $t/T$.
• Figure 3: Dynamic phase $\theta_d^-(t)$ and geometric phase $\theta_g^-(t)$ versus $t$ in the implementation of geometric quantum gates.
• Figure 4: Average fidelity $F_g(t)$ versus $t$ for different gates, where the system is governed by (a) the effective Hamiltonian $H_e$ and (b) the full Hamiltonian $H$.
• Figure 5: Final average fidelity $\overline{F}_g(T)$ versus the systematic error rate $\varepsilon$ for different quantum gates.