Characterization of a quantum bus between two driven qubits

TL;DR

The paper addresses implementing high-fidelity two-qubit gates when qubits and their common bus have mismatched frequencies by dressing each qubit with an external drive to achieve selective coupling to a low-frequency harmonic oscillator. Using a Lindblad quantum master equation, it analyzes both the qubit readout via a state-dependent shift of the bus resonance and the generation of a $\sqrt{i\mathrm{SWAP}}$-gate mediated by the bus, with gate time $t_{\mathrm{int}}=\pi|\Delta_R|/(4g^2)$ under dispersive conditions. Key findings show that dressed qubits yield more robust readout than bare qubits, especially at higher temperatures, and identify optimal detuning and rise-time ranges to maximize gate fidelity, while noting practical fidelity limits from the rotating-wave and dispersive approximations. The work provides practical guidance for implementing high-fidelity gates in nanoscale mechanical-resonator platforms and offers a general, tunable approach applicable to various qubit technologies for scalable quantum computation.

Abstract

We investigate the use of driven qubits coupled to a harmonic oscillator to implement a $\sqrt{i\mathrm{SWAP}}$-gate. By dressing the qubits through an external driving field, the qubits and the harmonic oscillator can be selectively coupled, allowing for the measurement of individual qubit states, as well as leading to effective qubit-qubit interactions. We compare the qubit readout on bare and dressed qubits, and demonstrate that when coupled to low-frequency resonators, dressed qubits provide a more robust readout than bare qubits in the presence of damping and thermal effects. Furthermore, we study the impact of various system parameters on the fidelity of the two-qubit gate, identifying an optimal range for quantum computation. Our findings guide the implementation of high-fidelity quantum gates in experimental setups, for example those employing nanoscale mechanical resonators.

Figures (5)

• Figure 1: (a) Dressing of a qubit through a driving field with frequency $\omega_d$ and amplitude $\Omega_R$. (b) Sketch of the harmonic-oscillator mediated qubit-qubit coupling.
• Figure 2: (a) Noise power spectral density for different temperatures for (a) a dressed qubit with $\omega_q=50\omega_h$, $\Delta=0$ and $\Delta_R=0.05\omega_h$, and (b) a bare qubit with $\omega_q=1.05\omega_h$. The solid lines correspond to the initial state $|1\rangle$ and the dashed lines to the initial state $|0\rangle$. The vertical dashed lines indicate the maximum of the spectral density. Time evolution of the qubit state for (c) dressed and (d) bare qubits, for thermal occupation $n_{\mathrm{th},h}=0$. All plots use the parameters $g=5 \cdot 10^{-3}\omega_h$, $\gamma_q=10^{-4}\omega_h$ and $\gamma_h=10^{-4}\omega_h$.
• Figure 3: Evolution of the qubit expectation values for an initial state $|10\rangle$ for thermal excitation amplitudes (a) $n_{\mathrm{th},h}=0$ and (b) $n_{\mathrm{th},h}=2$. Entanglement between the different subsystems as a function of time for (c) $n_{\mathrm{th},h}=0$ and (d) $n_{\mathrm{th},h}=2$. All plots use the parameters $\Delta=0$, $\Delta_R=5 \cdot 10^{-2}\omega_h$, $g=5 \cdot 10^{-3}\omega_h$, $\gamma_q=10^{-6}\omega_h$ and $\gamma_h=10^{-6}\omega_h$.
• Figure 4: (a) Fidelity of the $\sqrt{i\mathrm{SWAP}}$-gate as a function of the driving field detuning and the Rabi detuning. The parameters used are $n_{\mathrm{th},h}=0$, $g=5 \cdot 10^{-3}\omega_h$, $\gamma_q=10^{-6}\omega_h$ and $\gamma_h=10^{-6}\omega_h$. (b) Fidelity of the quantum gate as a function of the qubit and harmonic oscillator dampings. The parameters used are $n_{\mathrm{th},h}=0$, $\Delta=0$, $\Delta_R=5 \cdot 10^{-2}\omega_h$ and $g=5 \cdot 10^{-3}\omega_h$. (c) Depiction of the dressed qubit transition frequency for a nonvanishing dressing rise time, and (d) fidelity of the $\sqrt{i\mathrm{SWAP}}$-gate as a function of the rise time. All plots use the parameters $n_{\mathrm{th},h}=0$, $\Delta=0$, $\gamma_q=10^{-6}\omega_h$ and $\gamma_h=10^{-6}\omega_h$.
• Figure 5: Generation of a Bell state in the computational basis.