Enhanced energy relaxation process of a quantum memory coupled to a superconducting qubit

For quantum information processing, each physical system has a different advantage as regards implementation, so hybrid systems that benefit from the advantage of several systems would provide a promising approach. One common hybrid approach involves combining a superconducting qubit as a controllable qubit and another quantum system with a long coherence time as a memory qubit. The use of a superconducting qubit gives us excellent controllability of the quantum states, and the memory qubit is capable of storing information for a long time. It has been believed that selective coupling can be realized between a superconducting qubit and a memory qubit by tuning the energy splitting between them. However, we have shown that this detuning approach has a fundamental drawback as regards energy leakage from the memory qubit. Even if the superconducting qubit is effectively separated by reasonable detuning, a non-negligible incoherent energy relaxation in the memory qubit occurs via residual weak coupling when the superconducting qubit is affected by severe dephasing. This energy transport from the memory qubit to the control qubit can be interpreted as the appearance of the anti–quantum Zeno effect induced by the fluctuation in the superconducting qubit. We also discuss possible ways to avoid this energy relaxation process, which is feasible with existing technology.

Figure 1

Schematic of the enhanced relaxation of the memory qubit via imperfect decoupling from a superconducting qubit. We assume that the superconducting qubit is affected by decoherence, while there is no direct coupling between the environment and the memory qubit. Since we can tune the energy of the superconducting qubit, it is possible to make the energy of the superconducting qubit on resonance with the energy of the memory qubit to transfer the information. It is also possible to tune the energy of the superconducting qubit far from the resonance when keeping the stored information. However, this type of selective coupling has a significant drawback during the information storage in the memory qubit, as explained in the main text.

Figure 2

A plot of the relaxation time of the memory qubit induced by the anti-Zeno effect of as a function of the detuning. The discrete plot denotes a numerical result and the continuous line denotes an analytical result. We set parameters as $T_2^{\left(\text{sc}\right)}=10$ ns for the dephasing time of the superconducting qubit and at $g/2\pi =25$ MHz for the coupling strength between the qubits. These results show that the relaxation time is quadratically dependent on the energy detuning.

Figure 3

The population decay of the memory qubit induced by the anti-Zeno effect as a function of a time. The coupling constant between qubits is set at $2\pi \times 25$ MHz. From the bottom, we plot a numerical result with $T_1^{\left(\text{sc}\right)}=400$ ns and $T_2^{\left(\text{sc}\right)}=10$ ns, a numerical result with $T_2^{\left(\text{sc}\right)}=10$ and $T_1^{\left(\text{sc}\right)}=\infty$, and a numerical result with $T_2^{\left(\text{sc}\right)}=\infty$ and $T_1^{\left(\text{sc}\right)}=400$ ns.

Figure 4

The relaxation time of the memory qubit induced by the anti-Zeno effect. The horizontal line denotes the dephasing time of the superconducting qubit. Dots correspond to numerically obtained data. Also, continuous lines are drawn through the points as a guide to the eye. We set the relaxation time of the superconducting qubit at $T_1^{\left(\text{sc}\right)}=400$ ns and the coupling constant between qubits at $g/2\pi =25$ MHz. The lowest line is that where the detuning $\Delta /2\pi$ is 600 MHz, and the other lines are where $\Delta /2\pi =800,1000,$ and 1200 MHz, respectively.