Change in bit-flip times of Kerr parametric oscillators caused by their interactions

Abstract

We experimentally investigate how interactions between Kerr parametric oscillators (KPOs) degrade their bit-flip times, where a bit flip is defined as a transition between the two degenerate ground states of a KPO. Interactions between KPOs cause quantum states of KPOs to leak outside the computational subspace, leading to bit flips. Bit flips degrade fidelity and pose a significant problem for KPO-based quantum information processing. We performed an experiment in which a weak microwave signal is injected into one KPO to emulate photon injection from another KPO, and find that the bit-flip time decreases by an order of magnitude due to induced excitations, depending on the frequency and power of the injected signal. Methods to mitigate the decrease in bit-flip times caused by interactions between KPOs are discussed, including adjusting the pump frequencies, coherent-state amplitudes, and couplings between KPOs. These findings provide valuable insights for scaling up KPO-based quantum computers.

Figures (9)

• Figure 1: Schematic diagram of the metapotential of a KPO, together with the eigenenergies $\omega_n$ of the Hamiltonian eigenstates $\ket{\psi_{n}}$, and the process of bit flip. Some higher excited states are not confined within the two wells. Eigenenergies are shown for a KPO with a coherent-state amplitude of $\alpha=2.8$, corresponding to the experiment in Sec. \ref{['sec:exp1b']}.
• Figure 2: (a) Optical micrograph of the KPO chip. Setup of the experiment in Sec. \ref{['sec:exp1b']} is shown. (b) Schematic diagram of the KPO chip. "X" symbols represent Josephson junctions.
• Figure 3: (a) Timing chart of the experiment. Pump and input signals are pulses with a trapezoidal envelope, where the output voltages of the respective AWGs are increased linearly in 0.2 $\mathrm{\mu s}$ from 0 V to their set values. (b) An example histogram of the $IQ$ values of KPO1 without input signal. The measurement data for 2.0 $\mathrm{\mu s}$ after the pump pulses have reached the plateau are used. A rotation is applied in the $IQ$ plane so that the two peaks are aligned in the horizontal axis, to account for the electrical delay of the pump signal and the readout signal. (c) Experimental result of bit-flip time without input signal. Upper panel shows the temporal change in the $I$ value of KPO1. A condition $I>0$ is applied for the first temporal bin, i.e. $0<t<2~\mathrm{\mu s}$, to select measurement trials with the KPO initially in primarily one of the two qubit states. Lower panel shows the evaluation of the bit-flip time. Symbol $\langle I \rangle$ represents the average of $I$ value for each temporal bin. The bit-flip time is evaluated using data for both $I>0$ and $I<0$ for the first temporal bin. The error of the bit-flip time represents statistical uncertainty. (d) Simulation result of bit-flip time without input signal. Upper panel shows the temporal change in the probability $\braket{ (a+{a^\dagger})/2 | \rho | (a+{a^\dagger})/2 }$ averaged over 1 $\mathrm{\mu s}$.
• Figure 4: (a) Experimental and (b) simulation results of the bit-flip time evaluation with an input signal with a detuning ${\Delta_\mathrm{in}}/2\pi=-204~\mathrm{MHz}$.
• Figure 5: Bit-flip time of a KPO with respect to ${\Delta_\mathrm{in}}$. Experimental (blue circle) and simulation (orange line) results are compared. Error bars represent statistical uncertainty. The results for the input-signal detuning in $-1~\mathrm{MHz}<{\Delta_\mathrm{in}}/2\pi<1~\mathrm{MHz}$ are removed, because the readout signal is indistinguishable from the reflection of the input signal and thus cannot be measured. The vertical dotted lines represent the KPO excitation energies ${\Delta\omega_{n,m}}\equiv\omega_m-\omega_n$, with the labels representing the indexes $nm$. The eigenenergies $\omega_n$ are calculated numerically from the Hamiltonian given in Eq. \ref{['eq:oneKPO']} using the operation parameters shown in Table \ref{['tab:parameters1b']}.