Concurrent Fermionic Simulation Gate

TL;DR

This work tackles implementing flexible two-qubit gates by coupling iSWAP and CPHASE into a single, concurrent cfSim operation using bichromatic parametric drives on a transmon-coupler-transmon architecture. The authors develop a theoretical framework, starting from a toy two-qutrit model and extending to a full Kerr nonlinear circuit, to derive analytic expressions for the effective couplings and to quantify drive crosstalk and leakage. They demonstrate that both the iSWAP angle $\theta$ and the conditional phase $\varphi$ can be continuously tuned over their full ranges within a single gate, with fidelities typically exceeding $99.5\%$ and often above $99.9\%$ in simulations, depending on pulse shaping and non-RWA effects. The cfSim approach promises reduced circuit depth and greater versatility for fermionic simulations and other quantum algorithms on contemporary superconducting hardware, and it provides a pathway for practical, high-fidelity cfSim gates in the NISQ era.

Abstract

Introducing flexible native entanglement gates can significantly reduce circuit complexity. We propose a novel gate integrating iswap and cphase operations within a single gate cycle. We theoretically show one possible realization of this gate for superconducting qubits using bichromatic parametric drives at distinct frequencies. We show how various parameters, such as drive amplitudes and frequencies, can control entanglement parameters. This approach enhances gate versatility, opening pathways for more efficient quantum computing.

Figures (14)

• Figure 1: Setup of the system. Two transmons are coupled via a common coupler. The direct transmon-transmon coupling is ignored. Two parametric drives are applied to the two transmons separately. The two simultaneous drives induce a concurrent fSim gate between the two qubits, exchanging their excitations and adding a conditional phase.
• Figure 2: Schematic of BPD for cfSim gates. Relevant levels are shown. Two parametric drives target two transitions separately. When on resonance, drive frequency $\nu_{1,2}$ should match level detuning. Drive amplitudes $\Omega_{1,2}$ are not required to match detunings. For cfSim gates, we choose to drive 1 to resonantly drive $|01\rangle \leftrightarrow |10\rangle$ transition, therefore, $\nu_1=\omega_2-\omega_1$. The second drive is chosen to be near resonant with $|11\rangle \leftrightarrow|20\rangle$ or $|11\rangle \leftrightarrow |02\rangle$ transition. iSWAP and CPHASE transitions are happening simultaneously. Both iSWAP angle $\theta$ and conditional phase $\varphi$ can be controlled.
• Figure 3:
• Figure 4: Crosstalk effect of one drive on the other. Tthe first drive is fixed at $\Omega_1=150$ MHz, $\nu_1=\Delta_{010,100}$. The second drive is far detuned from $|010\rangle \leftrightarrow |100\rangle$ transition. We sweep drive amplitude $\Omega_2$ and frequency $\nu_2$ to see the crosstalk effects. \ref{['fig:g P crosstalk']}(a) Numerical simulation of static $\bar{g}_{100,010}$. The static coupling $\bar{g}_{100,010}$ is modulated by the second parametric drive. The dark stripes correspond to zeros of $J_0$ at $\Omega_2/\nu_2=2.40,5.52,8.65,\cdots$. The anomalous resonance around $\nu_2=225$ MHz is not captured by RWA formula, because at this spot $2\nu_2=\Delta_{010,100}$ and 2-photon transitions need to be included to account for this resonance. \ref{['fig:g P crosstalk']}(b) Numerical simulation of $P_{100}$ is consistent with analytical result except for 2-photon transition. \ref{['fig:g P crosstalk']}(c) Analytical calculation of static $\bar{g}_{010,100}$ using Eq. (\ref{['eq: g01 10 compact cross']}). The analytical plot confirms numerical simulation in (a). \ref{['fig:g P crosstalk']}(d) Analytical calculation of static $\bar{g}_{010,100}$. The x-axis is rescaled to illustrate the dependence of crosstalk effect on $\Omega_2/\nu_2$.
• Figure 5: Identify the optimal amplitude trajectory. The optimal trajectory is marked by the red dashed line. (a) Analytical plot of P11 vs $\Omega_2$ and $\nu_2$ while the first drive is resonant with $|01\rangle \leftrightarrow |10\rangle$ transition: $\Omega_1=150$ MHz, $\nu_1=\Delta_{01,10}$. The optimal drive amplitude $\Omega_2$ is defined as such that P11 is maximum. (b) Numerical plot of P11 vs $\Omega_2$ and $\nu_2$. It is consistent with the analytical plot. (c) Numerical plot of leakage vs $\Omega_2$ and $\nu_2$. We calculate the average leakage out of the computational subspace when the initial states are $|010\rangle$, $|100\rangle$ and $|110\rangle$. The optimal drive amplitude $\Omega_2$ can also be defined as such to minimize the leakage.