Enabling Modularity for Spin Qubits via Driven Quantum Dot-Mediated Entanglement

Abstract

We present an approach for entangling spin qubits via capacitive coupling mediated by an ac electric field-driven multielectron mediator quantum dot. To illustrate this method, we consider the case of a driven two-electron dot that mediates entanglement between resonant exchange qubits defined in three-electron triple quantum dots, which enable direct capacitive coupling and interaction with microwave fields via intrinsic spin-charge mixing. The method can also be applied to other types of spin qubits that can be coupled capacitively. We show that this approach leads to rapid, single-pulse universal entangling gates for resonant exchange qubits that are activated via the drive on the mediator dot. Unlike conventional tunneling-based two-qubit gates between exchange-only qubits, the capacitive interaction-based gates we describe do not require an extensive sequence of pulses to mitigate leakage. We describe how this drive-activated local entangling approach can be integrated with the driven sideband-based long-range approach for cavity-mediated entangling gates developed in our previous work in order to enable modularity for spin-based quantum information processing.

Figures (7)

• Figure 1: Schematic illustration of the quantum dot system investigated in this work for driven dot-mediated capacitive interaction of two resonant exchange (RX) qubits, along with the level diagram and associated parameters in the extended multiorbital Hubbard model description of the system [Eq. \ref{['eq:Hl']}]. The curved arrows between orbitals in the level diagram indicate the coupling terms in the Hamiltonian.
• Figure 2: Low-energy spectrum of the two-level, two-electron dot (see Appendix \ref{['sec:MEQDdipole']} for details) that mediates qubit-qubit entanglement in the approach presented in this work. (a) Spectrum of $H_{c}^{\prime}$ [Eq. (\ref{['eq:Hcpr']})] in the absence of driving (adapted from Ref. Srinivasa2015). (b) Spectrum of the driven mediator dot in the rotating frame and dressed singlet basis, as described by $\tilde{H}_{M}$ [Eq. (\ref{['eq:HMtilde']})].
• Figure 3: Charge stability diagrams for the triple dot systems (see Fig. \ref{['fig:RX-MEQD']}) associated with each RX qubit (left), represented by the charge configuration $\left(n_{\alpha1},n_{\alpha2},n_{\alpha3}\right)$ with the axes defined by Eq. (\ref{['eq:RXepsVm']}), and the center three dots (right), represented by $\left(n_{a3},n_{c},n_{b1}\right)$ with the axes defined by Eq. (\ref{['eq:centerTQDepsVm']}). The RX qubit index $\alpha$ has been suppressed in the axis labels of the left plot for notational simplicity. The fixed parameters used in the RX qubit triple dot (left) charging diagram are $V=0.33U$ and $\epsilon_{2}=0.90U,$ while those used in the center triple dot (right) charging diagram are $U_{c}=0.91U,$$V_{c}=0.28U,$ and $\epsilon_{m}=2.1U,$ where $U\sim1\ {\rm meV}$Malinowski2019.
• Figure 4: Strength $\mathcal{K}_{ab}$ of the driven dot-mediated capacitive interaction between RX qubits as a function of mediator dot size $\lambda$ for multiple values of the qubit-mediator dot separation $a$ and fixed electric field drive amplitude $\mathcal{E}_{M}=2\ {\rm V/m},$ calculated using the analysis and parameters given in Sec. \ref{['subsec:parameters_Kab']}.
• Figure 5: Fidelity $F$ for the driven dot-mediated gate generated by the interaction $V^{\prime}$ according to Eq. (\ref{['eq:meqpr']}) as a function of the qubit decay rate $\gamma$ and the mediator dot decay rate $\gamma_{M},$ calculated using Eq. (\ref{['eq:F']}) with the initial state $\left| \psi_{i}\right>=\left| eg,M_{-}\right>.$ The ideal evolution is given by $U_{xx}$ [Eq. (\ref{['eq:Uxx']})], which is equivalent to the action of $U_{i{\rm SW}}^{1/2}$ within the $\left\{ \left| eg,M_{-}\right>,\left| ge,M_{-}\right>\right\}$ subspace.