Enabling full localization of qubits and gates with a multi-mode coupler

TL;DR

The paper tackles leakage and crosstalk in superconducting qubits caused by conventional single-mode tunable couplers by introducing a multi-mode (two-mode) coupler architecture that enables full localization at idle and independent control over one- and two-excitation manifolds. It develops a theory based on locally confined qubit–coupler blocks and an overlap-based effective Hamiltonian to compute interactions in a frame-consistent manner, with a tunable mode–mode interaction parameter λ enabling both decoupling and on-demand coupling via shared coupler modes. A key result is the condition for full decoupling using a Bogoliubov transformation and a pair of circuit designs that realize this decoupling, along with analytic and numerical demonstrations of selective coupling: J00 can be strong for gates while J01 and J10 are suppressed, and iSWAP dynamics are shown to reach completion with minimal leakage. The work also outlines strategies for coupling many qubits through multi-mode couplers in modular quantum processors, illustrating practical pathways toward scalable, high-fidelity quantum gates. Overall, multi-mode couplers offer a flexible, localization-preserving route to suppress leakage and enable precise, scalable quantum logic in superconducting architectures.

Abstract

Tunable couplers are a key building block of superconducting quantum processors, enabling high on-off ratios for two-qubit entangling interactions. While crosstalk can be mitigated in idle mode, conventional single-mode couplers lack independent control over interactions in the one- and two-excitation manifolds, leading to unitary errors such as leakage during gate operations. Moreover, even at the nominal decoupled point, residual wavefunction delocalization persists, causing unintended qubit-qubit coupling. Here we propose a multi-mode tunable coupler that enables nonlinear control of interactions across excitation manifolds, achieving a high on-off ratio in the one-excitation manifold while suppressing coupling in the two-excitation manifold. The proposed design also realizes complete localization between qubits, providing perfect isolation at the decoupled point and opening new possibilities for scalable, high-fidelity quantum gates.

Figures (13)

• Figure 1: Comparison between a single-mode coupler (SMC) and a two-mode coupler (TMC). In (a) and (b), we compare wavefunction delocalization when interactions are turned off. We draw the spatial locations of qubit modes and coupler modes. For an SMC in (a), there is always-on delocalization of wavefunctions from one qubit to the other, whereas for a TMC in (b), this delocalization can be confined within the coupler. In (c), we compare the J coupling strength in the one-excitation subspace and the two-excitation subspace. The coupler states are dropped for simplicity. In the SMC case (left), residual interaction in the two-excitation subspace can not be independently controlled. In the TMC case (right), interactions in the two-excitation subspace can be suppressed to zero while the interaction in the one-excitation subspace is strong.
• Figure 2: Implementing qubit-coupler wavefunction localization. (a) Schematic of a system with $N$ qubits coupled through $M$ coupler modes. (b) Corresponding Hamiltonian decomposition (left), as in Eq. (\ref{['eq.H']}), into qubit and coupler subspaces and diagonalizing the coupler using the transformation $\mathcal{U}_c$. The qubit subspace will stay invariant however qubits are affected via the variation of qubit-coupler interactions.
• Figure 3: Partitioning of coupler modes. In the example shown, qubit $1$ couples to ${c_1,c_2}$ ($m_1=2$) and qubit $2$ couples to ${c_3,c_4}$ ($m_2=2$), yielding $N$ non-interacting qubit-coupler blocks. The ordering of the dressed modes after $\mathcal{U}_c$ need not match the original indexing.
• Figure 4: Localized decoupling at the Hamiltonian level. After an appropriate reordering of basis states, the full Hamiltonian becomes block-diagonal, with each block acting on a single qubit and its associated coupler modes. Consequently, each qubit evolves within its own invariant subspace (block).
• Figure 5: Overlap-based construction of effective couplings. Dressed eigenstates are projected onto a bare subspace to form $U_r$, which is optimally unitarized to obtain $U$. The effective Hamiltonian $H_{\text{eff}}$ is reconstructed from $U$ and dressed energies.