Cross-talk in superconducting qubit lattices with tunable couplers -- comparing transmon and fluxonium architectures

TL;DR

The paper addresses cross-talk in superconducting-qubit lattices by examining residual $ZZ$ interactions and localization in various architectures using DMRG-X on a 2-leg ladder. It compares fixed-capacitively coupled transmons, tunable transmon couplers, and C-shunt flux couplers, and extends to fluxonium qubits with transmon couplers, evaluating both $ZZ$ suppression and state localization via the $IPR$. The work finds that C-shunt flux couplers suppress $ZZ$ more effectively than tunable transmons, while fluxonium qubits with transmon couplers maintain strong $ZZ$ suppression and high localization across larger systems, suggesting potential scalability advantages. The results inform design choices for scalable superconducting quantum processors, highlighting trade-offs between gate speed, crosstalk, and architectural complexity, and outlining pathways to further study longer-range couplings and time-dependent gate dynamics.

Abstract

Cross-talk between qubits is one of the main challenges for scaling superconducting quantum processors. Here, we use the density-matrix renormalization-group to numerically analyze lattices of superconducting qubits from a perspective of many-body localization. Specifically, we compare different architectures that include tunable couplers designed to decouple qubits in the idle state, and calculate the residual ZZ interactions as well as the inverse participation ratio in the computational basis states. For transmon qubits outside of the straddling regime, the results confirm that tunable C-shunt flux couplers are significantly more efficient in mitigating the ZZ interactions than tunable transmons. A recently proposed fluxonium architecture with tunable transmon couplers is demonstrated to also maintain its strong suppression of the ZZ interactions in larger systems, while having a higher inverse participation ratio in the computational basis states than lattices of transmon qubits. Our results thus suggest that fluxonium architectures may feature lower cross talk than transmon lattices when designed to achieve similar gate speeds and fidelities.

Figures (8)

• Figure 1: Layout of the considered systems of superconducting qubits and couplers.
• Figure 2: (a) Interaction coefficients $w_{\bm{n}}$ for transmons without couplers on a ladder. The graphical labels indicate the positions of the involved $Z$ operators (up to rotations and translations), e.g., the red curves show horizontal and vertical nearest-neighbor couplings, and the green ones the next-nearest-neighbor couplings along the diagonals. Also included are the specific longer-ranged couplings discussed in the main text (purple and orange curves). In the shaded region, the state assignment is ambiguous. The dips in some curves signal sign changes of the corresponding interaction terms. (b) Average IPR for all computational basis states and separated based on the states of the qubits $3$ and $6$.
• Figure 3: Strengths of the residual interactions in a system with transmon qubits and tunable transmon couplers. The notation is the same as in Fig. \ref{['fig:walsh_nocouplers']}(a).
• Figure 4: (a) IPR averaged over all states of the computational basis for a ladder with either tunable transmons or C-shunt flux qubits as couplers. The inset shows the average hopping amplitudes between qubits and couplers, taking the factors in Eqs. \ref{['eq:cooperpairop_transmons']} and \ref{['eq:cooperpairop_cshunt']} into account. (b) average mutual information between a qubit and the remaining system excluding the connected couplers.
• Figure 5: Same as Fig. \ref{['fig:walsh_transmon_coupler']} but for tunable C-shunt flux couplers.