Long-distance photon-mediated and short-distance entangling gates in three-qubit quantum dot spin systems

TL;DR

This paper analyzes the performance of entangling gates in a three-qubit quantum dot system with superconducting resonator couplers, highlighting error sources and guiding optimal modular quantum dot architectures.

Contribution

It provides an effective Hamiltonian model for three-qubit dynamics and evaluates short- and long-range gate fidelities considering realistic noise and spectator effects.

Findings

Spectator qubits reduce gate fidelities in both short- and long-range operations.

Leakage errors dominate infidelity sources under current experimental conditions.

Charge noise and residual couplings significantly impact entangling gate performance.

Abstract

Superconducting microwave resonator couplers will likely become an essential component in modular semiconductor quantum dot (QD) spin qubit processors, as they help alleviate cross-talk and wiring issues as the number of qubits increases. Here, we focus on a three-qubit system composed of two modules: a two-electron triple QD resonator-coupled to a single-electron double QD. Using a combination of analytical techniques and numerical results, we derive an effective Hamiltonian that describes the three-qubit logical subspace and show that it accurately captures the dynamics of the system. We examine the performance of short-range and long-range entangling gates, revealing the effect of a spectator qubit in reducing the gate fidelities in both cases. We further study the competition between non-adiabatic errors and spectator-associated errors in short-range operations and quantify their relative importance across practical parameter ranges for short and long gate times. We also analyze the impact of charge noise together with residual coupling to the spectator qubit on inter-module entangling gates and find that for current experimental settings, leakage errors are the main source of infidelities in these operations. Our results help pave the way toward identifying optimal modular QD architectures for quantum information processing on semiconductor chips.