Impact of leakage on the dynamics of a ST$_0$ qubit implemented in a Double Quantum Dot device

Spin qubits in quantum dots are a promising technology for quantum computing due to their fast response time and long coherence times. An electromagnetic pulse is applied to the system for a specific duration to perform a desired rotation. To avoid decoherence, the amplitude and gate time must be highly accurate. In this work, we aim to study the impact of leakage during the gate time evolution of a spin qubit encoded in a double quantum dot device. We prove that, in the weak interaction regime, leakage introduces a shift in the phase of the time evolution operator, causing over- or under-rotations. Indeed, controlling the leakage terms is useful for adjusting the time needed to perform a quantum computation and increasing the coherence time of the readout process. This is crucial for running fault-tolerant algorithms and is beneficial for Quantum Error Mitigation techniques.

💡 Research Summary

The paper investigates how leakage—population transfer from the logical subspace to higher‑energy states—affects the dynamics of a singlet‑triplet (ST₀) spin qubit realized in a double quantum‑dot (DQD) device. The authors begin by reviewing the advantages of semiconductor spin qubits (fast gate times, long coherence) and the stringent requirements on pulse amplitude and duration needed to avoid coherent errors such as over‑ or under‑rotations. They point out that real DQD systems possess more than two accessible energy levels; besides the logical states |S⟩ (singlet) and |T₀⟩ (neutral triplet), the triplet states |T₊⟩ and |T₋⟩ are also present and can be coupled to the logical subspace by transverse magnetic fields (δbₓ, δb_y, bₓ, b_y).

In the theoretical section the authors write the full four‑dimensional Hamiltonian as a block matrix containing the logical ST₀ Hamiltonian H_ST₀, the leakage Hamiltonian H_leak, and the |T_±⟩ subspace. In the absence of leakage, H_ST₀ =