Mitigating decoherence in molecular spin qudits

TL;DR

This work develops a microscopic, non-Markovian model for pure dephasing in molecular spin qudits and shows that coherence of a superposition |α⟩+|β⟩ is preserved if and only if the conditional bath Hamiltonians commute, i.e. [H^{α},H^{β}] = 0. By linking this commutation condition to the equality of local spin expectations across the two states, the authors introduce a practical Δ parameter to quantify deviations and guide qudit design. Using cluster correlation expansion truncated at second order, they demonstrate in two paradigms—a single giant spin and a small AFM spin cluster—that smaller Δ yields significantly longer coherence times, emphasizing the importance of local spin textures over total spin. They culminate with a concrete qudit proposal based on six spin-½ centers that exhibits full connectivity among low-energy states and enhanced coherence, illustrating a viable route toward robust molecular qudits for quantum technologies. The study provides a general framework that can be paired with bath engineering to push forward practical quantum information processing with spin-based qudits.

Abstract

Molecular nanomagnets are quantum spin systems potentially serving as qudits for future quantum technologies thanks to their many accessible low-energy states. At low temperatures, the primary source of error in these systems is pure dephasing, caused by their interactions with the bath of surrounding nuclear spins degrees of freedom. Most importantly, as the system's dimensionality grows going from qubits to qudits, the control and mitigation of decoherence becomes more challenging. Here we analyze the characteristics of pure dephasing in molecular qudits under spin-echo sequences. We use a realistic description of their interaction with the bath, whose non-Markovian dynamics is accurately computed by the cluster correlation expansion technique. First, we demonstrate a necessary and sufficient condition to prevent the decay of coherence with time, also introducing a parameter to quantify the deviation from such ideal condition. We illustrate this with two paradigmatic systems: a single giant spin and a composite antiferromagnetic spin system. We then advance a proposal for optimized nanomagnets, identifying key ingredients for engineering robust qudits for quantum technologies.

Figures (10)

• Figure 1: Top: coherence factor over time of the pair superpositions of states corresponding to seven lowest energy levels of the spectrum. Bottom: legend displaying the representative color for each superposition and the corresponding value of $\Delta$.
• Figure 2: (a) Schematic structure of the system made of five spins 1/2. Spins $1,2,3$ are placed at the vertices of an equilateral triangle lying on the $x-y$ plane while spins $4$ and $5$ are placed along the $z-$axis. Each spin is positioned at a distance of 3 Å $\,$ from the center. However, even when this symmetry is disrupted, the qualitative results remain unchanged.
• Figure 3: Expectation values of the $S_i^z$ operators for the eigenstates of the system considered in \ref{['subsec:5_spins']}. In the legend, we reported the label of the states and the value of $\braket{S^z}=\sum_i \braket{S_i^z}$.
• Figure 4: Coherence factor curves for the superposition of eigenstates illustrated in the legend. The value of the $\Delta$ parameter is also shown. The arbitrary unit is the time requested for the superposition $\ket{\psi}_{9,14}$ to reach the value of $0.001$ of the coherence factor.
• Figure 5: The 21 coherence factor curves for the 7 eigenstates with $S^z\approx0$ of the AFM system (in blue). The uncoupled-spins curve, in black, is used to define the time scale arbitrary unit.