Exchange-only (EO) qubits, implemented in triple-quantum-dot systems, offer a compelling platform for scalable semiconductor-based quantum computing by enabling universal control through purely exchange interactions. While high-fidelity single- and two-qubit gates have been demonstrated, the synthesis of efficient multi-qubit operations—such as the Toffoli gate—remains a key bottleneck. Conventional gate decompositions into elementary operations lead to prohibitively long and error-prone pulse sequences, limiting practical deployment. In this work, we introduce a gradient-based optimization algorithm, Jenga-Krotov (JK), tailored to discover compact, high-fidelity EO gate sequences. Applying JK to the Toffoli gate, we reduce the number of required exchange unitaries from 216 (in direct decomposition) to 92, and compress the time steps required from 162 to 50, all while maintaining target fidelity. Under realistic noise, the accumulated gate error from our optimized sequence is an order of magnitude lower than that of conventional approaches. We have also applied the JK algorithm to other multi-qubit gates and algorithm. For the Fredkin gate, it reduces the number of time steps from 200 to 104 and the number of exchange unitaries from 276 to 172. For the quantum Fourier transform, it compresses the sequence from 180 to 80 time steps and from 237 to 202 exchange unitaries. These results demonstrate that the JK algorithm is a general and scalable strategy for multi-qubit gate synthesis in EO architectures, potentially facilitating realization of multi-qubit algorithms on semiconductor platforms.
Read more at Physical Review Research:
https://journals.aps.org/prresearch/abstract/10.1103/1x1x-j1xl
Photo caption:
Block matrix structure of the reduced 90×90 Hamiltonian in the total angular momentum basis, showing computational (green) and leakage (orange) subspaces. Yellow regions are identically zero. Three identical 8×8 computational subspaces appear along the diagonal.
Illustration of the JK algorithm. The left panel shows an initial dense pulse sequence, where one exchange unitary (highlighted by the shaded box) is randomly selected and removed. The sequence is then reoptimized, allowing the durations of the remaining exchange unitaries (indicated by the numbers in the boxes) to adjust. The right panel shows the resulting optimized sequence, now with one fewer exchange unitary, but maintaining the same level of gate fidelity. This iterative pruning-and-refinement process is key to the JK algorithm's ability to yield compact, high-fidelity pulse sequences.
12 Dec 2025
