Jenga-Krotov algorithm: Efficient compilation of multi-qubit gates for exchange-only qubits

TL;DR

Jenga-Krotov introduces a two-stage gradient-based optimization that expands the control landscape and then prunes to yield compact, high-fidelity multi-qubit gate sequences for exchange-only EO qubits. Applied to Toffoli, Fredkin, and QFT, it achieves drastic reductions in exchange unitaries and time steps compared with direct decompositions and standard optimal-control methods, while enhancing robustness to charge noise and crosstalk. The approach leverages decoherence-free subspace encoding to focus on a manageable computational subspace, enabling tractable optimization and scalable gate compilation. The results indicate that JK offers a practical path toward implementing multi-qubit quantum algorithms on semiconductor EO platforms.

Abstract

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.

Figures (13)

• Figure 1: The bullet notation for (a) a single EO qubit, and (b) three EO qubits labeled by A,B and C. The corresponding natural and computational orders are indicated.
• Figure 2: Quantum circuit showing direct decomposition of $T$ and $H$ gates, along with the accumulated number of exchange unitaries and number of time steps indicated. Each block corresponds to an exchange unitary as defined in Eq. \ref{['eq:fundamentalblock']}, with the $p$ value indicated inside the block.
• Figure 3: Quantum circuit showing the Fong-Wandzura sequence in the natural order (3,1,2,4,5,6) accomplishing a CNOT gate, along with the accumulated number of exchange unitaries and number of time steps indicated. Each block corresponds to an exchange unitary as defined in Eq. \ref{['eq:fundamentalblock']}, with the $p$ value indicated inside the block. Here $p_1=\arccos{\left(-1/\sqrt{3}\right)}/\pi$, $p_2=\arcsin{\left(1/3\right)}/\pi$.
• Figure 4: Quantum circuit illustrating the equivalent Fong-Wandzura sequence in the natural order (3,1,2,6,4,5) that implements a CNOT gate, with the accumulated number of exchange unitaries and number of time steps indicated. This sequence is the one used in this work. Each block corresponds to an exchange unitary as defined in Eq. \ref{['eq:fundamentalblock']}, with the $p$ value indicated inside the block. Here $p_1=\arccos{\left(\frac{2\sqrt{3}}{3}-1\right)}/\pi$, $p_2=\arcsin{\left(\frac{2\sqrt{3}-1}{3}\right)}/\pi$.
• Figure 5: Block matrix structure of the reduced $90 \times 90$ Hamiltonian in the total angular momentum basis, showing computational (green) and leakage (orange) subspaces. Yellow regions are identically zero. Three identical $8 \times 8$ computational subspaces appear along the diagonal.