Exact quantum circuits for a Heisenberg triangle with Dzyaloshinskii-Moriya interaction
Abstract
We construct short analytical quantum circuits for the exact evolution of a spin triangle with Dzyaloshinskii--Moriya (DM) interaction. We consider pure DM interaction with arbitrary real couplings and two Hamiltonian families with uniform Heisenberg exchange. For pure DM, a change of basis reduces the evolution to two single-qubit rotations. The circuits reproduce the full evolution operator at arbitrary time with a fixed gate count and admit implementations with both triangular and linear qubit connectivity. Experiments on a superconducting IBM quantum processor demonstrate directional quantum-state transfer and reproduce the amplitude and phase of transverse magnetization. In these experiments, the exact circuits reduce distortions relative to circuits based on the second-order Trotter formula. On a 12-spin kagome cluster, exact triangle blocks reduce the gate count at a prescribed accuracy. We also investigate the reduction of coherent errors by adjusting circuit angles and applying echo pulses to neighboring qubits.
Related
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BibTeX
@misc{zhukov2026exact,
title = {{Exact quantum circuits for a Heisenberg triangle with Dzyaloshinskii-Moriya interaction}},
author = {Andrey Zhukov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15411},
eprint = {2609.15411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15411},
}
RIS
TY - UNPB
TI - Exact quantum circuits for a Heisenberg triangle with Dzyaloshinskii-Moriya interaction
AU - Andrey Zhukov
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2609.15411
UR - https://arxiv.org/abs/2609.15411
AB - We construct short analytical quantum circuits for the exact evolution of a spin triangle with Dzyaloshinskii--Moriya (DM) interaction. We consider pure DM interaction with arbitrary real couplings and two Hamiltonian families with uniform Heisenberg exchange. For pure DM, a change of basis reduces the evolution to two single-qubit rotations. The circuits reproduce the full evolution operator at arbitrary time with a fixed gate count and admit implementations with both triangular and linear qubit connectivity. Experiments on a superconducting IBM quantum processor demonstrate directional quantum-state transfer and reproduce the amplitude and phase of transverse magnetization. In these experiments, the exact circuits reduce distortions relative to circuits based on the second-order Trotter formula. On a 12-spin kagome cluster, exact triangle blocks reduce the gate count at a prescribed accuracy. We also investigate the reduction of coherent errors by adjusting circuit angles and applying echo pulses to neighboring qubits.
ER -