Exact quantum circuits for lattice Boltzmann realization of the Dirac equation
N. Sawant, E. Young, K. Griffin, M. Martin · 2026 · arXiv:2608.06570
| 编号 QC094 | 主题 量子格子玻尔兹曼 | 链接 arXiv:2608.06570 |
摘要
摘要保留原文（英文）
摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。
The quantum lattice Boltzmann (QLB) scheme of Succi and Dellar advances a four–component Dirac spinor on a lattice by a fixed sequence of local, exactly norm–preserving operations: a basis rotation, a collision, a streaming shift, and the inverse rotation. This unitarity is a structural property of the scheme, not an approximation, which suggests that a QLB time step should map onto a sequence of quantum gates. Here we make that mapping explicit. We give a gate–level construction of every operation of the three–dimensional Dirac QLB scheme: the fixed rotation gates, the collision gate, the streaming shift as a controlled increment on a position register, the position–dependent potential as a phase oracle, and periodic and reflecting (bounce–back) boundary conditions as unitary circuits. We then compose them into single–axis, two– and three–dimensional time steps. On a state–vector emulator the resulting circuits reproduce the classical QLB solver to machine precision (maximum density deviation between and across the one–, two–, and three–dimensional tests), so the circuits are the scheme rather than an approximation of it. The scope is narrow: we establish that the Succi–Dellar theory can be implemented on a (gate–model) quantum computer, and report the associated gate counts. We make no claim of computational advantage; state preparation, measurement, and asymptotic cost are discussed as open questions. All operators, circuits, tests, and figures are reproducible from the open–source quantumKineticMethods library.
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