守恒与弛豫模式使多项式成功的相干Carleman格子玻尔兹曼演化成为可能
Conserved and relaxing modes enable polynomial-success coherent Carleman lattice Boltzmann evolution
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中文总结 AI 辅助
该研究提出基于多弛豫时间碰撞算子的量子Carleman格子玻尔兹曼方案，利用守恒与弛豫模式的块结构实现近单位成功概率的块编码，使相干多步演化的开销呈多项式增长，显著提升百步演化成功率并准确复现基准流非线性模式。
中文摘要 AI 辅助
Carleman线性化将非线性格子玻尔兹曼碰撞动力学表示为适合量子块编码的形式，但现有种群空间编码中的低后选择概率使得相干多步演化以指数级低概率成功。我们提出了一种基于加权Hermite矩基中多弛豫时间碰撞算子的量子Carleman格子玻尔兹曼方案。在该基中，提升后的碰撞算子分解为小的耦合块，由于守恒模式与弛豫模式之间的耦合，这些块的范数超过1。这种块结构使得范数达到的块编码具有接近1的单步成功概率。关键在于，针对指定的演化范围缩放成对扇区，使得组合的编码和扇区选择开销随步数呈多项式而非指数增长。对于一百步的演化，所得完整运行成功概率比种群空间编码高出数个数量级。在几十步的演化范围内，截断动力学以百分之几以内的误差复现了基准流的非线性生成模式。我们将组合的制备、演化和读出协议验证为单一酉电路，并给出了从相干Carleman演化中提取基准流非线性可观测量的完整门级资源估计。守恒与弛豫模式的块结构在三维格子上同样成立，并为具有二次平衡态的格子玻尔兹曼模型提供了达到范数编码的建设性途径。
英文摘要
Carleman linearization represents nonlinear lattice Boltzmann collision dynamics in a form amenable to quantum block encoding, but low postselection probabilities in existing population-space encodings make coherent multi-step evolution exponentially unlikely to succeed. We present a quantum Carleman lattice Boltzmann scheme based on the multi-relaxation-time collision operator in a weighted Hermite moment basis. In this basis, the lifted collision operator separates into small coupled blocks whose norm exceeds unity because of the coupling between conserved and relaxing modes. This block structure enables a norm-attaining block encoding with a single-step success probability close to unity. Crucially, scaling the pair sector for a prescribed evolution horizon makes the combined encoding and sector-selection overhead grow polynomially rather than exponentially with the number of steps. For a hundred-step evolution, the resulting complete-run success probability exceeds that of population-space encodings by orders of magnitude. Over horizons of several tens of steps, the truncated dynamics reproduces the nonlinearly generated modes of a benchmark flow to within a few percent. We verify the combined preparation, evolution and readout protocol as a single unitary circuit and give a complete gate-level resource estimate for extracting a nonlinear observable of the benchmark flow from a coherent Carleman evolution. The block structure of conserved and relaxing modes holds equally on three-dimensional lattices and provides a constructive route to norm-attaining encodings for lattice Boltzmann models with quadratic equilibria.
发表机构
- Chalmers University of Technology（查尔姆斯理工大学）
- Fondazione Istituto Italiano di Tecnologia, Center for Life Nano-Neuroscience at La Sapienza（意大利技术研究院基金会，拉撒普ienza生命纳米神经科学中心）
- Department of Physics, Harvard University（哈佛大学物理系）
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