论文标题
量子哈密顿模拟和二元性的数学框架
A mathematical framework for quantum Hamiltonian simulation and duality
论文作者
论文摘要
模拟汉密尔顿模拟是量子计算的近期应用，最近已成为理论上的基础。在哈密顿模拟中，一种物理哈密顿量的工程是与另一种相同的物理学（通常非常不同）的哈密顿人。这在质上与物理学上的二元性概念相似，在某种意义上，在数学上，两种表面上不同的理论在数学上是等效的。但是，哈密顿模拟的现有特征不足以扩展到物理学的所有二元性。特别是，它们不能涵盖强/弱和高温/低温双重性的重要情况。在这项工作中，我们给出了三个出于物理动机的双重性，分别根据可观察，分区功能和熵进行了表达。我们证明这些公理化是等效的，并且表征了满足这些公理必须采取的任何双重性的数学形式。我们的结果之一中的一个基础是增强熵保护图的早期结果，以熵呈现到嵌入式常数的地图，我们证明这是直接分解为单位和反独立组件的直接总和，这可能具有独立的数学利益。
Analogue Hamiltonian simulation is a promising near-term application of quantum computing and has recently been put on a theoretical footing. In Hamiltonian simulation, a physical Hamiltonian is engineered to have identical physics to another - often very different - Hamiltonian. This is qualitatively similar to the notion of duality in physics, whereby two superficially different theories are mathematically equivalent in some precise sense. However, existing characterisations of Hamiltonian simulations are not sufficiently general to extend to all dualities in physics. In particular, they cannot encompass the important cases of strong/weak and high-temperature/low-temperature dualities. In this work, we give three physically motivated axiomatisations of duality, formulated respectively in terms of observables, partition functions and entropies. We prove that these axiomatisations are equivalent, and characterise the mathematical form that any duality satisfying these axioms must take. A building block in one of our results is a strengthening of earlier results on entropy-preserving maps to maps that are entropy-preserving up to an additive constant, which we prove decompose as a direct sum of unitary and anti-unitary components, which may be of independent mathematical interest.
