论文标题
量子力学中坐标和动量的三元和二元表示
Ternary and Binary Representation of Coordinate and Momentum in Quantum Mechanics
论文作者
论文摘要
为了模拟基于量子数字的量子计算机上具有连续自由度的量子系统，有必要将连续可观察物（主要是坐标和矩）减少到离散的可观察物。我们认为这个问题基于将量子观测到串联的量子可观察力，分为两个和三个，类似于实数的二进制和三元表示。因此，该系列的系数（“数字”）是冬宫操作员。我们研究了相应的量子机械运算符及其之间的关系，并表明量子可观察物的二进制和三元扩展会自动导致某些不同积分和串联的重新归一化（给它们有限值）。
To simulate a quantum system with continuous degrees of freedom on a quantum computer based on quantum digits, it is necessary to reduce continuous observables (primarily coordinates and momenta) to discrete observables. We consider this problem based on expanding quantum observables in series in powers of two and three analogous to the binary and ternary representations of real numbers. The coefficients of the series ("digits") are, therefore, Hermitian operators. We investigate the corresponding quantum mechanical operators and the relations between them and show that the binary and ternary expansions of quantum observables automatically leads to renormalization of some divergent integrals and series (giving them finite values).
