We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on randomised measurements, which use decision diagrams to sample from probability distributions on measurement bases. This approach generalises previously known uniform and locally-biased randomised estimators. The decision diagrams are constructed given target quantum operators and can be optimised considering different strategies. We show numerically that the estimators introduced here can produce more precise estimates on some quantum chemistry Hamiltonians, compared to previously known randomised protocols and Pauli grouping methods.
翻译:我们考虑估计在聚合的qubits上观察到的量的问题,这是作为Pauli操作员的线性组合而给出的,而浅量子电路则由单量子旋转组成。我们采用基于随机测量的测算器,这些测算器使用决定图,从测量基数的概率分布中取样。这种方法概括了以前已知的统一和有地方偏差的随机测算器。决定图是给目标量子操作员设定的,可以结合不同的战略加以优化。我们从数字上表明,这里采用的测算器可以对某些量子化学汉密尔顿人进行更精确的估算,与以前已知的随机协议和保利组合方法相比。