arXiv:2103.07510quant-ph
Efficient estimation of Pauli observables by derandomization
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Abstract
We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements with fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any $L$ low-weight Pauli observables, a deterministic measurement on only of order $\log(L)$ copies of a quantum state suffices. In some cases, for example when some of the Pauli observables have a high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.
Read a paper with few hundreds of cites. They proposed a new algorithm to solve eigenvalue problem. I look at it, decrypt the equations, and then notice that it is just basically a bunch of if-then condition like this: count = 0 for x in list: if x == 1: count +=1 if count != 0…
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