  Estimation of the expectation value of observables is a key subroutine in
quantum computing and is also the bottleneck of the performance of many
near-term quantum algorithms. Many works have been proposed to reduce the
number of measurements needed for this task and they provide different
measurement schemes for generating the measurements to perform. In this paper,
we propose a new approach, composite measurement scheme, which composes
multiple measurement schemes by distributing shots to them with a trainable
ratio. As an example of our method, we study the case where only Pauli
measurements are allowed and propose Composite-LBCS (C-LBCS), a composite
measurement scheme made by composing locally-biased classical shadows. We
numerically demonstrate C-LBCS on molecular systems up to $\mathrm{CO}_2$ (30
qubits) and show that C-LBCS outperforms the previous state-of-the-art methods
despite its simplicity. We also show that C-LBCS can be efficiently optimized
by stochastic gradient descent and is trainable even when the observable
contains a large number of terms. We believe our method opens up a reliable way
toward efficient observable estimation on large quantum systems.
