Although the number of qubits is small and the fidelity of operations is not very high, programmable quantum computers have been made available, not only for researchers but also for public users. They are developed using superconducting 2 and trapped ion 3, 4 systems. The main reason is the rise of the noisy intermediate-scale quantum (NISQ) computers 1, which have 50–100 qubits, and its quantum error corrections are not yet implemented.
Recently, the development of quantum computing has been huge research attention. It has been reported that many researchers have been working tirelessly to build a fault-tolerant quantum computer and quantum algorithms for years. We hope that entangled measurements would become crucial resources, not only for joint measurements but also for quantum information processing. Our proposed method is expected to be used in conjunction with other related studies. We also propose using a part of entangled measurements for grouping to keep the depth of extra gates constant. In this paper, we show that entangled measurements enhance the efficiency of evaluation of observables, both theoretically and experimentally, by taking into account the covariance effect, which may affect the quality of evaluation of observables. Grouping of observables with separable measurements has been conventionally used, and the grouping with entangled measurements has also been proposed recently by several teams. By speeding up the evaluation of observables, it is possible to realize a faster algorithm and save resources of quantum computers. Evaluations of observables appear frequently in the variational quantum-classical hybrid algorithms for NISQ computers. In particular, it is necessary to study variational quantum-classical hybrid algorithms, which are executable on noisy intermediate-scale quantum (NISQ) computers.
The advent of cloud quantum computing has led to the rapid development of quantum algorithms.
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