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The advent of cloud quantum computing has led to the rapid development of quantum algorithms. In particular, it is necessary to study variational quantum-classical hybrid algorithms, which are executable on noisy intermediate-scale quantum (NISQ) computers. Evaluations of observables appear frequently in the variational quantum-classical hybrid algorithms for NISQ computers. By speeding up the evaluation of observables, it is possible to realize a faster algorithm and save resources of quantum computers. Grouping of observables with separable measurements has been conventionally used, and the grouping with entangled measurements has also been proposed recently by several teams. 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. We also propose using a part of entangled measurements for grouping to keep the depth of extra gates constant. Our proposed method is expected to be used in conjunction with other related studies. We hope that entangled measurements would become crucial resources, not only for joint measurements but also for quantum information processing.

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This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. Based upon a previous work of quantum circuit mapping that leverages gate commutation rules, this paper shows algorithms that utilize both transformation and commutation rules. Experiments on a standard benchmark dataset confirm the algorithms with more rules can find even better circuit mappings compared with the previously-known best algorithms.

The irregular strip packing problem is a combinatorial optimization problem that requires to place a given set of 2-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container. We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components into an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results.