We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between “quantum discord” and “asymmetric relative entropy of discord”: the former never exceeds the latter. We also prove that for all BDS the two coincide.

RePlAce is a state-of-the-art prototype of a flat, analytic, and nonlinear global cell placement algorithm, which models a placement instance as an electrostatic system with positively charged objects. It can handle large-scale standard-cell and mixed-cell placement, while achieving shorter wirelength and similar or shorter runtimes than other state-of-the-art placers on the ISPD-2005/2006 standard-cell benchmarks; however, the runtime of RePlAce on these benchmarks ranges from 15 minutes to 5+ hours on a 2.6 GHz Intel Xeon server running a single thread, rendering development cycles prohibitively long. To address this concern, this paper introduces a multi-threaded shared-memory implementation of RePlAce. The contributions include techniques to reduce memory contention and to effectively balance the workload among threads, targeting the most substantial performance bottlenecks. With 2-12 threads, our parallel RePlAce speeds up the bin density function by a factor of 4.2-10×, the wirelength function by a factor of 2.3-3×, and the cost gradient function by a factor of 2.9-6.6× compared to the single-threaded original RePlAce baseline. Moreover, our parallel RePlAce is ≈3.5× faster than the state-of-the-art PyTorch-based placer DREAMPlace, when both are running on 12 CPU cores.

We shortly review Bell-diagonal and Werner states of two quantum bits and their characterization, and carry out a detailed experimental study of their generation on the IBM Quantum Experience.To this end we propose new circuits and tomography. One circuit involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. For the first time the entire class of Bell-diagonal states is generated. A number of characteristic indicators, namely entanglement of formation, CHSH non-locality, steering and quantum discord, are evaluated over the full parameter space and compared with theory.