Quantum Physics (quant-ph)

Abstract: Consider two spins 1 and N, which are entangled and far from each other. As it is famous, performing any measurement on spin N does not change the reduced state of spin 1. In other words, spin 1 will never realize that a measurement has been performed on spin N. But, what does happen if spins 1 and N are connected to each other by a spin chain, including spins 2 to N - 1? In general, we expect that the information of performing a measurement on spin N achieves spin 1, after a period of time. In other words, we expect that the reduced state of spin 1 is changed, due to the measurement performed on spin N, after some while. In this paper, we show that, if the measurement on spin N is performed instantaneously, and if we choose the initial state of the whole spin chain, from 1 to N, appropriately, then the information of performing the measurement on spin N never achieves spin 1.

Abstract: Entanglement is a fundamental property in quantum mechanics that systems share inseparable quantum correlation regardless of their mutual distances. Owing to the fundamental significance and versatile applications, the generation of quantum entanglement between {\it macroscopic} systems has been a focus of current research. Here we report on the deterministic generation and tomography of the macroscopically entangled Bell state in a hybrid quantum system containing a millimeter-sized spin system and a micrometer-sized superconducting qubit. The deterministic generation is realized by coupling the macroscopic spin system and the qubit via a microwave cavity. Also, we develop a joint tomography approach to confirming the deterministic generation of the Bell state, which gives a generation fidelity of $0.90\pm0.01$. Our work makes the macroscopic spin system the largest system capable of generating the maximally entangled quantum state.

Abstract: We investigate the behavior of entanglement between a single fermionic level and a fermionic bath in three distinct dynamic and thermodynamic regimes. First, in thermal equilibrium, we observe the dependence of entanglement on the considered statistical ensemble: for the grand canonical state, it is generated only for a sufficiently strong system-bath coupling, whereas it is present for arbitrarily weak couplings for the canonical state with a fixed particle number. Second, it is shown that during the relaxation dynamics the transiently generated system-bath entanglement can be preserved at long times because of non-Markovian effects related to the formation of system-environment bound states. Finally, in voltage-driven junctions the steady state entanglement is generated for arbitrarily weak system-bath couplings at a certain threshold voltage; at the same time, it is reduced by either the particle-hole or the tunnel coupling asymmetry.

Abstract: The union$\unicode{x2013}$find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling near-linearly in the number of physical qubits. This complexity is achieved via optimisations provided by the disjoint-set data structure. We demonstrate, however, that the behaviour of the decoder at scale underutilises this data structure for twofold analytic and algorithmic reasons, and that improvements and simplifications can be made to architectural designs to reduce resource overhead in practice. To reinforce this, we model the behaviour of erasure clusters formed by the decoder and show that there does not exist a percolation threshold within the data structure for any mode of operation. This yields a linear-time worst-case complexity for the decoder at scale, even with a naive implementation omitting popular optimisations.

Abstract: The non-locality is a well-established property of single-photon states. It has been demonstrated theoretically using various approaches. In this article, we propose a demonstration based on the electromagnetic energy density observable and on the anti-local property of the frequency operator $\Omega=c(-\Delta)^{1/2}$. The present proof is completely general for all single-photon states while earlier proofs in the literature were limited to particular cases, either with some uniform localization condition or with some particular electric and magnetic localization restrictions.

Abstract: Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic oscillators, it is found that their dynamical variables can be replaced by a completely ontological set, which means that, here, quantum mechanics does not deviate from a purely geometric, ontological particle system. The effects of the mass terms are included. Locality holds for the quantum theory, and seems to be fully obeyed also by the classical treatment, although further discussion will be needed. Quantised interactions are briefly speculated on, but mostly postponed to later. We do discuss extensively the distinction between the quantum treatment and the classical one, even though they produce exactly the same equations mathematically. We briefly explain how this result can be squared with the usual quantum no-go theorems. It is suggested to apply this theory for real time quantum model simulations.

Abstract: The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external baths following the Caldeira-Leggett approach. Studying the mean-field model in the overdamped limit using Feynman-Vernon theory, we show how quantum mechanics modifies the phase diagram. Specifically, we demonstrate that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We examine the phase transition into the synchronized phase at various temperatures, revealing that classical results are recovered at high temperatures while a quantum phase transition occurs at zero temperature. Additionally, we derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters, and examine the differences between classical and quantum behavior.

Abstract: In this tutorial paper, we provide an introduction to the briskly expanding research field of Majorana fermions in topological superconductors. We discuss several aspects of topological superconductivity and the advantages it brings to quantum computing. Mathematical derivation of the Kitaev model and BdG Hamiltonian is carried out to explain the phenomena of superconductivity and Majorana fermions. The Majorana fermions and the Non-Abelian statistics are described in detail along with their significance for quantum engineers. The theory provided led towards the engineering of the topological qubits using Majoranas.

Abstract: This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief summary of quantum computing and an in-depth analysis of variational quantum algorithms. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models. Next, several novel contributions to the field based on previous work are presented, namely: a newly introduced model for a quantum perceptron with applications to recognition and classification tasks; a variational generalization of such a model to reduce the circuit footprint of the proposed architecture; an industrial use case of a quantum autoencoder followed by a quantum classifier used to analyze classical data from an industrial power plant; a study of the entanglement features of quantum neural network circuits; and finally, a noise deconvolution technique to remove a large class of noise when performing arbitrary measurements on qubit systems.

Abstract: We describe an experiment in which one member of a polarization-entangled photon pair is stored in an active Cyclical Quantum Memory (CQM) device, while the other propagates through a passive optical delay line. A comparison of Bell's inequality tests performed before and after the storage is used to investigate the ability of the CQM to maintain entanglement, and demonstrate a rudimentary entanglement distribution protocol. The entangled photons are produced by a conventional Spontaneous Parametric Down Conversion source with center wavelengths at 780 nm and bandwidths of $\sim$10 THz, while the CQM has an even wider operational bandwidth that is enabled by the weakly dispersive nature of the Pockels effect used for active switching in a loop-based quantum memory platform.

Abstract: In this Letter, we show that a periodically driven Aubry-Andr\'e-Harper model with imbalanced onsite gain/loss supports universal one-way transport that is immune to impurities and independent of initial excitations. We reveal the underlying mechanism that the periodic driving gives rise to the non-Hermitian skin effect in the effective Floquet Hamiltonian, thereby causing universal non-reciprocal transport. Additionally, we probe the Lyapunov exponent under long-time dynamics as a signature of the Floquet emergent non-Hermitian skin effect. Our results provide a feasible and controllable way to realize universal one-way transport that is easily accessible to experiments.