Related papers: A synchronous NPA hierarchy with applications
We explore the robustness of the correlation matrix Hamiltonian reconstruction technique with respect to the choice of operator basis, studying the effects of bases that are undercomplete and over-complete -- too few or too many operators…
Balanced Singular Perturbation Approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar…
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum…
Based on our recent paper [arXiv:2206.12176 (2022)], we propose a scalable heteronuclear architecture of parallel implementation of CNOT gates in arrays of alkali-metal neutral atoms for quantum information processing. We considered a…
Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different…
In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible…
Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating…
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each…
Man\v{c}inska and Roberson [FOCS'20] showed that two graphs are quantum isomorphic if and only if they admit the same number of homomorphisms from any planar graph. Atserias et al. [JCTB'19] proved that quantum isomorphism is undecidable in…
To establish a time reference frame between two users in quantum key distribution, a synchronization calibration process is usually applied for the case of using gated mode single-photon detectors (SPDs). Traditionally, the synchronization…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the…
$\mathcal{PT}$-symmetric systems have garnered significant attention due to their unconventional properties. Despite the growing interest, there remains an ongoing debate about whether these systems outperform their Hermitian counterparts…
In this work, we introduce a Self-Aware Polymorphic Architecture (SAPA) design approach to support emerging context-aware applications and mitigate the programming challenges caused by the ever-increasing complexity and heterogeneity of…
The hierarchy of pure states (HOPS) is a wavefunction-based method which can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However,…
Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad…
We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…
Modern concurrent programming benefits from a large variety of synchronization techniques. These include conventional pessimistic locking, as well as optimistic techniques based on conditional synchronization primitives or transactional…
Recent studies exploited external periodic synchronous signals to synchronize a pair of network nodes to address a threat of delaying the communications between the nodes. However, the sensing-based synchronization may yield faults due to…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…