Related papers: A synchronous NPA hierarchy with applications
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error…
We study efficient algorithms for Sparse PCA in standard statistical models (spiked covariance in its Wishart form). Our goal is to achieve optimal recovery guarantees while being resilient to small perturbations. Despite a long history of…
We optimize the matrix representation of the nucleon-pair approximation (NPA) of the nuclear shell model. The NPA is a widely adopted truncation approach of the nuclear shell model and proves to be effective in describing low-lying states…
Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine…
We propose a family of noncontextuality inequalities and show that they can be used for certification of multiqubit quantum systems. Our scheme, unlike those based on non-locality, does not require spatial separation between the subsystems,…
The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have…
Contrary to common belief, a recent work by Ellen, Gelashvili, Shavit, and Zhu has shown that computability does not require multicore architectures to support "strong" synchronization instructions like compare-and-swap, as opposed to…
We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, as well as the lower bounds of concurrence. We show by detailed…
Selecting an automatic metric that best emulates human annotators is often non-trivial, because there is no clear definition of "best emulates." A meta-metric is required to compare the human judgments to the automatic metric scores, and…
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these…
In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^\star$, and the goal is to find a certificate of size $\le \text{poly}(k)$ for $f$'s value at $x^\star$. This problem is in…
Symmetric kernel matrices are a well-researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly…
The incompatibility of quantum measurements, i.e. the fact that certain observable quantities cannot be measured jointly is widely regarded as a distinctive quantum feature with important implications for the foundations and the…
We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and…
We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and…
In the quantum optimisation setting, we build on a scheme introduced by Young et al [PRA 88, 062314, 2013], where physical qubits in multiple copies of a problem encoded into an Ising spin Hamiltonian are linked together to increase the…
The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…
We demonstrate that machine learning provides a powerful tool for discovering new approximate quantum error-correcting (AQEC) codes beyond conventional algebraic frameworks. Building upon direct observations through hybrid quantum-classical…
What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of…
We consider the certification of temporal quantum correlations using the pseudo-density matrix (PDM), an extension of the density matrix to the time domain, where negative eigenvalues are key indicators of temporal correlations.…