Classifying fermionic states via many-body correlation measures

Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic correlations and efficient computational physics methods is actively studied but remains ambiguous. We make progress in establishing this connection mathematically. In particular, we find a rigorous classification of states relative to k-fermion correlations, which admits a computational physics interpretation. Correlations are captured by a measure ωk, a function of k-fermion reduced density matrix that we call twisted purity. A condition ωk = 0 for a given k puts the state in a class Gk of correlated states. Sets Gk are nested in k, and Slater determinants correspond to k = 1. Classes Gk=O(1) are shown to be physically relevant, as ωk vanishes or nearly vanishes for truncated configuration-interaction states, perturbation series around Slater determinants, and some nonperturbative eigenstates of the 1D Hubbard model. For each k = O(1), we give an explicit ansatz with a polynomial number of parameters that covers all states in Gk. Potential applications of this ansatz and its connections to the coupled-cluster wavefunction are discussed

VCrypt: Leveraging Vectorized and Compressed Execution for Client-side Encryption

VCrypt is a novel extension on DuckDB that enables fine-grained client-side [en/de]cryption in a performance- and storage-efficient manner, by exploiting columnar compression as well as vectorized and compressed execution. We designed VCrypt such that in analytical queries, typically (i) data can be encrypted and decrypted batch-at-a-time instead of value-at-a-time, and (ii) the extra storage for cryptographic nonces gets compressed away. We also demonstrate the use of VCrypt inside MotherDuck, leveraging its hybrid processing model that evaluates SQL queries partly on a client DuckDB and partly on a cloud DuckDB, to achieve secure hybrid execution. This provides security even if the cloud server is untrusted, by forcing the [en/de]cryption of sensitive data to happen only client-side, while still allowing useful cloud-side work like filters and joins

Semidefinite approximations for bicliques and bi-independent pairs

We investigate some graph parameters dealing with bi-independent pairs (A, B) in a bipartite graph G= (V1 ∪ V2,E), that is, pairs (A, B) where A⊆ V1, B⊆ V2, and A∪ B are independent. These parameters also allow us to study bicliques in general graphs. When maximizing the cardinality |A∪ B|, one finds the stability number α(G), well-known to be polynomial-time computable. When maximizing the product |A| · |B|, one finds the parameter g(G), shown to be NP-hard by Peeters in 2003, and when maximizing the ratio |A| · |B|=|A∪ B|, one finds h(G), introduced by Vallentin in 2020 for bounding product-free sets in finite groups. We show that h(G) is an NP-hard parameter and, as a crucial ingredient, that it is NP-complete to decide whether a bipartite graph G has a balanced maximum independent set. These hardness results motivate introducing semidefinite programming (SDP) bounds for g(G), h(G), and αbal(G) (the maximum cardinality of a balanced independent set). We show that these bounds can be seen as natural variations of the Lovász ϑ-number, a well-known semidefinite bound on α(G). In addition, we formulate closed-form eigenvalue bounds, and we show relationships among them as well as with earlier spectral parameters by Hoffman and Haemers in 2001 and Vallentin in 2020

II Zebrawriter

This is the converted file of the 5 hole papertape. The source is X1 handcode assembler

Extreme values for the waiting time in large fork-join queues

We prove that the scaled maximum steady-state waiting time and the scaled maximum steady-state queue length among N GI/GI/1-queues in the N-server fork-join queue converge to a normally distributed random variable as N→∞. The maximum steady-state waiting time in this queueing system scales around 1γlogN, where γ is determined by the cumulant generating function Λ of the service times distribution and solves the Cramér–Lundberg equation with stochastic service times and deterministic interarrival times. This value 1γlogN is reached at a certain hitting time. The number of arrivals until that hitting time satisfies the central limit theorem, with standard deviation σAΛ′(γ)γ. By using the distributional form of Little’s law, we can extend this result to the maximum queue length. Finally, we extend these results to a fork-join queue with different classes of servers

An analysis of constraint-relaxation in PDE-based inverse problems

Many inverse problems are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which the inherent non-linearity of the problem is an important one. In this paper, we focus on a relaxed formulation of the PDE-constrained optimization problem and provide analysis for its properties including convexity under certain assumptions. Starting from an infinite-dimensional formulation of the inverse problem with discrete data, we propose a general framework for the analysis and discretisation of such problems. The relaxed formulation of the PDE-constrained optimization problem is shown to reduce to a weighted non-linear least-squares problem. The weight matrix turns out to be the Gram matrix of solutions of the PDE, and in some cases be estimated directly from the measurements. The latter observation points to a potential way to unify recently proposed data-driven reduced-order models for inverse problems with PDE-constrained optimization. We provide a number of representative case studies and numerical examples to illustrate our findings

Review argumentation at scale

Product reviews represent a valuable source of information for both (potential) customers and sellers. Usually, reviews come in pairs (score, motivation), where the motivation is a piece of unstructured text explaining the score given to a product. For reviews, this setting is ideal to combine a quantitative assessment of a product with a qualitative explanation. Aggregating the numerical scores might be uninformative while parsing large quantities of text might be challenging. Automated argument analysis can help in this process, and we previously developed an argument-based quality analysis pipeline that helps identify the most significant items from a corpus of reviews. Given that the pipeline is effective but time-consuming, this work sets out to improve its computational efficiency. Next to optimisation by conventional methods, we investigate the effect of reducing the number of text chunks that are used to build the argumentation graph. We find that conventional methods significantly improve the computation time, which allows us to analyse much larger datasets of real-world reviews. When the number of tokens is scaled down, accuracy remains similar compared to the original version of the pipeline. However, we find that this does not necessarily result in a computation time reduction

Alter Heritage: A web app to gather expert knowledge on inclusive cultural heritage metadata

In this demo paper, we present the web application Alter Heritage. Its goal is to support researchers in collecting domain experts' knowledge about inclusive cultural heritage metadata. While stakeholders in the cultural sector have been formulating strategies to mitigate biases in metadata, there is little empirical knowledge on how the metadata can be revised for inclusivity by users. With Alter Heritage, researchers can study what kind of alterations users make in artefacts' metadata to make it inclusive, how these alterations differ per artefacts and users. We develop the app's core metadata editing functionality based on requirements elicited from existing practices and guidelines in the cultural heritage domain. The data gathered via Alter Heritage will contribute to understanding of the specific alterations that make digital artefacts' metadata more inclusive

Mixed Schur-Weyl duality in quantum information

This thesis explores the interplay between representation theory and quantum information. Specifically, we focus on mixed Schur–Weyl duality, which considers the action of the unitary group on mixed tensors. This setting naturally arises in quantum information tasks involving unitary-equivariant channels, such as port-based teleportation, quantum majority vote, and universal transposition of unitary operators. A key contribution of this thesis is an explicit derivation of the action of the generators of the partially transposed permutation matrix algebra—the commutant of the mixed unitary action—in the Gelfand–Tsetlin basis. As another key result of this thesis, we develop efficient quantum circuits for the mixed quantum Schur transform, a novel primitive in quantum information. The key ingredient of our construction is new efficient circuits for the dual Clebsch–Gordan transform of the unitary group. A significant application of our findings is the construction of efficient quantum algorithms for port-based teleportation, a variant of quantum teleportation that eliminates the need for corrective operations. Another application is a symmetry reduction of semidefinite optimisation problems with unitary equivariance symmetry. Finally, we study the extendibility of quantum states possessing unitary, mixed unitary, or orthogonal symmetry on the complete graph. We obtain analytically the exact maximum values for projections onto the maximally entangled state and the antisymmetric state for each of the three symmetry classes. This thesis demonstrates the usefulness of mixed Schur–Weyl duality in quantum information and computing. We expect that our tools will help address other problems in other areas of quantum information processing, such as communication, cryptography, and simulation