Trading Permutation Invariance for Communication in Multi-Party Non-Locality Distillation

Quantum theory puts forward phenomena unexplainable by classical physics - or information, for that matter. A prominent example is non-locality. Non-local correlations cannot be explained, in classical terms, by shared information but only by communication. On the other hand, the phenomenon does not allow for (potentially faster-than-light) message transmission. The fact that some non-local and non-signaling correlations are predicted by quantum theory, whereas others fail to be, asks for a criterion, as simple as possible, that characterizes which joint input-output behaviors are ``quantum'' and which are not. In the context of the derivation of such criteria, it is of central importance to understand when non-local correlations can be amplified by a non-interactive protocol, i.e., whether some types of weak non-locality can be distilled into stronger by local operations. Since it has been recognized that the searched-for criteria must inherently be multi-partite, the question of distillation, extensively studied and understood two-party scenarios, should be adressed in the multi-user setting, where much less is known. Considering the space of intrinsically n-partite correlations, we show the possibility of distilling weak non-local boxes to the algebraically maximal ones without any communication. Our protocols improve on previously known methods which still required partial communication. The price we have to pay for dropping the need for communication entirely is the assumption of permutation invariance: Any correlation that can be realized between some set of players is possible between any such set. This assumption is very natural since the laws of physics are invariant under spacial translation.Comment: 7 pages, 4 figures, for a conferenc

Continuous-variable entanglement distillation and non-commutative central limit theorems

Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The flexibility of these protocols give rise to several beneficial trade-offs related to success probabilities or memory requirements, which that can be adjusted to reflect experimental demands. Despite these protocols involving measurements, we relate the convergence in this protocols to new instances of non-commutative central limit theorems, in a formalism that we lay out in great detail. Implications of the findings for quantum repeater schemes are discussed.Comment: published versio

Advancing Transformer Architecture in Long-Context Large Language Models: A Comprehensive Survey

Transformer-based Large Language Models (LLMs) have been applied in diverse areas such as knowledge bases, human interfaces, and dynamic agents, and marking a stride towards achieving Artificial General Intelligence (AGI). However, current LLMs are predominantly pretrained on short text snippets, which compromises their effectiveness in processing the long-context prompts that are frequently encountered in practical scenarios. This article offers a comprehensive survey of the recent advancement in Transformer-based LLM architectures aimed at enhancing the long-context capabilities of LLMs throughout the entire model lifecycle, from pre-training through to inference. We first delineate and analyze the problems of handling long-context input and output with the current Transformer-based models. We then provide a taxonomy and the landscape of upgrades on Transformer architecture to solve these problems. Afterwards, we provide an investigation on wildly used evaluation necessities tailored for long-context LLMs, including datasets, metrics, and baseline models, as well as optimization toolkits such as libraries, frameworks, and compilers to boost the efficacy of LLMs across different stages in runtime. Finally, we discuss the challenges and potential avenues for future research. A curated repository of relevant literature, continuously updated, is available at https://github.com/Strivin0311/long-llms-learning.Comment: 40 pages, 3 figures, 4 table

Excursions at the Interface of Topological Phases of Matter and Quantum Error Correction

Topological quantum error-correcting codes are a family of stabilizer codes that are built using a lattice of qubits covering some manifold. The stabilizers of the code are local with respect to the underlying lattice, and logical information is encoded in the non-local degrees of freedom. The locality of stabilizers in these codes makes them especially suitable for experiments. From the condensed matter perspective, their code space corresponds to the ground state subspace of a local Hamiltonian belonging to a non-trivial topological phase of matter. The stabilizers of the code correspond to the Hamiltonian terms, and errors can be thought of as excitations above the ground state subspace. Conversely, one can use fixed point Hamiltonian of a topological phase of matter to define a topological quantum error-correcting code.This close connection has motivated numerous studies which utilize insights from one view- point to address questions in the other. This thesis further explores the possibilities in this di- rection. In the first two chapters, we present novel schemes to implement logical gates, which are motivated by viewing topological quantum error-correcting codes as topological phases of matter. In the third chapter, we show how the quantum error correction perspective could be used to realize robust topological entanglement phases in monitored random quantum circuits. And in the last chapter, we explore the possibility of extending this connection beyond topological quan- tum error-correcting codes. In particular, we introduce an order parameter for detecting k-local non-trivial states, which can be thought of as a generalization of topological states that includes codewords of any quantum error-correcting code

Constructing networks of quantum channels for state preparation

Entangled possibly mixed states are an essential resource for quantum computation, communication, metrology, and the simulation of many-body systems. It is important to develop and improve preparation protocols for such states. One possible way to prepare states of interest is to design an open system that evolves only towards the desired states. A Markovian evolution of a quantum system can be generally described by a Lindbladian. Tensor networks provide a framework to construct physically relevant entangled states. In particular, matrix product density operators (MPDOs) form an important variational class of states. MPDOs generalize matrix product states to mixed states, can represent thermal states of local one-dimensional Hamiltonians at sufficiently large temperatures, describe systems that satisfy the area law of entanglement, and form the basis of powerful numerical methods. In this work we develop an algorithm that determines for a given linear subspace of MPDOs whether this subspace can be the stable space of some frustration free k-local Lindbladian and, if so, outputs an appropriate Lindbladian. We proceed by using machine learning with networks of quantum channels, also known as quantum neural networks (QNNs), to train denoising post-processing devices for quantum sources. First, we show that QNNs can be trained on imperfect devices even when part of the training data is corrupted. Second, we show that QNNs can be trained to extrapolate quantum states to, e.g., lower temperatures. Third, we show how to denoise quantum states in an unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip, dephasing errors, and random unitary noise. Finally, we develop recurrent QNNs (RQNNs) for denoising that requires memory, such as combating drifts. RQNNs can be thought of as matrix product quantum channels with a quantum algorithm for training and are closely related to MPDOs. The proposed preparation and denoising protocols can be beneficial for various emergent quantum technologies and are within reach of present-day experiments

Play Among Books

How does coding change the way we think about architecture? Miro Roman and his AI Alice_ch3n81 develop a playful scenario in which they propose coding as the new literacy of information. They convey knowledge in the form of a project model that links the fields of architecture and information through two interwoven narrative strands in an “infinite flow” of real books

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..