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Holant problems are a family of counting problems parameterised by sets of algebraic-complex valued constraint functions, and defined on graphs. They arise from the theory of holographic algorithms, which was originally inspired by concepts from quantum computation. Here, we employ quantum information theory to explain existing results about holant problems in a concise way and to derive two new dichotomies: one for a new family of problems, which we call Holant$^+$, and, building on this, a full dichotomy for Holant$^c$. These two families of holant problems assume the availability of certain unary constraint functions -- the two pinning functions in the case of Holant$^c$, and four functions in the case of Holant$^+$ -- and allow arbitrary sets of algebraic-complex valued constraint functions otherwise. The dichotomy for Holant$^+$ also applies when inputs are restricted to instances defined on planar graphs. In proving these complexity classifications, we derive an original result about entangled quantum states.

This paper presents two novel hybrid beamforming (HYBF) designs for a multi-cell massive multiple-input-multiple-output (mMIMO) millimeter wave (mmWave) full duplex (FD) system under limited dynamic range (LDR). Firstly, we present a novel centralized HYBF (C-HYBF) scheme based on alternating optimization. In general, the complexity of C-HYBF schemes scales quadratically as a function of the number of users and cells, which may limit their scalability. Moreover, they require significant communication overhead to transfer complete channel state information (CSI) to the central node every channel coherence time for optimization. The central node also requires very high computational power to jointly optimize many variables for the uplink (UL) and downlink (DL) users in FD systems. To overcome these drawbacks, we propose a very low-complexity and scalable cooperative per-link parallel and distributed (P$\&$D)-HYBF scheme. It allows each mmWave FD base station (BS) to update the beamformers for its users in a distributed fashion and independently in parallel on different computational processors. The complexity of P$\&$D-HYBF scales only linearly as the network size grows, making it desirable for the next generation of large and dense mmWave FD networks. Simulation results show that both designs significantly outperform the fully digital half duplex (HD) system with only a few radio-frequency (RF) chains, achieve similar performance, and the P$\&$D-HYBF design requires considerably less execution time.

The possibilities offered by quantum computing have drawn attention in the distributed computing community recently, with several breakthrough results showing quantum distributed algorithms that run faster than the fastest known classical counterparts, and even separations between the two models. A prime example is the result by Izumi, Le Gall, and Magniez [STACS 2020], who showed that triangle detection by quantum distributed algorithms is easier than triangle listing, while an analogous result is not known in the classical case. In this paper we present a framework for fast quantum distributed clique detection. This improves upon the state-of-the-art for the triangle case, and is also more general, applying to larger clique sizes. Our main technical contribution is a new approach for detecting cliques by encapsulating this as a search task for nodes that can be added to smaller cliques. To extract the best complexities out of our approach, we develop a framework for nested distributed quantum searches, which employ checking procedures that are quantum themselves. Moreover, we show a circuit-complexity barrier on proving a lower bound of the form $\Omega(n^{3/5+\epsilon})$ for $K_p$-detection for any $p \geq 4$, even in the classical (non-quantum) distributed CONGEST setting.

This paper focuses on stochastic saddle point problems with decision-dependent distributions in both the static and time-varying settings. These are problems whose objective is the expected value of a stochastic payoff function, where random variables are drawn from a distribution induced by a distributional map. For general distributional maps, the problem of finding saddle points is in general computationally burdensome, even if the distribution is known. To enable a tractable solution approach, we introduce the notion of equilibrium points -- which are saddle points for the stationary stochastic minimax problem that they induce -- and provide conditions for their existence and uniqueness. We demonstrate that the distance between the two classes of solutions is bounded provided that the objective has a strongly-convex-strongly-concave payoff and Lipschitz continuous distributional map. We develop deterministic and stochastic primal-dual algorithms and demonstrate their convergence to the equilibrium point. In particular, by modeling errors emerging from a stochastic gradient estimator as sub-Weibull random variables, we provide error bounds in expectation and in high probability that hold for each iteration; moreover, we show convergence to a neighborhood in expectation and almost surely. Finally, we investigate a condition on the distributional map -- which we call opposing mixture dominance -- that ensures the objective is strongly-convex-strongly-concave. Under this assumption, we show that primal-dual algorithms converge to the saddle points in a similar fashion.

Quantum noise is the key challenge in Noisy Intermediate-Scale Quantum (NISQ) computers. Previous work for mitigating noise has primarily focused on gate-level or pulse-level noise-adaptive compilation. However, limited research efforts have explored a higher level of optimization by making the quantum circuits themselves resilient to noise. We propose QuantumNAS, a comprehensive framework for noise-adaptive co-search of the variational circuit and qubit mapping. Variational quantum circuits are a promising approach for constructing QML and quantum simulation. However, finding the best variational circuit and its optimal parameters is challenging due to the large design space and parameter training cost. We propose to decouple the circuit search and parameter training by introducing a novel SuperCircuit. The SuperCircuit is constructed with multiple layers of pre-defined parameterized gates and trained by iteratively sampling and updating the parameter subsets (SubCircuits) of it. It provides an accurate estimation of SubCircuits performance trained from scratch. Then we perform an evolutionary co-search of SubCircuit and its qubit mapping. The SubCircuit performance is estimated with parameters inherited from SuperCircuit and simulated with real device noise models. Finally, we perform iterative gate pruning and finetuning to remove redundant gates. Extensively evaluated with 12 QML and VQE benchmarks on 14 quantum computers, QuantumNAS significantly outperforms baselines. For QML, QuantumNAS is the first to demonstrate over 95% 2-class, 85% 4-class, and 32% 10-class classification accuracy on real QC. It also achieves the lowest eigenvalue for VQE tasks on H2, H2O, LiH, CH4, BeH2 compared with UCCSD. We also open-source TorchQuantum (//github.com/mit-han-lab/torchquantum) for fast training of parameterized quantum circuits to facilitate future research.

The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.

Most Deep Reinforcement Learning (Deep RL) algorithms require a prohibitively large number of training samples for learning complex tasks. Many recent works on speeding up Deep RL have focused on distributed training and simulation. While distributed training is often done on the GPU, simulation is not. In this work, we propose using GPU-accelerated RL simulations as an alternative to CPU ones. Using NVIDIA Flex, a GPU-based physics engine, we show promising speed-ups of learning various continuous-control, locomotion tasks. With one GPU and CPU core, we are able to train the Humanoid running task in less than 20 minutes, using 10-1000x fewer CPU cores than previous works. We also demonstrate the scalability of our simulator to multi-GPU settings to train more challenging locomotion tasks.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.

The field of Multi-Agent System (MAS) is an active area of research within Artificial Intelligence, with an increasingly important impact in industrial and other real-world applications. Within a MAS, autonomous agents interact to pursue personal interests and/or to achieve common objectives. Distributed Constraint Optimization Problems (DCOPs) have emerged as one of the prominent agent architectures to govern the agents' autonomous behavior, where both algorithms and communication models are driven by the structure of the specific problem. During the last decade, several extensions to the DCOP model have enabled them to support MAS in complex, real-time, and uncertain environments. This survey aims at providing an overview of the DCOP model, giving a classification of its multiple extensions and addressing both resolution methods and applications that find a natural mapping within each class of DCOPs. The proposed classification suggests several future perspectives for DCOP extensions, and identifies challenges in the design of efficient resolution algorithms, possibly through the adaptation of strategies from different areas.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.