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We study fault-tolerant consensus in a variant of the synchronous message passing model, where, in each round, every node can choose to be awake or asleep. This is known as the sleeping model (Chatterjee, Gmyr, Pandurangan PODC 2020) and…
The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse…
Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the…
An economy of scale is found when storing many qubits in one highly entangled block of a topological quantum code. The code is defined by construction of a topologically convoluted 2-d surface and does not work by compressing redundancy in…
Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we…
We study the properties of energy flux in wave turbulence via the Majda-McLaughlin-Tabak (MMT) equation with a quadratic dispersion relation. One of our purposes is to resolve the inter-scale energy flux $P$ in the stationary state to…
Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error events is conveniently described within a scaling theory,…
The energy consumption issue in distributed computing systems has become quite critical due to environmental concerns. In response to this, many energy-aware scheduling algorithms have been developed primarily by using the dynamic…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the…
We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle $C_n$, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of $n \geq 3$, and runs in…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
This paper proposes a "quasi-synchronous" design approach for signal processing circuits, in which timing violations are permitted, but without the need for a hardware compensation mechanism. The case of a low-density parity-check (LDPC)…
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
Just as there are frictional losses associated with moving masses on a surface, what if there were frictional losses associated with moving information on a substrate? Indeed, many modes of communication suffer from such frictional losses.…
Recent advances in quantum error-correction (QEC) have shown that it is often beneficial to understand fault-tolerance as a dynamical process, a circuit with redundant measurements that help correct errors, rather than as a static code…