Related papers: Computing Linear Transformations with Unreliable C…

Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…

We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…

Polar codes are a family of capacity-achieving error-correcting codes, and they have been selected as part of the next generation wireless communication standard. Each polar code bit-channel is assigned a reliability value, used to…

Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…

The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…

The nascent computational paradigm of quantum reservoir computing presents an attractive use of near-term, noisy-intermediate-scale quantum processors. To understand the potential power and use cases of quantum reservoir computing, it is…

Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty…

We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…

In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…

Quantum memory systems are vital in quantum information processing for dependable storage and retrieval of quantum states. Inspired by classical reliability theories that synthesize reliable computing systems from unreliable components, we…

Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize physically. The core difficulty lies in the fact that when…

Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…

We consider transmission over a binary-input additive white Gaussian noise channel using low-density parity-check codes. One of the most popular techniques for decoding low-density parity-check codes is the linear programming decoder. In…

Fidelity is one of the most valuable and commonly used metrics for assessing the performance of quantum circuits on error-prone quantum processors. Several approaches have been proposed to estimate circuit fidelity without executing it on…

Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…

Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…

Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…

In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…

In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded…