Related papers: Unitary Averaging with Fault and Loss Tolerance

We propose and experimentally demonstrate an approximate universal-NOT (U-NOT) operation that is robust against operational errors. In our proposal, the U-NOT operation is composed of stochastic unitary operations represented by the…

Neural Networks (NN) have recently emerged as backbone of several sensitive applications like automobile, medical image, security, etc. NNs inherently offer Partial Fault Tolerance (PFT) in their architecture; however, the biased PFT of NNs…

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires…

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…

The traditional approach to fault tolerant computing involves replicating computation units and applying a majority vote operation on individual result bits. This approach, however, has several limitations; the most severe is the resource…

In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error…

The cat code is a promising encoding scheme for bosonic quantum error correction as it allows for correction against losses--the dominant error mechanism in most bosonic systems. However, for losses to be detected efficiently without…

Qubits encoded in a decoherence-free subsystem and realized in exchange-coupled silicon quantum dots are promising candidates for fault-tolerant quantum computing. Benefits of this approach include excellent coherence, low control…

Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a…

We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…

We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a…

For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…

With the increasing deployment of deep neural networks (DNNs) in terrestrial and aerospace safety-critical applications, system reliability has emerged as a co-equal design metric alongside computational efficiency. Algorithm-based fault…

We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…

Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than…

In this paper we show how the fault--tolerant error correction scheme recently proposed by DiVincenzo and Shor may be improved. Our scheme, unlike the earlier one, can also deal with a single error that might occur {\em during} the gate…

In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the…

Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more…

We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…