Related papers: Density Evolution and Functional Threshold for the…
Noise is a ubiquitous feature of the physical world. As a result, the first prerequisite of life is fault tolerance: maintaining integrity of state despite external bombardment. Recent experimental advances have revealed that biological…
We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present…
Understanding fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the…
An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent…
The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are…
Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the…
We consider the problem of sequential decision making on random fields corrupted by noise. In this scenario, the decision maker observes a noisy version of the data, yet judged with respect to the clean data. In particular, we first…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
Mutation analysis has long been used in classical software testing and has recently been adopted for assessing the robustness of quantum software testing techniques. However, existing studies assume ideal, noiseless execution, overlooking…
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the…
Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates…
We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to…
The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust…
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…
Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…
We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here, we revisit the question of its efficacy in the…