Related papers: On reliable computation by noisy random Boolean fo…
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study…
We establish a precise relationship between spherical harmonics and Fourier basis functions over a hypercube randomly embedded in the sphere. In particular, we give a bound on the expected Boolean noise sensitivity of a randomly rotated…
We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many…
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. (FOCS 2012) converts any boolean formula into a resilient formula of polynomial…
Overcoming the influence of noise and imperfections in quantum devices is one of the main challenges for viable quantum applications. In this article, we present different protocols, which we denote as "superposed quantum error mitigation",…
Noise-based logic, by utilizing its multidimensional logic hyperspace, has significant potential for low-power parallel operations in beyond-Moore-chips. However universal gates for Boolean logic thus far had to rely on either time…
I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum computations can be executed reliably provided that noise…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed…
We analyse a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
One of the crucial steps in building a scalable quantum computer is to identify the noise sources which lead to errors in the process of quantum evolution. Different implementations come with multiple hardware-dependent sources of noise and…
Let $0 < \epsilon < 1/2$ be a noise parameter, and let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$. We upper bound the entropy of $T_{\epsilon}…
The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause…
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…
In the Quantum Supremacy regime, quantum computers may overcome classical machines on several tasks if we can estimate, mitigate, or correct unavoidable hardware noise. Estimating the error requires classical simulations, which become…
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…