Related papers: On reliable computation by noisy random Boolean fo…

Postselected quantum computation is distinguished from regular quantum computation by accepting the output only if measurement outcomes satisfy predetermined conditions. The output must be accepted with nonzero probability. Methods for…

This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that…

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…

We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…

Recent advances in associative memory design through strutured pattern sets and graph-based inference algorithms have allowed the reliable learning and retrieval of an exponential number of patterns. Both these and classical associative…

We provide here a universal approximation theorem with precise quantitative error bounds for noisy quantum neural networks. We focus on applications to Quantitative Finance, where target functions are often given as expectations. We further…

We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on $n$ qubits subject to noise…

Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…

It is shown that the counting function of n Boolean variables can be implemented with the formulae of size O(n^3.06) over the basis of all 2-input Boolean functions and of size O(n^4.54) over the standard basis. The same bounds follow for…

Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender…

We study the space of functions computed by random-layered machines, including deep neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed on the recurrent and layer-dependent architectures, we…

In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and…

As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…

This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that…

A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…

We present a numerical study of the robustness of a specific class of non-abelian holonomic quantum gates . We take into account the parametric noise due to stochastic fluctuations of the control fields which drive the time-dependent…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is a fundamental challenge since all physical qubits suffer a considerable level of noise. Moreover, real…

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…

We reformulate the information causality in a more general framework by adopting the results of signal propagation and computation in a noisy circuit. In our framework, the information causality leads to a broad class of Tsirelson…