Related papers: Testing classical properties from quantum data
The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope…
The standard model of Boolean function property testing is not well suited for testing $\textit{sparse}$ functions which have few satisfying assignments, since every such function is close (in the usual Hamming distance metric) to the…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
Superposition is the core feature that sets quantum theory apart from classical physics. Here, we investigate whether sets of quantum measurements can be modelled by using only devices that are operationally classical, in the sense that…
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for…
We study the query complexity of testing for properties defined by read once formulas, as instances of {\em massively parametrized properties}, and prove several testability and non-testability results. First we prove the testability of any…
In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on $n$ bits requires either $\Omega(n^2)$ bits of classical memory or an exponential number (in~$n$) of random samples. A line of recent works…
We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion…
In this paper, we inaugurate the field of quantum fair machine learning. We undertake a comparative analysis of differences and similarities between classical and quantum fair machine learning algorithms, specifying how the unique features…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and…
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box.…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being…
We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical…