Related papers: Quantum hardness of learning shallow classical cir…
Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…
Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$…
We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable.…
We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result…
The rapid evolution of quantum devices fuels concerted efforts to experimentally establish quantum advantage over classical computing. Many demonstrations of quantum advantage, however, rely on computational assumptions and face…
We show direct and conceptually simple reductions between the classical learning with errors (LWE) problem and its continuous analog, CLWE (Bruna, Regev, Song and Tang, STOC 2021). This allows us to bring to bear the powerful machinery of…
We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes…
Learning an unknown $n$-qubit quantum state $\rho$ is a fundamental challenge in quantum computing. Information-theoretically, it is known that tomography requires exponential in $n$ many copies of $\rho$ to estimate it up to trace…
Density modelling is the task of learning an unknown probability density function from samples, and is one of the central problems of unsupervised machine learning. In this work, we show that there exists a density modelling problem for…
We present two protocols for classical verification of quantum depth. Our protocols allow a purely classical verifier to distinguish devices with different quantum circuit depths even in the presence of classical computation. We show that a…
It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information.…
We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples…
Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
Our main result is a quantum public-key encryption scheme based on the Extrapolated Dihedral Coset problem (EDCP) which is equivalent, under quantum polynomial-time reductions, to the Learning With Errors (LWE) problem. For limited number…
The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…
We study here the conditions to perform the distribution of a pure state on a quantum network using quantum operations which can succeed with a non-zero probability, the Stochastic Local Operation and Classical Communication (SLOCC)…
Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: Can…
Despite the theoretical significance and wide practical use of regular expressions, the computational complexity of learning them has been largely unexplored. We study the computational hardness of improperly learning regular expressions in…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…