Related papers: Variations on Classical and Quantum Extractors
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown…
The extraction of randomness from weakly random seeds is a problem of central importance with multiple applications. In the device-independent setting, this problem of quantum randomness amplification has been mainly restricted to specific…
Although classical computing has excelled in a wide range of applications, there remain problems that push the limits of its capabilities, especially in fields like cryptography, optimization, and materials science. Quantum computing…
Quantum differential equation solvers aim to prepare solutions as $n$-qubit quantum states over a fine grid of $O(2^n)$ points, surpassing the linear scaling of classical solvers. However, unlike classically stored vectors of solutions, the…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The…
The rapid development of quantum technology demands efficient characterization of complex quantum many-body states. However, full quantum state tomography requires an exponential number of measurements in system size, preventing its…
When the wavefunction of a large quantum system unitarily evolves away from a low-entropy initial state, there is strong circumstantial evidence it develops "branches": a decomposition into orthogonal components that is indistinguishable…
The conditional disclosure of secrets (CDS) setting is among the most basic primitives studied in information-theoretic cryptography. Motivated by a connection to non-local quantum computation and position-based cryptography, CDS with…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
Motivated by the limited qubit capacity of current quantum systems, we study the quantum sample complexity of $k$-qubit quantum operators, i.e., operations applicable on only $k$ out of $d$ qubits. The problem is studied according to the…
An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a…
The Single-Source Shortest Path (SSSP) problem is a cornerstone of computer science with vast applications, for which Dijkstra's algorithm has long been the classical baseline. While various quantum algorithms have been proposed, their…
We study the correlation structure of separable and classical states in 2x2- and 2x3-dimensional quantum systems with fixed spectra. Even for such simple systems the maximal correlation - as measured by mutual information - over the set of…
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…
Quantum entanglement is a key enabling ingredient in diverse applications. However, the presence of unwanted adversarial entanglement also poses challenges in many applications. In this paper, we explore methods to "break" quantum…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…
Quantum spectroscopy with single two level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by…