Related papers: Variations on Classical and Quantum Extractors
Boson sampling stands out as a promising approach toward experimental demonstration of quantum computational advantage. However, the presence of physical noise in near-term experiments hinders the realization of the quantum computational…
Informally, an extractor delivers perfect randomness from a source that may be far away from the uniform distribution, yet contains some randomness. This task is a crucial ingredient of any attempt to produce perfectly random…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
We make progress in the following three problems: 1. Constructing optimal seeded non-malleable extractors; 2. Constructing optimal privacy amplification protocols with an active adversary, for any security parameter; 3. Constructing…
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…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which…
A $(k,\varepsilon)$-non-malleable extractor is a function ${\sf nmExt} : \{0,1\}^n \times \{0,1\}^d \to \{0,1\}$ that takes two inputs, a weak source $X \sim \{0,1\}^n$ of min-entropy $k$ and an independent uniform seed $s \in \{0,1\}^d$,…
The very old problem of extracting frequencies from time signals is addressed in the case of signals that are very short as compared to their intrinsic time scales. The solution of the problem is not only important to the classic signal…
Quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators, may be built with capabilities exceeding classical computers. A quantum…
As the scale of quantum programs grows to match that of classical software, the nascent field of quantum software engineering must mature and tools such as debuggers will become increasingly important. However, developing a quantum debugger…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…
Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…
Recent works by Bravyi, Gosset and K\"onig (Science 2018), Bene Watts et al. (STOC 2019), Coudron, Stark and Vidick (QIP 2019) and Le Gall (CCC 2019) have shown unconditional separations between the computational powers of shallow (i.e.,…
At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…
Recently, quantum computing experiments have for the first time exceeded the capability of classical computers to perform certain computations -- a milestone termed "quantum computational advantage." However, verifying the output of the…
Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators is that they generally require less memory than their…
Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is…