Related papers: Separating QMA from QCMA with a classical oracle
We study the forrelation problem: given a pair of $n$-bit Boolean functions $f$ and $g$, estimate the correlation between $f$ and the Fourier transform of $g$. This problem is known to provide the largest possible quantum speedup in terms…
We study the limitations of black-box amplification in the quantum complexity class QMA. Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result…
We consider the problems of weighted constrained sampling and weighted model counting, where we are given a propositional formula and a weight for each world. The first problem consists of sampling worlds with a probability proportional to…
Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work,…
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus…
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and…
Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
A proof of quantumness (PoQ) allows a classical verifier to efficiently test if a quantum machine is performing a computation that is infeasible for any classical machine. In this work, we propose a new approach for constructing PoQ…
The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…
We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical"…
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…
We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
We introduce Quantum Spectral Authentication (QSA), a primitive for verifying that a remote quantum endpoint still possesses a previously installed secret quantum resource, such as a hidden state or state-preparation capability, without…
There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the…