Related papers: Forrelation is Extremally Hard
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
Given a Boolean function $f:\{0,1\}^n\to\{0,1\}$, the goal in the usual query model is to compute $f$ on an unknown input $x \in \{0,1\}^n$ while minimizing the number of queries to $x$. One can also consider a "distinguishing" problem…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…
A basic condition for efficient transfer learning is the similarity between a target model and source models. In practice, however, the similarity condition is difficult to meet or is even violated. Instead of the similarity condition, a…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
The key step in classical convolution and correlation algorithms, the componentwise multiplication of vectors after initial Fourier Transforms, is shown to be physically impossible to do on quantum states. Then this is used to show that…
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.…
Classical machine learning models struggle with learning and prediction tasks on data sets exhibiting long-range correlations. Previously, the existence of a long-range correlational structure known as contextuality was shown to inhibit…
This paper studies the gap between quantum one-way communication complexity $Q(f)$ and its classical counterpart $C(f)$, under the {\em unbounded-error} setting, i.e., it is enough that the success probability is strictly greater than 1/2.…
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…
The results showing a quantum query complexity of $\Theta(N^{1/3})$ for the collision problem do not apply to random functions. The issues are two-fold. First, the $\Omega(N^{1/3})$ lower bound only applies when the range is no larger than…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
Given a function f as an oracle, the collision problem is to find two distinct inputs i and j such that f(i)=f(j), under the promise that such inputs exist. Since the security of many fundamental cryptographic primitives depends on the…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random…
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…
Let $f\subseteq\{0,1\}^n\times\Xi$ be a relation and $g:\{0,1\}^m\to\{0,1,*\}$ be a promise function. This work investigates the randomised query complexity of the relation $f\circ g^n\subseteq\{0,1\}^{m\cdot n}\times\Xi$, which can be…
In this paper, we theoretically and experimentally analyze sequential processors with limited communication between parts. We compare the expressivity of sequential quantum and classical processors under the same constraints. They consist…