Related papers: Quantum Algorithms for Learning Symmetric Juntas v…
In this paper, we consider the problem of tolerant junta testing for boolean function. Compared with the prior work by Blais et al., we provide improved results in terms of both the parameter gap and query complexity. Compared with the…
The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh coefficients of an $n$ variable Boolean function. Roughly speaking, it takes a…
Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where the depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean…
Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…
We give an efficient algorithm to strongly refute \emph{semi-random} instances of all Boolean constraint satisfaction problems. The number of constraints required by our algorithm matches (up to polylogarithmic factors) the best-known…
The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the…
The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query…
We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x.…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…