Related papers: Separations in query complexity using cheat sheets
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…
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…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
We show a partial Boolean function $f$ together with an input $x\in f^{-1}\left(*\right)$ such that both $C_{\bar{0}}\left(f,x\right)$ and $C_{\bar{1}}\left(f,x\right)$ are at least $C\left(f\right)^{2-o\left(1\right)}$. Due to recent…
The pointer function of G{\"{o}}{\"{o}}s, Pitassi and Watson \cite{DBLP:journals/eccc/GoosP015a} and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized and…
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…
This paper explores a fine-grained version of the Watrous conjecture, including the randomized and quantum algorithms with success probabilities arbitrarily close to $1/2$. Our contributions include the following: i) An analysis of the…
Early in 1992, Deutsch-Jozsa algorithm computed a symmetric partial Boolean function with a single quantum query, and thus achieved the best separation between classical deterministic and exact quantum query complexity. Until recent years,…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the…
In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…
We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a…
We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…
We give an exponential separation between one-way quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean Hidden Matching Problem of Bar-Yossef et al.) Earlier such an exponential separation…
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 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…