Related papers: Closed-Form Optimal Quantum Circuits for Single-Qu…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
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…
The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…
Gate-model quantum computers provide an experimentally implementable architecture for near term quantum computations. To design a reduced quantum circuit that can simulate a high complexity reference quantum circuit, an optimization should…
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.…
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,…
In this paper we present a generic construction to obtain an optimal T depth quantum circuit for any arbitrary $n$-input $m$-output Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}^m$ having algebraic degree $k\leq n$, and it achieves an…
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is…
We propose a quantum algorithm (in the form of a quantum oracle) that estimates the closeness of a given Boolean function to one that satisfies the ``strict avalanche criterion'' (SAC). This algorithm requires $n$ queries of the Boolean…
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…
So far, only the results on 3 qubit spaces (both on superconducting and ion-trap realisations of quantum processors) have beaten the classical unstructured search in the expected number of oracle calls using optimal protocols in both…
From an operational point of view, we propose several new entanglement detection criteria using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…
We study the computational limits of learning $k$-bit Boolean functions (specifically, $\mathrm{AND}$, $\mathrm{OR}$, and their noisy variants), using a minimalist single-head softmax-attention mechanism, where $k=\Theta(d)$ relevant bits…
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…