Related papers: On the Complexity of Searching Maximum of a Functi…

We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…

Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…

While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…

In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a…

We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…

In this paper we present a supervised machine learning quantum classifier. It consists of a quantum data re-uploading classifier with binary trainable parameters, the optimal values of which are found by a quantum search algorithm. We show…

Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to…

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…

Consider a function f which is defined on the integers from 1 to N and takes the values -1 and +1. The parity of f is the product over all x from 1 to N of f(x). With no further information about f, to classically determine the parity of f…

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…

An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…

Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…

Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…

Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…

Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic…

Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…

In previous works, we showed that an optimal quantum algorithm can always be seen as a sum over classical histories in each of which the problem solver knows in advance one of the possible halves of the solution she will read in the future…