Related papers: Assessing fault-tolerant quantum advantage for $k$…

Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…

Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…

Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M? Here we answer this question to the affirmative. We present a hybrid…

Over the past decade, the rapid advancement of deep learning and big data applications has been driven by vast datasets and high-performance computing systems. However, as we approach the physical limits of semiconductor fabrication in the…

In this paper we present a backtracking version of the survey propagation algorithm. We show that the introduction of the simplest form of backtracking greatly improves the ability of the original survey propagation algorithm in solving…

We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…

Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is…

Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…

Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…

Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we…

The classical 3SUM conjecture states that the class of 3SUM-hard problems does not admit a truly subquadratic $O(n^{2-\delta})$-time algorithm, where $\delta >0$, in classical computing. The geometric 3SUM-hard problems have widely been…

Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without…

Classical simulation of quantum computation has often been viewed as the method to determine where the horizon of quantum supremacy is located---that is, where quantum computation can no longer be simulated by classical methods. As of now,…

While real quantum devices have been increasingly used to conduct research focused on achieving quantum advantage or quantum utility in recent years, executing deep quantum circuits or performing quantum machine learning with large-scale…

The \emph{Dominating $H$-Pattern} problem generalizes the classical $k$-Dominating Set problem: for a fixed \emph{pattern} $H$ and a given graph $G$, the goal is to find an induced subgraph $S$ of $G$ such that (1) $S$ is isomorphic to $H$,…

Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…

Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…

We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…

We present an optimized adiabatic quantum schedule for unstructured search building on the original approach of Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. Our schedule adiabatically varies the Hamiltonian even more rapidly at the…

We give quantum speedups of several general-purpose numerical optimisation methods for minimising a function $f:\mathbb{R}^n \to \mathbb{R}$. First, we show that many techniques for global optimisation under a Lipschitz constraint can be…