Related papers: Quantum supremacy and high-dimensional integration
Sampling problems demonstrating beyond classical computing power with noisy intermediate scale quantum devices have been experimentally realized. In those realizations, however, our trust that the quantum devices faithfully solve the…
We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Quantum image processing (QIP) means the quantum based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency are theoretically higher than their corresponding classical schemes.…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
Quantum resource theories identify the features of quantum computers that provide their computational advantage over classical systems. We investigate the resources driving the complexity of classical simulation in the standard model of…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
As Moore's law reaches its limits, quantum computers are emerging with the promise of dramatically outperforming classical computers. We have witnessed the advent of quantum processors with over $50$ quantum bits (qubits), which are…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as…
Realizing a large-scale quantum computer requires hardware platforms that can simultaneously achieve universality, scalability, and fault tolerance. As a viable pathway to meeting these requirements, quantum computation based on…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…