Related papers: Quantum Complexity of Parametric Integration
An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in…
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
Quantum computers (QCs) are maturing. When QCs are powerful enough, they may be able to handle problems in chemistry, physics, and finance that are not classically solvable. However, the applicability of quantum algorithms to speed up…
The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
The Feynman-Kac path integration problem was studied in the worst case setting by Plaskota et al. (J. Comp. Phys. 164 (2000) 335) for the univariate case and by Kwas and Li (J. Comp. 19 (2003) 730) for the multivariate case with d space…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…
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…
Using the properties of quantum superposition, we propose a quantum classification algorithm to efficiently perform multi-class classification tasks, where the training data are loaded into parameterized operators which are applied to the…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…