Related papers: Improved maximum-likelihood quantum amplitude esti…
Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE),…
Quantum Machine Learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources…
Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and…
Quantum computers progress toward outperforming classical supercomputers, but quantum errors remain their primary obstacle. The key to overcoming errors on near-term devices has emerged through the field of quantum error mitigation,…
In this paper, we show new algorithms, hardness results and applications for $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the…
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA),…
We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of "early fault tolerance" where limited error correction is available. We propose a framework for designing early…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
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…
Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most…
This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle $U_\varphi$ on an eigenstate $|x\rangle$ is to apply a state-dependent…
Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental…
Higher-order theory predictions are crucial for the precision LHC program, but the time-consuming amplitude evaluation challenges the corresponding Monte-Carlo simulations. Machine-learned amplitude surrogates can resolve this problem, if…
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…
Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ…
Quantum algorithms have gained increasing attention for addressing complex combinatorial problems in finance, notably portfolio optimization. This study systematically benchmarks two prominent variational quantum approaches, Variational…
Quantum machine learning holds promise for advancing time series forecasting. The Quantum Recurrent Neural Network (QRNN), inspired by classical RNNs, encodes temporal data into quantum states that are periodically input into a quantum…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…