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Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the…
Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues, but its standard, eigenstate-centric form relies on carefully prepared coherent inputs that are costly or impractical for many strongly…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms,…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for…
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…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…
Determining the energy gap in a quantum many-body system is critical to understanding its behavior and is important in quantum chemistry and condensed matter physics. The challenge of determining the energy gap requires identifying both the…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve…
Since the initial discovery of the Wootters-Zurek no-cloning theorem, a wide variety of quantum cloning machines have been proposed aiming at imperfect but optimal cloning of quantum states within its own context. Remarkably, most previous…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…