arXiv subjects

Alexander Gresch

Publications and source records attributed to Alexander Gresch.

9 recordsLinked to original sources

arXiv2025

Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information

We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy estimates with error bounds, as captured by guarantees on the problem's sampling complexity. In particular, when limited to Pauli basis measurements, the smallest sampling complexity guarantee comes from a simple single-shot estimator via a straightforward argument based on Hoeffding's inequality. In this work, we construct an adaptive estimator using the state's actual variance. Technically, our estimation method is based on the Empirical Bernstein stopping (EBS) algorithm and grouping schemes, and we provide a rigorous tail bound, which leverages the state's empirical variance. In a numerical benchmark of estimating ground-state energies of several Hamiltonians, we demonstrate that EBS consistently improves upon elementary readout guarantees up to one order of magnitude.

quant-ph↗

arXiv2024

Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware

Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.

quant-ph↗

arXiv2023

Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping

Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. As a central tool, we establish new tail bounds for empirical estimators of the energy. They are helpful for identifying measurement settings that improve the energy estimate the most. This task constitutes an NP-hard problem. However, we are able to circumvent this bottleneck and use the tail bounds to develop a practical, efficient estimation strategy, which we call ShadowGrouping. As the name indicates, it combines shadow estimation methods with grouping strategies for Pauli strings. In numerical experiments, we demonstrate that ShadowGrouping improves upon state-of-the-art methods in estimating the electronic ground-state energies of various small molecules, both in provable and practical accuracy benchmarks. Hence, this work provides a promising way, e.g., to tackle the measurement bottleneck associated with quantum many-body Hamiltonians.

quant-ph↗

arXiv2022

Light-shift induced behaviors observed in momentum-space quantum walks

Over the last decade there have been many advances in studies of quantum walks (QWs) including a momentum-space QW recently realized in our spinor Bose-Einstein condensate system. This QW possessed behaviors that generally agreed with theoretical predictions; however, it also showed momentum distributions that were not adequately explained by the theory. We present a theoretical model which proves that the coherent dynamics of the spinor condensate is sufficient to explain the experimental data without invoking the presence of a thermal cloud of atoms as in the original theory. Our numerical findings are supported by an analytical prediction for the momentum distributions in the limit of zero-temperature condensates. This current model provides more complete explanations to the momentum-space QWs that can be applied to study quantum search algorithms and topological phases in Floquet-driven systems.

quant-ph↗

arXiv2022

Modern applications of machine learning in quantum sciences

In this book, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.

quant-ph↗

arXiv2022

Scalable approach to many-body localization via quantum data

We are interested in how quantum data can allow for practical solutions to otherwise difficult computational problems. A notoriously difficult phenomenon from quantum many-body physics is the emergence of many-body localization (MBL). So far, is has evaded a comprehensive analysis. In particular, numerical studies are challenged by the exponential growth of the Hilbert space dimension. As many of these studies rely on exact diagonalization of the system's Hamiltonian, only small system sizes are accessible. In this work, we propose a highly flexible neural network based learning approach that, once given training data, circumvents any computationally expensive step. In this way, we can efficiently estimate common indicators of MBL such as the adjacent gap ratio or entropic quantities. Our estimator can be trained on data from various system sizes at once which grants the ability to extrapolate from smaller to larger ones. Moreover, using transfer learning we show that already a two-dimensional feature vector is sufficient to obtain several different indicators at various energy densities at once. We hope that our approach can be applied to large-scale quantum experiments to provide new insights into quantum many-body physics.

cond-mat.dis-nn↗

arXiv2019

Experimental realization of a momentum-space quantum walk

We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We carry out a comprehensive experimental study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment; potential applications include atom interferometry and engineering asymmetric walks.

quant-ph↗

arXiv2018

Quantum Walk in Momentum Space with a Bose-Einstein Condensate

We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly flexible and can provide a platform for a wide range of applications such as quantum search algorithms, the observation of topological phases, and the realization of walks with higher dimensionality. Along with the investigation of the quantum-to-classical transition, we demonstrate the distinctive features of a quantum walk and contrast them to those of its classical counterpart. Also, by manipulating either the walk or coin operator, we show how the walk dynamics can be steered or even reversed.

quant-ph↗

arXiv2018

Quantum Walks of kicked Bose-Einstein condensates

We analytically investigate the recently proposed and implemented discrete-time quantum walk based on kicked ultra-cold atoms. We show how the internal level structure of the kicked atoms leads to the emergence of a relative light-shift phase immediately relevant for the experimental realization. Analytical solutions are provided for the momentum distribution for both the case of quantum resonance and the near-resonant quasimomenta.

quant-ph↗