Entanglement as a tool in holography and quantum simulators

Projektinformationen

ETHOQS

ID Finanzhilfevereinbarung: 101151139

DOI

10.3030/101151139

Projekt abgeschlossen

EK-Unterschriftsdatum 4 April 2024

Startdatum 1 Mai 2024

Enddatum 30 April 2026

Finanziert unter

• Marie Skłodowska-Curie Actions (MSCA)

Gesamtkosten

Keine Daten

EU-Beitrag

€ 188 590,08

Koordiniert durch

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Italy

Periodic Reporting for period 1 - ETHOQS (Entanglement as a tool in holography and quantum simulators)

Berichtszeitraum: 2024-05-01 bis 2026-04-30

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

In recent decades, quantum simulators have emerged as one of the most promising platforms for exploring complex quantum systems, with applications ranging from condensed matter physics and quantum chemistry to materials science and quantum information processing. However, unlocking their full potential requires both a deeper understanding of non-equilibrium quantum dynamics and robust methods to characterize, verify, and certify the behaviour of increasingly large and complex quantum devices. Various goals of quantum simulators lie largely in the expectation to have engineered the desired quantum states and quantum dynamics. However, there exists a basic challenge; that is to have a precise verification of the engineered dynamics, as well as about the predictions from a device. The project ETHOQS is situated within the broader research interest to develop reliable and scalable quantum technologies capable of accessing behaviour of complex many-body quantum systems. Whereas the long term objective is to attain controls that take us beyond the reach of classical computers, ETHOQS has focused on small scale proof-of-principle examples in various theory and experiment collaborations.

The project addresses several new aspects of many-body quantum systems, and their measurements in present day noisy intermediate scale quantum devices. First, we probe complete statistical information from quantum measurements, enabling the measurements of probability distributions and full counting statistics of general observables during out of equilibrium dynamics. Second, we investigated the preparation and characterization of highly entangled random quantum states. Third, we developed learning and certification frameworks, allowing reliable predictions of system behaviour. Along these works, we have followed a coherent pathway to make a meaningful impact by combining theoretical methods with experimental demonstrations.

Together, these advances strengthen the reliability, characterization, and benchmarking of quantum simulation platforms, contributing essential tools and small scale exampled to set the stage for the next generation of quantum technologies as well as theoretical developments. The project has also shown entanglement measurements, in particular the role of experimental errors and their mitigation has been discussed in detail, allowing reliable measurements from a noisy data. Therefore, the project will be useful in the direction of noise models, noise mitigations and accessing various dynamical properties, including the role of symmetries.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

During the project duration, we have been working on the observation of many-body quantum dynamical properties in quantum simulators. In particular, we can divide our work in three central frontiers, as we describe below.

1- Non-equilibrium quantum dynamics: Probability Distributions and Full Counting Statistics.

In quantum mechanics, outcomes of measurements are not fixed but governed by probabilities. To fully describe the fluctuations of a quantum observable, such as magnetization, we need more than just its average value. Two powerful tools capture this complete statistical information: the probability distribution function (PDF) and the full counting statistics (FCS). Using data from two previous experiments, in a theory-experiment collaboration, we could monitor the PDF and FCS during out of equilibrium quantum dynamics. The key ingredient in our work has been the postprocessing of the experimental data measured in random bases. This work is published in Physical Review Letters and is openly available on the arxiv under the handle arXiv: 2511.23392.

2- Entanglement properties of random quantum states.

In another experiment and theory collaboration, we have accessed entanglement structure in an ensemble of random states prepared in a quantum simulator based on superconducting qubits. While preparation of many-body product states is a basic task in NISQ devices, the preparation of Haar random states require non-trivial effort. We achieve high fidelity approximately Haar random states (in particular n−designs) using kicked dynamics with low depth circuits. The protocol uses native interactions of the underlying experimental set up. On these states, we study entanglement and symmetries using measurements done in random Pauli bases. We report entanglement entropy, entanglement asymmetry and mixed state entanglement, showing excellent agreement with theoretical prediction after the error mitigation. In addition, we also show entanglement phases in prepared random states by accessing moments of partial transposed reduced density matrices. The work is openly available as preprint at arXiv:2601.22224

3) Hamiltonian and Lindbladian learning in quantum devices.

In this part of the work, we developed verification frameworks to establish reliability of quantum simulators as computational tools. We systematically certify performance of a quantum simulator. In the first step we learn the implemented Hamiltonian and Lindbladian using measurements performed in Pauli basis, and for different sets of initial states. Then in the second step, the learned Hamiltonian, only from a few time steps in the experiment, provides error bounds in measurements of observables at any time. While the main lead work is done in Innsbruck in the experimental team using trapped ions, we provide theoretical support, in particular for the long ion chain of 51 ions. Here, we use tensor networks to perform numerical calculations. The openly available preprint is at- arXiv:2511.23392 and was finished during the secondment of the project.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

First, we showed a general framework for accessing probability distribution functions (PDFs) and full counting statistics (FCS) of arbitrary quantum observables during non-equilibrium dynamics. Unlike many existing approaches, which are restricted to conserved quantities or specific Hamiltonian symmetries, our method reconstructs the complete statistics of general observables using measurements performed in random bases. This significantly broadens the range of quantum phenomena that can be experimentally characterized and provides a versatile tool for studying quantum fluctuations and correlations in many-body systems. Though the theoretical basis for the measurement protocol existed before, the implementation in a noisy device and demonstration to show a very good error mitigation is done for the first time in trapped ions, and for arbitrary size of subsystems.

Second, we demonstrated efficient preparation and characterization of highly entangled approximate Haar-random quantum states using low-depth circuits based on native interactions in superconducting-qubit devices. Our work lays the groundwork for probing the universal features of generic many-body quantum dynamics in quantum simulators, providing a small-scale example that can be scaled up through combined measurement protocols for larger systems. Furthermore, this represents a fundamental step toward the experimental investigation of generic quantum many-body ergodic dynamics, going beyond the study of specific microscopic models and enabling access to universal features of chaotic quantum systems.

Third, we developed a two-step framework for learning and certifying the dynamics of quantum simulators. By reconstructing the effective Hamiltonian and Lindbladian from experimentally accessible measurements, the framework enables accurate prediction of system dynamics together with rigorous error bounds, even from measurements at only a limited number of time steps. The theoretical methods, including tensor-network simulations for large trapped-ion systems, contribute to the development of reliable verification protocols that are essential for establishing confidence in quantum simulators as scientific and computational tools.

Collectively, these results provide a comprehensive toolkit for quantum characterization, entanglement verification, and device certification, advancing the reliability and scalability of quantum simulation beyond existing methodologies. The work strengthens the foundations needed for future applications of quantum technologies in physics, chemistry, materials science, and quantum information processing. The developed protocols are broadly applicable across multiple hardware architectures facilitating their adoption by the wider quantum research community. Future work will focus on extending these techniques to larger quantum systems, improving robustness against experimental noise, and incorporating the verification frameworks into routine benchmarking of emerging quantum devices. The open dissemination of results through peer-reviewed publications and publicly available preprints further supports international collaboration and accelerates the transfer of these methods to future quantum technologies.