Quantum Synthetic Models for Entangled Matter Out of Equilibrium

Projektinformationen

QUANTHEM

ID Finanzhilfevereinbarung: 101114881

DOI

10.3030/101114881

EK-Unterschriftsdatum 30 Oktober 2023

Startdatum 1 Januar 2024

Enddatum 31 Dezember 2028

Finanziert unter

• European Research Council (ERC)

Gesamtkosten

€ 1 405 750,00

EU-Beitrag

€ 1 405 750,00

Koordiniert durch

ALMA MATER STUDIORUM - UNIVERSITA DI BOLOGNA
Italy

Periodic Reporting for period 1 - QUANTHEM (Quantum Synthetic Models for Entangled Matter Out of Equilibrium)

Berichtszeitraum: 2024-01-01 bis 2026-06-30

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

Digital quantum simulators, or quantum computers, are very promising experimental arenas where to investigate to unprecedented accuracy the exceptional features of many-body quantum systems. However, in the current era of Noisy-Intermediate-Scale-Quantum (NISQ) devices, large-scale fault-tolerant quantum computation is out of reach, making full-fledged quantum simulation an ambitious long-term goal.

Despite these limitations, NISQ devices already provide new horizons for fundamental research in many-body physics. Most prominently, the possibility to implement new elementary building blocks such as discrete local updates, measurements, and feedback, have motivated a significant amount of theoretical work investigating new quantum-circuit models for many-body physics, including the so-called quantum cellular automata (QCA). NISQ devices have also motivated the development of new preparation protocols to realize non-trivial quantum states with minimal operations compatible with their possibilities.

The QUANTHEM project has the ambitious goal of finding and theoretically characterizing new phases of matter which could be natively implemented in NISQ platforms, charting their largely unexplored phenomenology and possibilities. Taking on a fundamental perspective, at the intersection of many-body physics and quantum information theory, the project pursues this goal based on the study of quantum-circuit models and QCA. The target results of this project include: (1) the characterization of new dynamical phases arising thanks to the building blocks of NISQ technology; (2) the identification of quantum state-preparation protocols suitable for existing platforms; (3) a deeper understanding of topical but hard problems in many-body physics out of equilibrium, made possible by the simplifying minimal structure of quantum-circuit models and QCA. The proposed research is expected to stimulate new synergies between different communities, reflecting the dual nature and interdisciplinary interest of NISQ devices, being both early prototypes for quantum computers and experimental platforms for many-body physics.

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

The project has reached many milestones, in collaboration with different international research groups.

Several results were obtained in the context of quantum-state preparation and in the characterization of quantum states prepared by shallow quantum circuits. First, we have developed new algorithms for the preparation of entangled many-body quantum states: our main result is the introduction of a new method to prepare low-entangled quantum states using only shallow quantum circuits, local measurements and feedback. The method goes beyond previous protocols by relaxing the condition of exact and fully deterministic preparation. Second, we have derived theoretical results characterizing and classifying properties of quantum states up to shallow quantum circuits. Most prominently, we have obtained a full characterization of so-called ''long-range nonstabilizerness" in one-dimensional quantum systems, introducing a framework inspired by the study of long-range entanglement.

Several results have also been obtained in the context of non-equilibrium phenomena. Most prominently, we have developed a generalized-hydrodynamic description for integrable quantum circuits and predicted novel hydrodynamic effects that can be observed in these systems. In addition, we have identified quantum circuits which are exactly solvable by a new type of mathematical mapping named "free-fermions in disguise". We have also studied classes of hybrid random-circuit dynamics, including monitored free-fermionic dynamics, Haar-random and random-permutation circuits, clarifying and answering questions previously raised in the literature.

The project has also obtained results on the implementation of quantum-circuit models in current NISQ devices. Precisely, in a recent preprint, we have put forward a proposal for an implementation of QCA dynamics in dual-species Rydberg-atom arrays. While Rydberg-atom arrays are well-known to be a particularly appealing quantum platform, in these systems atom excitation is often driven by global lasers. Conversely, engineering discrete quantum-circuit dynamics, seemingly requires local control of interactions. In our work, we overcome this expectation and propose a protocol based on global driving only, drastically simplifying the technological requirements.

Finally, the project has also obtained results in the context of retrieving information on quantum states prepared on a quantum computer. We have developed two new algorithms based on so-called classical-shadow tomography. The first approach makes use of shallow quantum circuits and leverages their scrambling properties. The second protocol is based on tensor-network post-processing of classical shadows and is tailored to learn experimentally prepared mixed states with low entanglement and in the absence of long-range correlations. The method has been benchmarked to learn mixed states to unprecedented sizes.

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)

The main achievements described above represent important progress beyond the state of the art.

First, the algorithms for quantum-state preparation go beyond previous protocols, requiring less resources such as the number of ancillary qubits or the preparation time. In the same context, our results on the characterization of nonstabilizerness up to shallow quantum circuits have opened a fruitful line of theoretical research.

In the context of non-equilibrium physics, our development of a generalized hydrodynamic theory for integrable quantum circuits represents significant progress and has allowed us to predict new dynamical behavior that cannot be observed in traditional quantum-integrable Hamiltonians. Similarly, our results on quantum circuits featuring free fermions in disguise provide new types of integrable discrete dynamics with features that do not fit the traditional integrability framework and are expected to generate significant follow-up work.

Our results on quantum-state learning also go significantly beyond the state of the art. For instance, in the context of tensor-network states, the reconstruction of mixed states is considered to be significantly harder than the corresponding pure-state problem. We introduce an efficient method based on classical shadows that we benchmark to reconstruct an experimentally prepared state up to unprecedented system sizes.

Finally, our proposal for implementation of quantum circuits in dual-species Rydberg-atom arrays represent important progress beyond the state of the art. Dual-species arrays are a new experimental frontier in neutral atom platforms and our proposed protocol leverages their unique possibilities to allow for an implementation of QCA dynamics with simple technological requirements. As our protocol is based on demonstrated capabilities of Rydberg-atom systems only, our approach is expected to enable informative near-term studies of non-equilibrium many-body physics through discrete local dynamics in Rydberg arrays.