Nonequilibrium Many Body Control of Quantum Simulators

Project Information

QuSimCtrl

Grant agreement ID: 101113633

DOI

10.3030/101113633

EC signature date 17 November 2023

Start date 1 December 2023

End date 30 November 2028

Funded under

• European Research Council (ERC)

Total cost

€ 1 500 000,00

EU contribution

€ 1 500 000,00

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Germany

Periodic Reporting for period 1 - QuSimCtrl (Nonequilibrium Many Body Control of Quantum Simulators)

Reporting period: 2023-12-01 to 2026-05-31

Summary of the context and overall objectives of the project

Controlling matter at the quantum level has been one of physics' greatest triumphs, but this success has been largely confined to equilibrium systems. The next frontier lies in extending control to far-from-equilibrium systems—a regime where fundamentally new phenomena emerge but theoretical understanding remains limited. QuSimCtrl addresses a critical gap: manipulating strongly interacting quantum systems subjected to intense nonequilibrium drives, where conventional approaches fail, and exotic states without equilibrium counterparts can emerge.

Periodically driven quantum systems occupy a unique position between equilibrium and nonequilibrium physics. Through periodic driving, experimenters can engineer artificial gauge fields, topological insulators, and time crystals in platforms from ultracold atoms to superconducting circuits. However, our ability to control quantum states in such systems lags behind our capacity to create them. Current methods rely on slow, adiabatic parameter changes, conflicting with limited coherence times, fundamentally constraining achievable outcomes.

QuSimCtrl aims to advance understanding and control of driven quantum matter by developing an entirely new theoretical framework combining quantum control theory with machine learning algorithms. At its core is a geometric reformulation of periodically driven systems theory that resolves longstanding ambiguities in defining and manipulating driven quantum states. Building on this foundation, we will develop fast, nonadiabatic control protocols using variational counterdiabatic driving — techniques enabling high-fidelity quantum state manipulation on significantly shorter timescales. We will integrate deep reinforcement learning into quantum control, leveraging AI's ability to discover effective strategies when underlying physical structures are not obvious.

The expected impact spans multiple dimensions. Scientifically, this work will establish missing links between quantum dynamics, statistical mechanics, optimal control, and machine learning, revealing new organizing principles for nonequilibrium physics. Technologically, our control techniques will directly benefit quantum computing, simulation, and sensing platforms requiring rapid, high-fidelity state manipulation. Ultimately, this research will establish a roadmap for designing future materials and technologies based on controlled nonequilibrium processes—building the theoretical and computational infrastructure needed as quantum technologies transition from laboratory demonstrations to practical devices.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

We developed methods bridging physics and machine learning to control rapidly evolving quantum systems. Our key results unify shortcuts-to-adiabaticity techniques for accelerating slow quantum processes with the theory of periodically driven systems. This reveals fundamental connections between anomalous topological order and time crystals, and offers both theoretical insights and potential applications in quantum sensing. We use numerical techniques to optimize control of large, strongly-interacting quantum systems—previously impossible to calculate exactly. We also introduced control designs using square-wave-like Walsh functions instead of smooth Fourier waves, which are simpler for near-term quantum computers.

Using cutting-edge machine learning algorithms, we built deep reinforcement learning (RL) frameworks incorporating attention mechanisms to control entanglement in over 100 qubits. The RL agent learns which particles and correlations matter most, autonomously discovering control strategies for systems too complex for human analysis.

Key Achievements:

1. Geometric Floquet Theory: We reformulated Floquet theory using geometric concepts, separating quantum dynamics into geometric and dynamical components. This resolved the longstanding problem of identifying ground states in driven systems and revealed fundamental connections between geometry, topology, and exotic phases like time crystals.

2. Rondeau Time Crystals: We discovered and experimentally realized a new form of time crystal exhibiting simultaneous short-time disorder and long-time order. This challenges the conventional understanding of temporal patterns. Demonstrated in nuclear magnetic resonance systems with potential applications in quantum sensing.

3. Control Landscape Phase Transitions: We showed that optimization landscapes for quantum control can undergo phase transitions, with distinct phases (controllable, glassy, overconstrained) determining optimization difficulty. This bridges quantum control and statistical physics, providing practical guidance for robust protocol design.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Our work transforms fundamentally the understanding and control of periodically driven quantum systems. By reformulating 150-year-old Floquet theory through quantum geometry, we have solved longstanding puzzles—such as identifying ground states in driven systems—and converted quantum control from intuition-based approaches into systematic design algorithms. This enables researchers to methodically engineer quantum gates, extend topological pumping to previously inaccessible frequencies, and diagnose heating problems before they corrupt quantum states.

We have discovered rondeau time crystals, a new phase of matter simultaneously disordered at short timescales yet ordered at long times, with promising applications for noise-resistant quantum memory. Our control landscape theory predicts when quantum optimization will be tractable versus trapped in glassy complexity, providing engineers with crucial foresight. Our deep reinforcement learning framework demonstrates artificial intelligence's capacity to control systems exceeding 100 qubits by autonomously discovering strategies beyond human analytical reach.

Realizing the full impact of this work requires overcoming interconnected challenges. Current methods face computational limitations around several hundred particles; while GPU acceleration and tensor networks are being employed, fundamental algorithmic breakthroughs may prove necessary. Our theoretically powerful adiabatic gauge potential remains experimentally challenging—we are developing new approaches to identify implementable approximations that preserve essential physics while eliminating unnecessary complexity.

Critical next steps include experimental validation across trapped ions, superconducting qubits, and cold atoms platforms. Near-term projects target quantum sensing enhancement, improved gate fidelities, and prototype quantum memories protected by artificial intelligence.

In summary, we have created unified theoretical frameworks connecting previously separate research areas, developed computational methods enabling large-scale quantum control optimization, discovered experimentally confirmed new phases of matter, and demonstrated machine learning-driven autonomous quantum control. These achievements provide both fundamental insights into non-equilibrium quantum physics and practical tools for quantum technology development, establishing new paradigms bridging quantum physics, geometry, machine learning, and statistical mechanics.