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Significant Advances in Hamiltonian Learning for Quantum Simulators
Recent research conducted by an interdisciplinary team involving Freie Universität Berlin, the University of Maryland and NIST, along with Google AI and Abu Dhabi, has pioneered methods to effectively estimate the free Hamiltonian parameters of bosonic excitations within a superconducting quantum simulator. This work, detailed in a preprint published on arXiv, promises to enhance the precision of quantum simulations, potentially surpassing classical computational limits.
Jens Eisert, the lead author of the study, recounted the initial outreach from the Google AI team during a conference in Brazil. They were facing significant challenges in calibrating their Sycamore superconducting quantum chip and sought assistance in Hamiltonian learning. Intrigued by the problem, Eisert soon realized it would be more complex than initially anticipated, as accurate recovery of the Hamiltonian system’s frequencies was necessary for proper identification.
Eisert brought two promising Ph.D. students, Ingo Roth and Dominik Hangleiter, into the project. Together, they explored solutions rooted in superresolution techniques but faced additional hurdles when beginning tests with actual data. It took years of rigorous research, including collaboration with Pedram Roushan, the experimental lead from Google AI, to finally address the issues raised at the outset.
The researchers implemented a variety of sophisticated techniques to decode the Hamiltonian dynamics of the superconducting simulator. They initially applied superresolution methods to accurately determine the Hamiltonian frequencies and subsequently employed manifold optimization for the recovery of the Hamiltonian’s eigenspaces. This optimization approach is tailored to handle complex problem spaces, recognizing that variables often exist within a manifold rather than simply within Euclidean space.
Eisert emphasized the importance of understanding the switching processes involved in Hamiltonian operations, which are not instantaneous and can complicate the fitting of Hamiltonian evolution. Ultimately, new signal processing methodologies, specifically the TensorEsprit technique, enabled the team to achieve reliable recovery of data even on a larger scale.
The work led to the introduction of TensorEsprit, a novel super-resolution technique that, when combined with the manifold optimization method, allowed for precise identification of Hamiltonian parameters across up to 14 coupled superconducting qubits in the Sycamore ecosystem. Eisert noted the significance of thoroughly grasping the methodological underpinnings of Hamiltonian learning to enhance the accuracy and applicability of eigenspace recovery.
The initial results indicate the scalability and robustness of their techniques for larger quantum processors, potentially guiding the development of analogous methods for characterizing Hamiltonians in quantum technologies. Looking ahead, the research team intends to apply their methodologies to systems of interacting quantum variables and to explore tensor network concepts in quantum systems with cold atoms, continuing a tradition of inquiry first established by physicist Immanuel Bloch.
Eisert expressed a forward-looking perspective on the implications of their research, emphasizing the longstanding question of the true nature of a system’s Hamiltonian. This foundational inquiry lies at the heart of quantum mechanics and is critical for predictive power in experiments, as accurate knowledge of the Hamiltonian is essential for interpreting experimental data.
Ultimately, the research not only advances theoretical understanding but also holds promise for the practical development of technologies involving quantum simulators. By shedding light on Hamiltonian characterization, the group aims to open new frontiers in high-precision quantum simulations, allowing researchers to recreate complex quantum systems in controlled lab settings.
More information: Dominik Hangleiter et al, Robustly learning the Hamiltonian dynamics of a superconducting quantum processor, arXiv (2024). DOI: 10.48550/arxiv.2108.08319
Source
phys.org