Neue Perspektiven in Stark Gekoppelten Systeme: Vorbereitung auf Quantensimulatoren.
Zusammenfassung der Projektergebnisse
Quantum computers are playing an increasing role in the investigation of natural sciences, which currently largely relies on classical algorithmic methods. It is only natural to keep adapting our investigative techniques in order to exploit the growing relevance of quantum computing methods. The aim of the project was to explore certain novel formulation of lattice gauge theories as viable candidates to explore the continuum field theoretical aspects of strongly interacting gauge theories. Gauge theories are the building blocks of the microscopic theories used to describe a wide range of phenomena in nature from electrodynamics to hadronic physics, and even the interior of neutron starts. Given the funding time-frame and the allotted resources, the project examined the role of microscopic theory using quantum link models in three major areas — statics, dynamics, and tentative use in experimental building blocks. The first application was to investigate if the so-called Schwinger model, a toy model of electrodynamics in (1 + 1)-d, now formulated with quantum link gauge fields show the same physics in continuum as the usual formulation, credited to Wilson. Using novel theoretical and numerical methods we were able to show that this was indeed the case. While this was already expected, the non-trivial result from the project was that reasonably small values of the Hilbert space of the gauge link was necessary in order to reproduce the low-energy continuum physics of the Schwinger model. The second application to dynamical aspects of gauge theories has helped to uncover a new class of states which play a role in dynamics of gauge theories, and particularly in the context of dynamics under a Hamiltonian evolution. These are described more in the next section, and constitute a surprise in terms of the results. The third application was to explore the suitability of implementation of these models in quantum computers, for example on superconducting qubit based open source quantum computers such as the IBMQ. One of the basic building blocks of the complex gauge theories used to describe nature, such as the self-interaction between gauge fields, was implemented via quantum circuits on quantum computers. Since the machines are extremely noisy with poor decoherence, only the results on the simplest of the systems could be benchmarked with exact calculations. However, with appropriate error mitigation methods, the results could be consistently improved beyond what could be naively expected. The greatest (unpleasant) surprise in terms of organization during the duration of the project was the corona pandemic, which hindered collaboration-related visits, and slowed down the pace of obtaining the results. In terms of physics results, the greatest surprise was about the existence of the excited scar states in lattice gauge theories which we discovered for the first time in the literature. The scar states violate the expectations from the eigenstate thermalization hypothesis about excited states, and have anomalously low entanglement, and only polynomial (in lattice volume) complexity. Subsequent work (beyond the time-frame of the project) gives rise to the expectation that there may be an exponential number (in the lattice size) of such states which are unusually robust. With appropriate technical improvements, it may become possible to encode information in these states.
Projektbezogene Publikationen (Auswahl)
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Quantum Scars from Zero Modes in an Abelian Lattice Gauge Theory on Ladders. Physical Review Letters, 126(22).
Banerjee, Debasish & Sen, Arnab
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Toward the continuum limit of a (1+1)D quantum link Schwinger model. Physical Review D, 106(9).
Zache, Torsten V.; Van Damme, Maarten; Halimeh, Jad C.; Hauke, Philipp & Banerjee, Debasish
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Toward the real-time evolution of gauge-invariant Z2 and U(1) quantum link models on noisy intermediate-scale quantum hardware with error mitigation. Physical Review D, 106(9).
Huffman, Emilie; García Vera, Miguel & Banerjee, Debasish
