QSE Quantum Seminar - “Can effective descriptions of bosonic systems be considered complete?”

Please join us for the QSE Center Quantum Seminar with Ulysse Chabaud from École Normale Supérieure in Paris, who will give the talk "Can effective descriptions of bosonic systems be considered complete?" on Thursday March 13. 
Location: BS 260.

Pizzas will be available before the seminar at 12:00. All PhDs, postdocs, students, and PIs are welcome to join us.

TITLE: "Can effective descriptions of bosonic systems be considered complete?"

ABSTRACT: Bosonic statistics give rise to remarkable phenomena, from the Hong-Ou-Mandel effect to Bose-Einstein condensation, with applications spanning fundamental science to quantum technologies. Modelling bosonic systems relies heavily on effective descriptions: typically, truncating their infinite-dimensional state space or restricting their dynamics to a simple class of Hamiltonians, such as polynomials of canonical operators. However, many natural bosonic Hamiltonians do not belong to these simple classes, and some quantum effects harnessed by bosonic computers inherently require infinite-dimensional spaces. Can we trust that results obtained with such simplifying assumptions capture real effects?
We solve this outstanding problem, showing that these effective descriptions do correctly capture the physics of bosonic systems. Our technical contributions are twofold: firstly, we prove that any physical bosonic unitary evolution can be accurately approximated by a finite-dimensional unitary evolution; secondly, we show that any finite-dimensional unitary evolution can be generated exactly by a bosonic Hamiltonian that is a polynomial of canonical operators. Beyond their fundamental significance, our results have implications for classical and quantum simulations of bosonic systems, provide universal methods for engineering bosonic quantum states and Hamiltonians, show that polynomial Hamiltonians generate universal gate sets for quantum computing over bosonic modes, and lead to a bosonic Solovay-Kitaev theorem.

Joint work with F. Arzani and R. I. Booth: arXiv:2501.13857

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