Emergent Quantum State Designs from Individual Many-Body Wave Functions

By Jordan S. Cotler, D. Mark, Hsin-Yuan Huang, F. Hernández, Joon‐Young Choi, Adam L. Shaw, M. Endres, Soonwon Choi. PRX Quantum, 2021

143 citations recorded by the source corpus.

Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single non-random quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state $k$-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that $k$-designs arise naturally from generic states as well as individual states associated with strongly interacting, time-independent Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3e74cb3255bc0bcd31d97abbfd30725357e45232

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Citations in the corpus

The randomized measurement toolbox (2022, methodology): “This approach can be generalized to quantum states generated via ergodic Hamiltonian dynamics using the concept of projected state ensembles 88,89 .”
Provably efficient machine learning for quantum many-body problems (2021, background): “How can we make use of that measurement data to predict properties reliably (90, 91)? For that matter, might we be able to generalize from experimental”