Quantum Magic in Topological Vacuum Dynamics
Mentor:
Sebastian Grieninger (INSPIRE-HEP, email: segrie@uw.edu)
Prerequisites:
Basic knowledge of quantum mechanics; some basic coding skills are helpful but not required.
What Students Will Learn:
Students will learn about topological vacuum structure in quantum theories and the strong CP problem, what quantum complexity measures like magic and stabilizer entropy and entanglement entropy are, and how to simulate quantum theories using quantum simulation tools.
Expected Project Length:
One year
Project Description:
In quantum chromodynamics (QCD), a parameter called the theta angle can theoretically introduce a violation of the CP symmetry. However, experiments constrain it to be extraordinarily small which is referred to as the strong CP problem. One elegant solution proposes that theta is a dynamical field, the “axion,” now actively sought in dark matter experiments. However, studying the theta dynamics far from equilibrium remains extremely challenging in QCD.
The Schwinger model – 1+1D quantum electrodynamics—provides an ideal testbed to investigate these questions. Recent work has shown that sudden changes (quenches) in the theta angle can drive dynamical transitions between different vacuum states detectable in (quantum) correlations [3, 4].
In this project, we will investigate whether modern quantum complexity measures – particularly the recently introduced notion of “magic” or non-stabilizerness – can provide new signatures of these transitions, potentially revealing new aspects into the dynamics that are inaccessible to traditional observables. We may also explore developing quantum algorithms to prepare and test these states on real quantum computers [5].
A complementary direction are Neural Network Quantum States (NNQS) [6] where machine learning is applied to learn a quantum state. Surprisingly, NNQS have difficulty to faithfully represent quantum states with high magic and we will use our intuition about magic in the Schwinger model to understand this obstacle.
References:
[2] https://www.nytimes.com/2023/06/14/science/ibm-quantum-computing.html.
[3] T. V. Zache, N. Mueller, J. T. Schneider, F. Jendrzejewski, J. Berges, and P. Hauke. Dynamical topological transitions
in the massive Schwinger model with a θ-term. Phys. Rev. Lett., 122(5):050403, 2019.
[4] Dmitri E. Kharzeev and Yuta Kikuchi. Real-time chiral dynamics from a digital quantum simulation. Phys. Rev. Res.,
2(2):023342, 2020.
[5] Roland C. Farrell, Marc Illa, Anthony N. Ciavarella, and Martin J. Savage. Scalable Circuits for Preparing Ground States
on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits. PRX Quantum, 5(2):020315, 2024.
[6] Hannah Lange, Anka Van de Walle, Atiye Abedinnia, Annabelle Bohrdt, From Architectures to Applications: A Review of Neural Quantum States, arxiv:2402.09402