)%20Variational Quantum Simulation of Anyonic Chains%20%3A%20a variational quantum simulation scheme is presented for analyzing anyonic chains, specifically the restricted solid-on-solid (rsos) models of andrews, baxter, and forrester. the scheme is demonstrated for the a family of dynkin diagrams with 4 ≤ p ≤ 8, using a variational quantum-classical algorithm based on the euler-cartan circuit ansatz.?width=1280&height=720&seed=623862700&nologo=true&model=turbo)
Summary
A variational quantum simulation scheme is presented for analyzing anyonic chains, specifically the restricted solid-on-solid (RSOS) models of Andrews, Baxter, and Forrester. The scheme is demonstrated for the A family of Dynkin diagrams with 4 ≤ p ≤ 8, using a variational quantum-classical algorithm based on the Euler-Cartan circuit ansatz.
Highlights
- Variational quantum simulation scheme for anyonic chains
- Focus on RSOS models associated with Dynkin diagrams
- Demonstration for A family with 4 ≤ p ≤ 8
- Use of variational quantum-classical algorithm
- Euler-Cartan circuit ansatz for parameterized circuit
- Measurement of observables captures anyonic nature
- Topological symmetry operators analyzed at quantum-critical points
Key Insights
- The proposed scheme provides a systematic approach to realizing a large family of quantum field theories that have largely eluded physical realizations.
- The RSOS models can be mapped to qubit systems, allowing for the investigation of anyonic chains using digital quantum simulators.
- The Euler-Cartan circuit ansatz is used to parametrize the unitary operator, enabling the realization of low-lying eigenstates of the RSOS models at their respective quantum critical points.
- The measurement of n-qubit observables can capture the signatures of the anyonic nature of the Hilbert space and the corresponding topological symmetry operators.
- The scheme can be generalized to other types of anyonic chains, enabling the investigation of a wide range of quantum field theories.
- The use of a variational quantum-classical algorithm allows for the optimization of the circuit parameters to realize the desired anyonic state.
- The proposed approach has the potential to enable the study of non-perturbative phenomena in low-dimensional quantum field theories using near-term quantum simulators.
Mindmap
Citation
Roy, A. (2024). Variational Quantum Simulation of Anyonic Chains (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17781