Quantum Spin Chains and Symmetric Functions
- URL: http://arxiv.org/abs/2404.04322v2
- Date: Tue, 23 Jul 2024 11:54:49 GMT
- Title: Quantum Spin Chains and Symmetric Functions
- Authors: Marcos Crichigno, Anupam Prakash,
- Abstract summary: We consider the question of what quantum spin chains naturally encode in their Hilbert space.
quantum spin chains are examples of "quantum integrable systems"
- Score: 1.7802147489386628
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory, and algebraic geometry. In the case of the XX Heisenberg spin chain these are given by skew Kostka numbers, skew characters of the symmetric group, and Littlewood-Richardson coefficients. As we show, this is revealed by a fermionic representation of the theory of "quantized" symmetric functions formulated by Fomin and Greene, which provides a powerful framework for constructing operators extracting this data from the Hilbert space of quantum spin chains. Furthermore, these operators are diagonalized by the Bethe basis of the quantum spin chain. Underlying this is the fact that quantum spin chains are examples of "quantum integrable systems." This is somewhat analogous to bosons encoding permanents and fermions encoding determinants. This points towards considering quantum integrable systems, and the combinatorics associated with them, as potentially interesting targets for quantum computers.
Related papers
- Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon [34.80375275076655]
Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions.
We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon.
arXiv Detail & Related papers (2024-07-03T18:00:52Z) - A dynamic programming interpretation of quantum mechanics [0.0]
We introduce a transformation of the quantum phase $S'=S+frachbar2logrho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of particles.
We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as Hamilton-Jacobi-Bellman equations.
arXiv Detail & Related papers (2024-01-08T18:43:40Z) - Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries.
One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system.
We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
arXiv Detail & Related papers (2023-10-11T15:59:54Z) - A Bottom-up Approach to Constructing Symmetric Variational Quantum
Circuits [0.0]
We show how to construct symmetric quantum circuits using representation theory.
We show how to derive the particle-conserving exchange gates, which are commonly used in constructing hardware-efficient quantum circuits.
arXiv Detail & Related papers (2023-08-17T10:57:15Z) - Reconstructing the spatial structure of quantum correlations [0.0]
Quantum correlations are a fundamental property of quantum many-body states.
Yet they remain elusive, hindering certification of genuine quantum materials.
Here we show that the momentum-dependent neutron scattering scattering expresses in terms of quantum correlation functions.
arXiv Detail & Related papers (2023-06-20T17:55:09Z) - Topological Quantum Computation on Supersymmetric Spin Chains [0.0]
Quantum gates built out of braid group elements form the building blocks of topological quantum computation.
We show that the fusion spaces of anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains.
arXiv Detail & Related papers (2022-09-08T13:52:10Z) - Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems.
Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
arXiv Detail & Related papers (2021-08-30T23:50:05Z) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z) - Experimental Validation of Fully Quantum Fluctuation Theorems Using
Dynamic Bayesian Networks [48.7576911714538]
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems.
We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
arXiv Detail & Related papers (2020-12-11T12:55:17Z) - Characterizing quantum correlations in spin chains [0.0]
We show that a single element of the density matrix carries the answer to how quantum is a chain of spins.
This method can be used to tailor and witness highly non-classical effects in many-body systems.
As a proof of principle, we investigate the extend of non-locality and entanglement in ground states and thermal states of experimentally accessible spin chains.
arXiv Detail & Related papers (2020-05-19T17:25:37Z) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.