0
votes
0answers
26 views

Ising formulation of the graph isomorphism problem

Context I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I ...
3
votes
1answer
142 views

Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle ...
5
votes
1answer
150 views

What are qubits made of in Wen's string-net theory?

In Prof. Xiaogang Wen's theory, photons and electrons are described as quasi-particles appeared as a result of the existence of the string-net liquid, which is the topological order of the qubits that ...
2
votes
0answers
42 views

Qubit in Type 1.5 superconductor?

I'm interested in Type 1.5 superconductors, first proposed by Egor Babaev in 2002 and found in the laboratory in 2009 (magnesium dibromide). Such conductors favor small bundles of vortices. The most ...
4
votes
0answers
116 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
1
vote
0answers
143 views

How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
4
votes
2answers
110 views

Approaches to Fault tolerant quantum computation

What are the various approaches to fault tolerant quantum computation ? Two examples are 1. topological quantum computation which uses topological phases in quantum states (2-Dimensional for ...
2
votes
1answer
132 views

Topological quantum computation: abelian vs. non-abelian anyons

We need non-abelian fractional hall states because of the ground state degeneracy http://rmp.aps.org/abstract/RMP/v80/i3/p1083_1 (arXiv version for free). But we can also have degeneracy even in case ...
5
votes
2answers
208 views

Toric Code and Random Bond Ising Model

It was established by Dennis, Kitaev et al. that the 2D Toric Code can be mapped to a 2D Random Bond Ising Model. The original derivation was given in the paper "Topological quantum memory" which ...
11
votes
1answer
802 views

Quantum dimension in topological entanglement entropy

In 2D the entanglement entropy of a simply connected region goes like \begin{align} S_L \to \alpha L - \gamma + \cdots, \end{align} where $\gamma$ is the topological entanglement entropy. $\gamma$ is ...
7
votes
1answer
537 views

Topological Order and Entanglement

I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
29
votes
10answers
3k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
4
votes
3answers
796 views

Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
7
votes
1answer
334 views

How many stabilised qubits have been achieved in Quantum Computing?

The latest I read is 3 but that was in Oct. With Lene Hau of Harvard's "frozen light" and with quantum donuts, newer strategies for stabilization are appearing, but the problem of keeping the qubit in ...