Graph-States
Compatability
We currently have compatability with:
Introduction
What are Graph States? Graph States are systems of interacting particles, usually 2-level systems (qubits), which are represented by graphs like the ones seen below found in the Nature paper Experimental entanglement of six photons in graph states and Estimating localizable entanglement from witnesses:
Applications
Measurement Based (One-Way) Quantum Computing
Measurement Based Quantum Computing (MBQC) (see Completeness of classical spin models and universal quantum computation), also known as One-Way Quantum Computing is one way of performing adaptive measurements on a highly entangled system of qubits so that entanglement is used as a resource, which is gradually reduced after each adaptive measurement on individual qubits. This is one of the primary uses of graph states, and using the graphs given by surface codes, this can be done in a way that is topologically protected from errors. Morevover, the measurement based approach makes the computation "one-way", which can also protect against errors by making the thermal requirements less strict (see From molecular biology to quantum computing - Charles H. Bennett).
Error Correction
Any stabilizer code can be modeled as a graph state, so understanding quantum error correction through graph states gives a graphical presentation of stabilizer codes.
Quantum Cryptography and blind quantum computation
See for example
Papers:
- Graph States for Quantum Secret Sharing
- Verifiable measurement-only blind quantum computing with stabilizer testing,
- Experimental demonstration of graph-state quantum secret sharing
Videos:
- Matthew G. Parker / Exclusivity graphs from quantum graph states โ and mixed graph generalisations
- Simon Perdrix: Quantum Secret Sharing with Graph States
Modeling Ising type models
Graph states are naturally an example of Ising models in statistical mechanics, with entanglement/interactions represented by edges of the graph between nodes representing the particles.
Quantum Complexity using Partition Functions
See
- Section 5: Measurement-based quantum computation
- Commuting quantum circuits and complexity of Ising partition functions
Modeling Quantum Phase Transitions
See A. Kitaev's lecture on Topological quantum phases
Measurement Based Quantum Computing, Entanglement Entropy, and Entanglement as a Computational Resource
See
- Entanglement in Graph States and its Applications
- Physical-depth architectural requirements for generating universal photonic cluster states
Modeling Condensed Matter Physics on Quantum Computers
Modeling Quantum/Classical Information Processing in DNA
This is useful for applications to Bio-informatics, protien folding, and understanding applications of CRISPR, see for example
which also has an accompanying Google lecture: