The-Singularity-Research/Graph-States

Graph states for quantum computing, quantum cryptography, and error correction

Graph-States

Compatability

We currently have compatability with:

• IBM Qiskit
• Google Cirq

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

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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 – 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.

• Mapping Classical Spin Models to the Graph State Formalism

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

• Adiabatic graph-state quantum computation

• Quantum entanglement between the electron clouds of nucleic acids in DNA,

which also has an accompanying Google lecture:

• Classical and Quantum Information in DNA (Google Workshop on Quantum Biology)