Introduction to MERA

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# Introduction to MERA - PowerPoint PPT Presentation

Introduction to MERA. Sukhwinder Singh Macquarie University. Tensor s. M ultidimensional array of complex numbers. Cost of Contraction. =. a. a. b. c. d. Made of layers. Disentanglers &amp; Isometries. Different ways of looking at the MERA. Coarse-graining transformation.

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### Introduction to MERA

Sukhwinder Singh

Macquarie University

Tensors

Multidimensional array of complex numbers

Different ways of looking at the MERA
• Coarse-graining transformation.
• Efficient description of ground states on a classical computer.
• Quantum circuit to prepare ground states on a quantum computer.
• A specific realization of the AdS/CFT correspondence.
MERA defines an RG flow

Wavefunction on coarse-grained lattice with two sites

Types of MERA

Ternary MERA

Binary MERA

Different ways of looking at the MERA
• Coarse-graining transformation.
• Efficient description of ground states on a classical computer.
• Quantum circuit to prepare ground states on a quantum computer.
• A specific realization of the AdS/CFT correspondence.
But is the MERA good for representing ground states?

Claim: Yes!

Naturally suited for critical systems.

Recall!
• Gapped Hamiltonian 
• Critical Hamiltonian 
Different ways of looking at the MERA
• Coarse-graining transformation.
• Efficient description of ground states on a classical computer.
• Quantum circuit to prepare ground states on a quantum computer.
• A specific realization of the AdS/CFT correspondence.

Time

Space

Different ways of looking at the MERA
• Coarse-graining transformation.
• Efficient description of ground states on a classical computer.
• Quantum circuit to prepare ground states on a quantum computer.
• A specific realization of the AdS/CFT correspondence.
MERA and spin networks

(Wigner-Eckart Theorem)

Summary – MERA can be seen as ..
• As defining a RG flow.
• Efficient description of ground states on a classical computer.
• Quantum circuit to prepare ground states on a quantum computer.
• Specific realization of the AdS/CFT correspondence.