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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 & Isometries. Different ways of looking at the MERA. Coarse-graining transformation.

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introduction to mera

Introduction to MERA

Sukhwinder Singh

Macquarie University

tensor s
Tensors

Multidimensional array of complex numbers

different ways of looking at the 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.
mera defines an rg flow
MERA defines an RG flow

Wavefunction on coarse-grained lattice with two sites

types of mera1
Types of MERA

Ternary MERA

Binary MERA

different ways of looking at the mera1
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
But is the MERA good for representing ground states?

Claim: Yes!

Naturally suited for critical systems.

recall
Recall!
  • Gapped Hamiltonian 
  • Critical Hamiltonian 
different ways of looking at the mera2
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.
slide43

Time

Space

different ways of looking at the mera3
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 networks2
MERA and spin networks

(Wigner-Eckart Theorem)

summary mera can be seen as
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.