Qudit Models

Key: QdLH01
Hamiltonian: The $1$–dim $12$–state Local Hamiltonian $$ H = \displaystyle\sum_{j=1}^m H_j $$
Problem: Ground state energy
Complexity: QMA–complete
Ref: [AGIK09]
Conditionals:
  • The particles are arranged on a $1$–dimensional line
Reductions:
  • To an $8$–local Hamiltonian on a $1$–dimensional line
Key: QdLH02
Hamiltonian: The $1$–dim $11$–state Local Hamiltonian $$ H = \displaystyle\sum_{j=1}^m H_j $$
Problem: Ground state energy
Complexity: QMA–complete
Ref: [Nag08]
Conditionals:
  • The particles are arranged on a $1$–dimensional line
Key: QdLH03
Hamiltonian: The $1$–dim $8$–state Local Hamiltonian $$ H = \displaystyle\sum_{j=1}^m H_j $$
Problem: Ground state energy
Complexity: QMA–complete
Ref: [HNN13]
Conditionals:
  • The particles are arranged on a $1$–dimensional line