How to define quantum mean-field solvable Hamiltonians using Lie algebras

Abstract

Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field theories have not been formulated so far. To resolve this problem, first, we define what mean-field theory is, independently of a Hamiltonian realization in a particular set of operators. Second, using a Lie-algebraic framework we formulate a criterion for a Hamiltonian to be mean-field solvable. The criterion is applicable for both distinguishable and indistinguishable particle cases. For the electronic Hamiltonians, our approach reveals the existence of mean-field solvable Hamiltonians of higher fermionic operator powers than quadratic. Some of the mean-field solvable Hamiltonians require different sets of quasi-particle rotations for different eigenstates, which reflects a more complicated structure of such Hamiltonians.

References in corpus (9)

• Fermionic quantum computation
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Generalizations of entanglement based on coherent states and convex sets
• Operator Locality in Quantum Simulation of Fermionic Models
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• On the order problem in construction of unitary operators for the Variational Quantum Eigensolver
• Characterization of solvable spin models via graph invariants
• Efficient solvability of Hamiltonians and limits on the power of some quantum computational models
• Quantum circuit synthesis for generalized coherent states

Cited by in corpus (2)

• Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
• Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation