On the order problem in construction of unitary operators for the variational quantum eigensolver
Artur F. Izmaylov, Manuel Díaz-Tinoco, Robert A. Lang
Abstract
- 1, which makes the choice of a polynomial subset of generators an exponentially difficult process. Moreover, due to non-commutativity of generators, the order in which they are used strongly affects results. Choosing the optimal order in a particular subset of generators requires testing the factorial number of combinations. We propose an approach based on the Lie algebra-Lie group connection and corresponding closure relations that systematically eliminates the order problem.
Topics & Concepts
Unitary stateLie algebraConnection (principal bundle)QuantumAlgebra over a fieldOrder (exchange)Lie groupMathematicsSpecial unitary groupPure mathematicsPhysicsQuantum algorithmGroup (periodic table)Quantum computerQuantum phase estimation algorithmUnitary transformationQuantum mechanicsQuantum algebraMathematical physicsQuantum operationUnitary matrixUnitary representationFirst orderQuantum Computing Algorithms and ArchitectureQuantum many-body systemsAlgebraic and Geometric Analysis