Bethe states on a quantum computer: success probability and correlation functions
Wen Li, Mert Okyay, Rafael I. Nepomechie
Abstract
Abstract A probabilistic algorithm for preparing Bethe eigenstates of the spin-1/2 Heisenberg spin chain on a quantum computer has recently been found. We derive an exact formula for the success probability of this algorithm in terms of the Gaudin determinant, and we study its large-length limit. We demonstrate the feasibility of computing antiferromagnetic ground-state spin–spin correlation functions for short chains. However, the success probability decreases exponentially with the chain length, which precludes the computation of these correlation functions for chains of moderate length. Some conjectures for estimates of the Gaudin determinant are noted in an appendix.
Topics & Concepts
Spin (aerodynamics)ComputationEigenvalues and eigenvectorsProbabilistic logicAntiferromagnetismQuantum computerLimit (mathematics)Quantum mechanicsChain (unit)MathematicsQuantumStatistical physicsPhysicsMathematical physicsAlgorithmStatisticsMathematical analysisThermodynamicsQuantum many-body systemsAlgebraic structures and combinatorial modelsPhysics of Superconductivity and Magnetism