Preparing exact eigenstates of the open XXZ chain on a quantum computer
John S. Van Dyke, Edwin Barnes, Sophia E. Economou, Rafael I. Nepomechie
Abstract
Abstract The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mfenced close=")" open="("> <mml:mfrac linethickness="0.0pt"> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:mfrac> </mml:mfenced> <mml:mspace width="0.17em"/> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msup> <mml:mspace width="0.17em"/> <mml:mi>M</mml:mi> <mml:mo>!</mml:mo> </mml:math> terms, the algorithm requires L + M 2 + 2 M qubits.