Preparation of the single-spinon wave function on a quantum computer

We address the problem of how to prepare single-spinon wave functions, relevant for one-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>S</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:math> spin models, in a quantum computer. We adopt the recently proposed ansatz [Kulka , ] for the single-spinon wave function, where a state with <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>S</b:mi> <b:mo>=</b:mo> <b:mn>1</b:mn> <b:mo>/</b:mo> <b:mn>2</b:mn> </b:mrow> </b:math> is built in a spin chain with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>L</c:mi> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> sites, adding a site with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>S</d:mi> <d:mi>z</d:mi> </d:msub> <d:mo>=</d:mo> <d:mn>1</d:mn> <d:mo>/</d:mo> <d:mn>2</d:mn> </d:mrow> </d:math> to the configurations of the ground-state wave function for the spin chain with length <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>L</e:mi> </e:math> . We extend the original work to the case of the Haldane-Shastry model. We discuss how to prepare the single-spinon ansatz for both the Heisenberg and Haldane-Shastry models in quantum computers, using a linear combination of unitaries. We consider three different strategies to compute the single-spinon energy in a quantum computer, we analyze their cost in terms of the number of qubits, gates, and circuits, and we test them .