Ion trap long-range XY model for quantum state transfer and optimal spatial search
Dylan Lewis, Leonardo Banchi, Yi Hong Teoh, Rajibul Islam, Sougato Bose
Abstract
Abstract Linear ion trap chains are a promising platform for quantum computation and simulation. The XY model with long-range interactions can be implemented with a single side-band Mølmer–Sørensen scheme, giving interactions that decay as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msup> <mml:mi>r</mml:mi> <mml:mi>α</mml:mi> </mml:msup> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> parameterises the interaction range. Lower <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> causes an increased generation of coherent phonons and appears to dephase the effective XY interaction model. We characterise and show how to correct for this effect completely, allowing lower <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> interactions to be coherently implemented. Ion trap chains are thus shown to be a viable platform for spatial quantum search in optimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msqrt> <mml:mi>N</mml:mi> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> </mml:math> time, for N ions. Finally, we introduce a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msqrt> <mml:mi>N</mml:mi> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> </mml:math> quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.