Toward a Mølmer Sørensen gate with .9999 fidelity

Abstract Realistic fault-tolerant quantum computing at reasonable overhead requires two-qubit gates with the highest possible fidelity. Typically, an infidelity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>≲</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> is recommended in the literature. Focusing on the phase-sensitive architecture used in laboratories and by commercial companies to implement quantum computers, we show that even under noise-free, ideal conditions, neglecting the carrier term and linearizing the Lamb–Dicke term in the Hamiltonian used for control-pulse construction for generating Mølmer–Sørensen XX gates based on the Raman scheme are not justified if the goal is an infidelity target of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . We obtain these results with a gate simulator code that, in addition to the computational space, explicitly takes the most relevant part of the phonon space into account. With the help of a Magnus expansion carried to the third order, keeping terms up to the fourth order in the Lamb–Dicke parameters, we identify the leading sources of coherent errors, which we show can be eliminated by adding a single linear equation to the phase-space closure conditions and subsequently adjusting the amplitude of the control pulse (calibration). This way, we obtain XX gates with infidelities <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> .