Author Correction: Two-qubit sweet spots for capacitively coupled exchange-only spin qubits

Correction to: npj Quantum Information https://doi.org/10.1038/s41534-021-00449-4, published online 16 July 2021

The original version of this Article contained errors in Equation (15) and (16), in which the expressions for ε_A and ε_B 2QSS were mistakenly given in place of ε_mA and ε_mB 2QSS

$$\begin{array}{ll}\frac{{t_{{{{\mathrm{lA}}}}}}}{{t_{{{{\mathrm{rA}}}}}}} = \sqrt {\left( { - \frac{{C_{51} - C_{11}}}{{C_{21} - C_{11}}}} \right)\left( {\frac{{\frac{2}{{\left( {U - U{^\prime}{^\prime} + 2\varepsilon _{{{\mathrm{A}}}}} \right)^3}} - \frac{1}{{\left( {U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{{{{\mathrm{mA}}}}} + \varepsilon _{{{\mathrm{A}}}}} \right)^3}}}}{{\frac{2}{{\left( {U - U{^\prime}{^\prime} - 2\varepsilon _{{{\mathrm{A}}}}} \right)^3}} - \frac{1}{{\left( {U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{{{{\mathrm{mA}}}}} - \varepsilon _{{{\mathrm{A}}}}} \right)^3}}}}} \right)} ,\\\qquad \quad \left( {\varepsilon _{{{{\mathrm{mA}}}}}2{{{\mathrm{QSS}}}}} \right),\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\left({15} \right)\end{array}$$

$$\begin{array}{ll}\frac{{t_{{{{\mathrm{lB}}}}}}}{{t_{{{{\mathrm{rB}}}}}}} = \sqrt {\left( { - \frac{{C_{13} - C_{11}}}{{C_{14} - C_{11}}}} \right)\left( {\frac{{\frac{2}{{\left( {U - U{^\prime}{^\prime} + 2\varepsilon _{{{\mathrm{B}}}}} \right)^3}} - \frac{1}{{\left( {U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{{{{\mathrm{mB}}}}} + \varepsilon _{{{\mathrm{B}}}}} \right)^3}}}}{{\frac{2}{{\left( {U - U{^\prime}{^\prime} - 2\varepsilon _{{{\mathrm{B}}}}} \right)^3}} - \frac{1}{{\left( {U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{{{{\mathrm{mB}}}}} - \varepsilon _{{{\mathrm{B}}}}} \right)^3}}}}} \right)} ,\\ \qquad \quad \left( {\varepsilon _{{{{\mathrm{mB}}}}}\,2{{{\mathrm{QSS}}}}} \right).\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \left( {16} \right)\end{array}$$

The correct forms of Eqs. (15) and (16) are:

$$\frac{{t_{lA}}}{{t_{rA}}} = \sqrt {\frac{{C_{51} - C_{11}}}{{C_{21} - C_{11}}}} \left( {\frac{{U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{mA} - \varepsilon _A}}{{U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{mA} + \varepsilon _A}}} \right)^{3/2},\quad \quad \left( {\varepsilon _{{{{\mathrm{mA}}}}}2{{{\mathrm{QSS}}}}} \right),$$

(15)

$$\frac{{t_{lB}}}{{t_{rB}}} = \sqrt {\frac{{C_{13} - C_{11}}}{{C_{14} - C_{11}}}} \left( {\frac{{U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{mB} - \varepsilon _B}}{{U - 2U^\prime + U{^\prime}{^\prime} - \varepsilon _{mB} + \varepsilon _B}}} \right)^{3/2},\quad \quad \left( {\varepsilon _{{{{\mathrm{mB}}}}}2{{{\mathrm{QSS}}}}} \right),$$

(16)

This has been corrected in both the PDF and HTML versions of the Article.