sensitivity is proportional to the number of spins $N$: It is the Heisenberg Limit [@PhysRevLett.79.3865; @Giovannetti:2011aa].

Jones et al. demonstrated the above measurement scheme with star-topology molecules schematically shown in Fig. \[fig:q\_circuit\](a). They employed two molecules, trimethyl phosphite (TMP) [@Jones1166] and tetramethyl silane (TMS) [@PhysRevA.82.022330]. TMP (TMS) molecule consists of the center $^{31}$P ($^{29}$Si) and three (four) methyl groups and thus the center $^{31}$P ($^{29}$Si) is surrounded by 9 (12) $^1$H spins. The highly symmetric structure of these molecules allows to address all surrounding spins (small open circles in Fig. \[fig:q\_circuit\](a)) globally, and thus the operations required to measure a magnetic field can be simplified. In this work, we employed the simplest star topology molecule that consists of the center spin ($\bigcirc$) and the two side spins ($\circ$’s), as shown in Fig. \[fig:q\_circuit\](b).

![ (a, b, c) Three different interaction topologies among spins ($\bigcirc, \circ$, and $\bullet$) discussed in this work and (d) a quantum circuit for an entangled magnetic field sensor simulation. (a) a sketch of a star-like interaction structure among spins, (b) the simplest star topology structure. The small open circles ($\circ$’s) in (a) and (b) play the role of entangled sensors. (c) the two step star topology 