Comparison to charge qubit Transmon

scehmatical qubit energy levels diagram evolution charge qubit (top,




e

j



/


e

c


=
1


{\displaystyle e_{j}/e_{c}=1}

) transmon (bottom,




e

j



/


e

c


=
50


{\displaystyle e_{j}/e_{c}=50}

), plotted first 3 energy levels (



m
=
0
,
1
,
2


{\displaystyle m=0,1,2}

), function of average number




n

g




{\displaystyle n_{g}}

of cooper pairs across junction, normalized gap between ground , first excited state. charge qubit (top) operated @




n

g


=
0.5


{\displaystyle n_{g}=0.5}

sweet spot , fluctuations in




n

g




{\displaystyle n_{g}}

cause less energy shift, , anharmonicity maximal. transmon (bottom) energy levels insensitive




n

g




{\displaystyle n_{g}}

fluctuations, anharmonicity reduced

the transmon design similar charge qubit, both described same hamiltonian, difference being increase in




e

j



/


e

c




{\displaystyle e_{j}/e_{c}}

ratio, achieved shunting josephson junction additional large capacitor. here




e

j




{\displaystyle e_{j}}

josephson energy of junction, ,




e

c




{\displaystyle e_{c}}

charging energy inversely proportional total capacitance of qubit circuit. benefit of increasing




e

j



/


e

c




{\displaystyle e_{j}/e_{c}}

ratio insensitivity charge noise - energy levels become independent of electrical charge across junction, coherence times of qubit prolonged. disadvantage decrease in anharmonicity







e

2


−

e

1





e

1


−

e

0







{\displaystyle {\frac {e_{2}-e_{1}}{e_{1}-e_{0}}}}

,




e

i




{\displaystyle e_{i}}

energy of state




|

i
⟩


{\displaystyle |i\rangle }

. reduced anharmonicity complicates device operation 2 level system, e.g. exciting device ground state first excited state resonant pulse populates second excited state. complication overcome complex microwave pulse design, takes account higher energy levels, , prohibits excitation destructive interference.

measurement, control , coupling of transmons performed means of microwave resonators techniques of circuit quantum electrodynamics, applicable other superconducting qubits. coupling resonators done putting capacitor between qubit , resonator, @ point resonator electromagnetic field biggest. example, in ibm quantum experience devices, resonators implemented quarter wave coplanar waveguide maximal field @ signal-ground short @ waveguide end, every ibm transmon qubit has long resonator tail . initial proposal included similar transmission line resonators coupled every transmon, becoming part of name. however, charge qubits operated @ similar




e

j



/


e

c




{\displaystyle e_{j}/e_{c}}

regime, coupled different kinds of microwave cavities referred transmons well.