Transmon

Inquantum computing,and more specifically insuperconducting quantum computing,atransmonis a type ofsuperconductingcharge qubitdesigned to have reduced sensitivity to charge noise. The transmon was developed byRobert J. Schoelkopf,Michel Devoret,Steven M. Girvin,and their colleagues atYale Universityin 2007.Its name is an abbreviation of the termtransmission lineshuntedplasma oscillationqubit;one which consists of aCooper-pair box"where the two superconductors are also [capacitively] shunted in order to decrease the sensitivity to charge noise, while maintaining a sufficient anharmonicity for selective qubit control".

A device consisting of four transmon qubits, fourquantum buses,and four readoutresonatorsfabricated byIBMand published innpj Quantum Informationin January 2017.

The transmon achieves its reduced sensitivity to charge noise by significantly increasing the ratio of theJosephson energyto the charging energy. This is accomplished through the use of a large shunting capacitor. The result is energy level spacings that are approximately independent of offset charge. Planar on-chip transmon qubits haveT₁coherence timesapproximately 30 μs to 40 μs.Recent work has shown significantly improvedT₁times as long as 95 μs by replacing the superconductingtransmission linecavity with a three-dimensional superconducting cavity,and by replacingniobiumwithtantalumin the transmon device,T₁is further improved up to 0.3 ms.These results demonstrate that previousT₁times were not limited byJosephson junctionlosses. Understanding the fundamental limits on the coherence time insuperconducting qubitssuch as the transmon is an active area of research.

Comparison to Cooper-pair box

Eigenenergies$E_{m}$(first three levels,$m=0,1,2$) of the qubit Hamiltonian as a function of the effective offset charge$n_{g}$for different ratios$E_{J}/E_{c}$.Energies are given in units of the transition energy$E_{01}$,evaluated at the degeneracy point$n_{g}=0.5$.The zero point of energy is chosen as the bottom of the$m=0$level. The charge qubit (small$E_{J}/E_{c}$,top) is normally operated at the$n_{g}=0.5$"sweet spot", where fluctuations in cause less energy shift, and the anharmonicity is maximal. Transmon (large$E_{J}/E_{c}$,bottom) energy levels are insensitive to fluctuations, but the anharmonicity is reduced.

The transmon design is similar to the first design of thecharge qubitknown as a "Cooper-pair box"; both are described by the same Hamiltonian, with the only difference being the$E_{\rm {J}}/E_{\rm {C}}$ratio. Here$E_{\rm {J}}$is theJosephson energyof the junction, and$E_{\rm {C}}$is the charging energy inversely proportional to the total capacitance of the qubit circuit. Transmons typically have$E_{\mathrm {J} }/E_{\mathrm {C} }\gg 1$(while$E_{\mathrm {J} }/E_{\mathrm {C} }\lesssim 1$for typical Cooper-pair-box qubits), which is achieved by shunting theJosephson junctionwith an additional largecapacitor.

The benefit of increasing the$E_{\rm {J}}/E_{\rm {C}}$ratio is the insensitivity to charge noise—the energy levels become independent of the offset charge$n_{g}$across the junction; thus thedephasingtime of the qubit is prolonged. The disadvantage is the reduced anharmonicity$\ Alpha =(E_{21}-E_{10})/E_{10}$,where$E_{ij}$is the energy difference between eigenstates$|i\rangle$and$|j\rangle$.Reduced anharmonicity complicates the device operation as a two level system, e.g. exciting the device from the ground state to the first excited state by a resonant pulse also populates the higher excited state. This complication is overcome by complex microwave pulse design, that takes into account the higher energy levels, and prohibits their excitation by destructive interference. Also, while the variation of$E_{10}$with respect to$n_{g}$tend to decrease exponentially with$E_{\mathrm {J} }/E_{\mathrm {C} }$,the anharmonicity only has a weaker, algebraic dependence on$E_{\mathrm {J} }/E_{\mathrm {C} }$as$\sim (E_{\mathrm {J} }/E_{\mathrm {C} })^{-1/2}$.The significant gain in the coherence time outweigh the decrease in the anharmonicity for controlling the states with high fidelity.

Measurement, control and coupling of transmons is performed by means of microwave resonators with techniques fromcircuit quantum electrodynamicsalso applicable toother superconducting qubits.Coupling to the resonators is done by placing a capacitor between the qubit and the resonator, at a point where the resonatorelectromagnetic fieldis greatest. For example, inIBM Quantum Experiencedevices, the resonators are implemented with "quarter wave"coplanar waveguideswith maximal field at the signal-ground short at the waveguide end; thus every IBM transmon qubit has a long resonator "tail". The initial proposal included similartransmission lineresonators coupled to every transmon, becoming a part of the name. However, charge qubits operated at a similar$E_{\rm {J}}/E_{\rm {C}}$regime, coupled to different kinds of microwave cavities are referred to as transmons as well.

Transmons as qudits

Transmons have been explored for use asd-dimensionalquditsvia the additional energy levels that naturally occur above the qubit subspace (the lowest two states). For example, the lowestthreelevels can be used to make a transmonqutrit;in the early 2020s, researchers have reported realizations of single-qutritquantum gateson transmonsas well as two-qutritentanglinggates.Entangling gates on transmons have also been explored theoretically and in simulations for the general case of qudits of arbitraryd.

See also

• Charge qubit
• Anharmonicity
• Circuit quantum electrodynamics(cQED)
• Dilution refrigerator
• List of quantum processors
• Quantum harmonic oscillator
• Superconducting quantum computing