Transmon

Part of a series of articles about
Quantum mechanics
${\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser Delayed-choice Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Overview Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Many-worlds Objective collapse Quantum logic Relational Transactional
Advanced topics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Scientists Aharonov Bell Bethe Blackett Bloch Bohm Bohr Born Bose de Broglie Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Simmons Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger
v t

In quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of superconducting charge qubit that was designed to have reduced sensitivity to charge noise. The transmon was developed by Robert J. Schoelkopf, Michel Devoret, Steven M. Girvin and their colleagues at Yale University in 2007.^[1][2] Its name is an abbreviation of the term transmission line shunted plasma oscillation qubit; one which consists of a Cooper-pair box "where the two superconductors are also capacitatively shunted in order to decrease the sensitivity to charge noise, while maintaining a sufficient anharmonicity for selective qubit control".^[3]

A device consisting of four transmon qubits, four quantum buses, and four readout resonators fabricated by IBM and published in npj Quantum Information in January 2017.^[4]

The transmon achieves its reduced sensitivity to charge noise by significantly increasing the ratio of the Josephson energy to 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 have T₁ coherence times ~ 30 μs to 40 μs.^[5] By replacing the superconducting transmission line cavity with a three-dimensional superconducting cavity, recent work on transmon qubits has shown significantly improved T₁ times, as long as 95 μs.^[6][7] These results demonstrate that previous T₁ times were not limited by Josephson junction losses. Understanding the fundamental limits on the coherence time in superconducting qubits such as the transmon is an active area of research.

Comparison to Cooper-pair box[]

Schematical qubit energy levels diagram evolution from charge qubit (top, ${\displaystyle E_{\rm {J}}/E_{\rm {C}}=1}$) to transmon (bottom, ${\displaystyle E_{\rm {J}}/E_{\rm {C}}=50}$), plotted for the first 3 energy levels (${\displaystyle m=0,1,2}$), as function of the average number ${\displaystyle n_{g}}$ of Cooper pairs across the junction, normalized to the gap between the ground and the first excited state.^[1] The charge qubit (top) is normally operated at the ${\displaystyle n_{g}=0.5}$ "sweet spot", where fluctuations in ${\displaystyle n_{g}}$ cause less energy shift, and the anharmonicity is maximal. Transmon (bottom) energy levels are insensitive to ${\displaystyle n_{g}}$ fluctuations, but the anharmonicity is reduced

The transmon design is similar to the first design^[8] of Cooper-pair box, both are described by the same Hamiltonian, with the only difference being the increase in the ${\displaystyle E_{\rm {J}}/E_{\rm {C}}}$ ratio, achieved by shunting the Josephson junction with an additional large capacitor. Here ${\displaystyle E_{\rm {J}}}$ is the Josephson energy of the junction, and ${\displaystyle E_{\rm {C}}}$ is the charging energy inversely proportional to the total capacitance of the qubit circuit. The benefit of increasing the ${\displaystyle E_{\rm {J}}/E_{\rm {C}}}$ ratio is insensitivity to charge noise - the energy levels become independent of electrical charge across the junction, thus the coherence times of the qubit are prolonged. The disadvantage is decrease in the anharmonicity ${\displaystyle {\frac {(E_{2}-E_{1})-(E_{1}-E_{0})}{E_{1}-E_{0}}}}$, where ${\displaystyle E_{i}}$ is the energy of the state ${\displaystyle |i\rangle }$. 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 second 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.

Measurement, control and coupling of the transmons is performed by means of microwave resonators with techniques of circuit quantum electrodynamics, also applicable to other superconducting qubits. The coupling to the resonators is done by putting a capacitor between the qubit and the resonator, at a point where the resonator electromagnetic field is biggest. For example, in IBM Quantum Experience devices, the resonators are implemented with "" coplanar waveguide with 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 similar transmission line resonators coupled to every transmon, becoming a part of the name. However, charge qubits operated at a similar ${\displaystyle E_{\rm {J}}/E_{\rm {C}}}$ regime, coupled to different kinds of microwave cavities are referred to as transmons as well.

See also[]

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

References[]