Charge qubit

Cooper-Pair Boxes are fabricated using techniques similar to those used for microelectronics. The devices are usually made on silicon or sapphire wafers using electron beam lithography (different from phase qubit, which uses photolithography) and metallic thin film evaporation processes. To create Josephson junctions, a technique known as shadow evaporation is normally used; this involves evaporating the source metal alternately at two angles through the lithography defined mask in the electron beam resist. This results in two overlapping layers of the superconducting metal, in between which a thin layer of insulator (normally aluminum oxide) is deposited.

If the Josephson Junction has a junction capacitance ${\displaystyle C_{J}}$, and the gate capacitor ${\displaystyle C_{g}}$, then the charging (Coulumb) energy of one Cooper-pair is:

${\displaystyle E_{C}=(2e)^{2}/2(C_{g}+C_{J}).}$

If ${\displaystyle n}$ denotes the number of excess Cooper-pairs in the island (i.e. its net charge is ${\displaystyle -2ne}$), then the Hamiltonian is[4]:

${\displaystyle H=\sum _{n}{\big [}E_{C}(n-n_{g})^{2}|n\rangle \langle n|-{\frac {1}{2}}E_{J}(|n\rangle \langle n+1|+|n+1\rangle \langle n|){\big ]},}$

where ${\displaystyle n_{g}=C_{g}V_{g}/(2e)}$ is a control parameter known as effective offset charge (${\displaystyle V_{g}}$ is the gate voltage), and ${\displaystyle E_{J}}$ the Josephson energy of the tunneling junction.

At low temperature and low gate voltage, one can limit the analysis to only the lowest ${\displaystyle n=0}$ and ${\displaystyle n=1}$ states, and therefore obtain a two-level quantum system (a.k.a. qubit).

Note that some recent papers[8][9] adopt a different notation, and define the charging energy as that of one electron:

${\displaystyle E_{C}=e^{2}/2(C_{g}+C_{J}),}$

and then the corresponding Hamiltonian is:

${\displaystyle H=\sum _{n}{\big [}4E_{C}(n-n_{g})^{2}|n\rangle \langle n|-{\frac {1}{2}}E_{J}(|n\rangle \langle n+1|+|n+1\rangle \langle n|){\big ]}.}$

To-date, the realizations of qubits that have had the most success are ion traps and NMR, with Shor's algorithm even being implemented using NMR.[10] However, it is hard to see these two methods being scaled to the hundreds, thousands, or millions of qubits necessary to create a quantum computer. Solid-state representations of qubits are much more easily scalable, but they themselves have their own problem: decoherence. Superconductors, however, have the advantage of being more easily scaled, and they are more coherent than normal solid-state systems.[10]

Superconducting charge qubits have been progressing quickly. They were first suggested in 1997 by Shnirman,[11] and by 2001 coherent oscillations were observed.