Inquantum computing, acharge qubit (also known asCooper-pair box) is aqubit whose basisstates arecharge states (i.e. states which represent the presence or absence of excessCooper pairs in the island).^[1][2][3] Insuperconducting quantum computing, a charge qubit^[4] is formed by a tinysuperconducting island coupled by aJosephson junction (or practically,superconducting tunnel junction) to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs that have tunneled across the junction. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltageU that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitiveelectrometer such as theradio-frequencysingle-electron transistor.

TypicalT₂ coherence times for a charge qubit are on the order of 1–2 μs.^[5] Recent work has shownT₂ times approaching 100 μs using a type of charge qubit known as atransmon inside a three-dimensional superconducting cavity.^[6][7] Understanding the limits ofT₂ is an active area of research in the field ofsuperconducting quantum computing.

Charge qubits are fabricated using techniques similar to those used formicroelectronics. The devices are usually made on silicon or sapphire wafers usingelectron beam lithography (different fromphase qubit, which usesphotolithography) and metallic thin film evaporation processes. To createJosephson junctions, a technique known asshadow 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 (normallyaluminum oxide) is deposited.

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

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

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]

${\displaystyle H=\sum _n[E_{\mathrm{C}}(n-n_{\mathrm{g}}{)}^2|n⟩⟨n|-\frac{1}{2}{E}_{\mathrm{J}}(|n⟩⟨n+1|+|n+1⟩⟨n|)],}$

where${\displaystyle n_{\mathrm{g}}=C_{\mathrm{g}}{V}_{\mathrm{g}}/(2e)}$ is a control parameter known as effective offset charge (${\displaystyle V_{\mathrm{g}}}$ is the gate voltage), and${\displaystyle E_{\mathrm{J}}}$ 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:

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

and then the corresponding Hamiltonian is:

${\displaystyle H=\sum _n[4E_{\mathrm{C}}(n-n_{\mathrm{g}}{)}^2|n⟩⟨n|-\frac{1}{2}{E}_{\mathrm{J}}(|n⟩⟨n+1|+|n+1⟩⟨n|)].}$

To-date, the realizations of qubits that have had the most success areion traps andNMR, withShor'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 aquantum 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]

The implementation of superconducting charge qubits have been progressing quickly since 1996. Design was theoretically described in 1997 by Shnirman,^[11] while the evidence of quantum coherence of the charge in a Cooper pair box was published in February 1997 byVincent Bouchiat et al.^[12] In 1999, coherent oscillations in the charge qubit were first observed by Nakamura et al.^[13] Manipulation of the quantum states and full realization of the charge qubit was observed 2 years later.^[14] In 2007, a more advanced device known astransmon showing enhanced coherence times due to its reduced sensitivity to charge noise was developed at Yale University byRobert J. Schoelkopf,Michel Devoret,Steven M. Girvin and their colleagues.^{[citation needed]}

• Quantum information science
• Quantum electronics
• Superconductivity

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