In
quantum computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
, a charge qubit (also known as Cooper-pair box) is a
qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
whose basis
states are
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
states (i.e. states which represent the presence or absence of excess
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
s in the island). In
superconducting quantum computing
Superconducting quantum computing is a branch of solid state quantum computing which implements superconducting electronic circuits using superconducting qubits as artificial atoms, or quantum dots. For superconducting qubits, the two logic sta ...
, a charge qubit
is formed by a tiny
superconducting
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
island coupled by a
Josephson junction
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...
(or practically,
superconducting tunnel junction
The superconducting tunnel junction (STJ) — also known as a superconductor–insulator–superconductor tunnel junction (SIS) — is an electronic device consisting of two superconductors separated by a very thin layer of insulating material. Cu ...
) to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs which 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 voltage ''U'' that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitive
electrometer
An electrometer is an electrical instrument for measuring electric charge or electrical potential difference. There are many different types, ranging from historical handmade mechanical instruments to high-precision electronic devices. Modern ...
such as the
radio-frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...
single-electron transistor
A single-electron transistor (SET) is a sensitive electronic device based on the Coulomb blockade effect. In this device the electrons flow through a tunnel junction between source/drain to a quantum dot (conductive island). Moreover, the electric ...
.
Typical
''T''2 coherence times for a charge qubit are on the order of 1–2 μs.
Recent work has shown ''T''
2 times approaching 100 μs using a type of charge qubit known as a
transmon
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. Schoelko ...
inside a three-dimensional superconducting cavity.
[C. Rigetti ''et al.'', "Superconducting qubit in waveguide cavity with coherence time approaching 0.1 ms,]
arXiv:1202.5533
(2012) Understanding the limits of ''T''
2 is an active area of research in the field of
superconducting quantum computing
Superconducting quantum computing is a branch of solid state quantum computing which implements superconducting electronic circuits using superconducting qubits as artificial atoms, or quantum dots. For superconducting qubits, the two logic sta ...
.
Fabrication
Charge qubits are fabricated using techniques similar to those used for
microelectronics
Microelectronics is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture (or microfabrication) of very small electronic designs and components. Usually, but not always, this means micrometre-sc ...
. The devices are usually made on silicon or sapphire wafers using
electron beam lithography
Electron-beam lithography (often abbreviated as e-beam lithography, EBL) is the practice of scanning a focused beam of electrons to draw custom shapes on a surface covered with an electron-sensitive film called a resist (exposing). The electron b ...
(different from
phase qubit In quantum computing, and more specifically in superconducting quantum computing, the phase qubit is a superconducting device based on the superconductor–insulator–superconductor (SIS) Josephson junction, designed to operate as a quantum bit, ...
, which uses
photolithography
In integrated circuit manufacturing, photolithography or optical lithography is a general term used for techniques that use light to produce minutely patterned thin films of suitable materials over a substrate, such as a silicon wafer, to protect ...
) and metallic thin film evaporation processes. To create
Josephson junction
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...
s, 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.
Hamiltonian
If the Josephson junction has a junction capacitance
, and the gate capacitor
, then the charging (Coulomb) energy of one Cooper pair is:
:
If
denotes the number of excess Cooper pairs in the island (i.e. its net charge is
), then the Hamiltonian is:
:
where
is a control parameter known as effective offset charge (
is the gate voltage), and
the Josephson energy of the tunneling junction.
At low temperature and low gate voltage, one can limit the analysis to only the lowest
and
states, and therefore obtain a two-level quantum system (a.k.a.
qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
).
Note that some recent papers adopt a different notation, and define the charging energy as that of one electron:
:
and then the corresponding Hamiltonian is:
:
Benefits
To-date, the realizations of qubits that have had the most success are
ion trap
An ion trap is a combination of electric and/or magnetic fields used to capture charged particles — known as ions — often in a system isolated from an external environment. Atomic and molecular ion traps have a number of applications in phy ...
s and
NMR
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with ...
, with
Shor's algorithm
Shor's algorithm is a quantum algorithm, quantum computer algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor.
On a quantum computer, to factor an integer N , Shor's algorithm ...
even being implemented using NMR.
[Superconducting Charge Qubits]
by Denzil Anthony Rodrigues, page 3 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
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
.
Solid-state
Solid state, or solid matter, is one of the four fundamental states of matter.
Solid state may also refer to:
Electronics
* Solid-state electronics, circuits built of solid materials
* Solid state ionics, study of ionic conductors and their use ...
representations of qubits are much more easily scalable, but they themselves have their own problem:
decoherence
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
. Superconductors, however, have the advantage of being more easily scaled, and they are more coherent than normal solid-state systems.
Experimental progresses
The implementation of Superconducting charge qubits have been progressing quickly since 1996. Design was theoretically described in 1997 by Shnirman, while the evidence of quantum coherence of the charge in a Cooper pair box was published in February 1997 by
Vincent Bouchiat et al. In 1999, coherent oscillations in the charge Qubit were first observed by Nakamura et al. Manipulation of the quantum states and full realization of the charge qubit was observed 2 years later.
In 2007, a more advanced device known as
Transmon
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. Schoelko ...
showing enhanced coherence times due to its reduced sensitivity to charge noise was developed at Yale University by
Robert J. Schoelkopf
Robert J. Schoelkopf III (born January 24, 1964) is an American physicist, most noted for his work on quantum computing as one of the inventors of superconducting qubits. Schoelkopf's main research areas are quantum transport, single-electron d ...
,
Michel Devoret
Michel Devoret is a French physicist and F. W. Beinecke Professor of Applied Physics at Yale University. He also holds a position as the Director of the Applied Physics Nanofabrication Lab at Yale. He is known for his pioneering work on macroscopi ...
,
Steven M. Girvin and their colleagues .
References
{{Quantum computing
Quantum information science
Quantum electronics
Superconductivity