Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

1.2 Implementations
Semiconductor Few-Electron Quantum Dots as Spin Qubits 29
A number of features are required for building an actual quantum computer
[17]:
1. A scalable physical system with well-characterized qubits
2. A “universal” set of quantum gates to implement any algorithm
3. The ability to initialize the qubits to a known pure state
4. A qubit-specific measurement capability
5. Decoherence times much longer than the gate operation time
Many systems can be found which satisfy some of these criteria, but it is
very hard to find a system that satisfies all of them. Essentially, we have to
reconcile the conflicting demands of good access to the quantum system (in
order to perform fast and reliable operations or measurements) with sufficient
isolation from the environment (for long coherence times). Current state-ofthe-art
is a seven-bit quantum computer that has factored the number 15 into
its prime factors 3 and 5, in fewer steps than is possible classically [18]. This
was done using an ensemble of molecules in liquid solution, with seven nuclear
spins in each molecule acting as the seven qubits. These could be controlled
and read out using nuclear magnetic resonance (NMR) techniques. Although
this experiment constitutes an important proof-of-principle for quantum computing,
practical limitations do not allow the NMR approach to be scaled up
to more than about ten qubits.
Therefore, many other implementations are currently being studied [19].
For instance, trapped ions have been used to demonstrate a universal set of
one- and two-qubit operations, an elementary quantum algorithm, as well as
entanglement of up to three qubits and quantum teleportation [19]. Typically,
microscopic systems such as atoms or ions have excellent coherence properties,
but are not easily accessible or scalable – on the other hand, larger systems
such as solid-state devices, which can be accessed and scaled more easily, usually
lack long decoherence times. A solid-state device with a long decoherence
time would represent the best of both worlds. Such a system could be provided
by the spin of an electron trapped in a quantum dot: a spin qubit.
1.3 The Spin Qubit
Our programme to build a solid-state qubit follows the proposal by Loss and
DiVincenzo [2]. This describes a quantum two-level system defined by the spin
orientation of a single electron trapped in a semiconductor quantum dot. The
electron spin can point “up” or “down” with respect to an external magnetic
field. These eigenstates, |↑〉and |↓〉, correspond to the two basis states of the
qubit.
The quantum dot that holds the electron spin is defined by applying negative
voltages to metal surface electrodes (“gates”) on top of a semiconductor
(GaAs/AlGaAs) heterostructure (see Fig. 2). Such gated quantum dots are