13.5 Decoherence and quantum error correction 29113.4 Summary of quantum computers
Qubits are quantum objects that store information and can exist in
arbitrary superpositionsa| 0 〉+b| 1 〉. A quantum computer is a set of
qubits on which the following operations can be carried out.
(1) Each qubit can be prepared in a given state, so the quantum registers
of the computer have a well-defined initial state.
(2) In quantum computation the quantum logic gates (unitary transfor-
mations) act on a chosen subset of the qubits. During these processes
the system is in an entangled state where the information is encoded
in the state of the entire quantum register. This cannot be reduced
to a description of terms of the individual qubits, like a list of 0s
and 1s for a classical computer. Some of these operations are control
operations in which the change in the state of a qubit depends on
the state of other qubits.
(3) The final state of the qubits is read out by making a quantum mea-
surement.
For quantum information processing with a string of trapped ions, the
three stages of initialisation, quantum logic and read out correspond to
the following operations:
(1) Preparation of the initial state—all of the ions must be cooled to
the ground vibrational state and be in the same internal state. Any
state|F, MF〉of a given hyperfine level will do and the choice is
based on practical considerations.^99 In the NMR experiments the prepara-
tion of the initial state, or the resetting
of the device after a computation, are
not straightforward since those systems
do not have a dissipative process equiv-
alent to laser cooling.
(2) Raman transitions change both the internal and the vibrational
states of the ions (qubits) to implement the operation of quantum
gates.
(3) Laser beams resonant with a strong transition determine which hy-
perfine level each ion is in at the end of the process (Section 12.6).
The ions lie at least 10μm apart, so that each one is seen individually
(as in Fig. 13.1).
Quantum computing needs only a few basic types of quantum logic gate.
A control gate between a single pair of qubits in a multiple-particle
system can be combined with swap operations to effectively extend the
operation to all pairs of qubits. These manipulations combined with
arbitrary rotations of individual qubits give a universal set of operators
from which all other unitary operators can be constructed.
13.5 Decoherence and quantum error correction
The power of quantum computing to solve important problems has
been proved mathematically, but so far experiments have only used