Page 89 - Principles and Applications of NanoMEMS Physics

76 Chapter 2

wave function collapsed along Ψ + , and that for its qubit to embody the
12
unknown state and, hence, complete the teleportation, it has to effect the
unitary transformations: 0 → 1 and 1 → 0 on its qubit 3.
3 3 3 3

2.4.3 Decoherence

A quantum system is said to decohere when, in the course of its time
evolution, it loses energy to the environment. Under these circumstances its
transition matrix, U, no longer conserves the norm of the states it acts upon.
Since the states change in a random manner, the property of superposition of
states is no longer maintained. From thermodynamics we know that systems
that experience energy loss are irreversible, therefore, decoherence precludes
the realization of quantum gates, e.g., the Toffoli gate, which must be
reversible. The ability of a quantum system to maintain its coherence and,
thus, be capable of manifesting superposition and entanglement, is captured
by the decoherence time. Obviously, the system is useful for quantum
information processing only during this period of time. A system made up of
o
many qubits will exhibit a comp unded amount of errors as it approaches its
decoherence time. i.e., as it becomes irreversible. The decoherence of a
,
qubit, in particular, is quantitatively captured by the quality factor of
quantum coherence [112],

Q ϕ = πν T , (96)
ϕ
01
where ν is its transition frequency and T is the coherence time of a
ϕ
01
superposition of states. While error-correcting codes techniques have been
proposed to combat errors stemming from decoherence, the need for an
intrinsically coherent system to begin with, remains. Therefore, the
conception of approaches exhibiting long decoherence times, with respect to
the intended computational function to be implemented, is crucial, if
quantum information processing is to become practical. Vion et al. [112]
point out that, given a quantum computation with elementary operations
taking time t , active compensation of deciherence requires Q s ' greater
op ϕ
than 10 ν t . A number of approaches to the physical implementation of
4
01 op
qubits, and their respective decoherencetimes, are discussed in Chapter 4.