Q2L8a.txt

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Quantum computation can be accomplished
with available resources using a variety of different models.
So far we have seen models which use states, gates,
and measurement in different ways.
Our first step was using the quantum circuit model
which employed zero qubits, controlled
NOTs and arbitrary single qubit rotations, and measurement
in the computational basis non-fault
tolerantly to achieve universal quantum computation.
A second model which we have seen
was explicitly fault tolerant.
It employed zero states, and magic states,
and Clifford gates, and stabilizer codes
to achieve fault tolerant quantum computation.
Some overhead that was required for these magic states.
Another model we consider is teleportation
based quantum computation.
It also uses some resource states,
which are entangled states, Pauli operators for gates,
and a variety of controlled Clifford gates
and measurement in the bell bases to achieve fault tolerant
quantum computation.
Teleportation is the basic idea underlying a very unusual model
known as measurement based quantum computation.
This employs a specific state known as a cluster state.
No gates at all, but measurement which is a little stronger,
namely measurement of any qubit rotated around the zed axis.
This is not a fault tolerant model by itself,
and it requires a number of qubits
which is proportional to the depth of the circuit.
Yet another interesting model is Adiabatic quantum computation,
which uses the ground state of a Hamiltonian varying in time.
A Hamiltonian, instead of unitary gates and measurement
at the and in the computational basis.
Whether this model can be made fault tolerant or not
is still open for discussion.
Our understanding of these models is still evolving.
For fault tolerant quantum computation,
for example, novel codes might be
discovered or novel approaches to fault tolerant procedures.
For measurement based quantum computation,
an interesting question is whether a natural Hamiltonian
might exist for creation of cluster states.
And the model of Adiabatic quantum computation
is tightly connected to questions about novel quantum
algorithms.