A new
algorithm for fixed point quantum search
(pp483-494)
Tathagat Tulsi, Lov K. Grover, and
Apoorva Patel
doi:
https://doi.org/10.26421/QIC6.6-2
Abstracts:
The standard quantum search lacks a feature, enjoyed by many classical
algorithms, of having a fixed point, i.e. monotonic convergence towards
the solution. Recently a fixed point quantum search algorithm has been
discovered, referred to as the Phase-\pi/3 search
algorithm, which gets around this limitation. While searching a database
for a target state, this algorithm reduces the error probability from \epsilon to \epsilon^{2q+1} using q oracle
queries, which has since been proved to be asymptotically optimal. A
different algorithm is presented here, which has the same worst-case
behavior as the Phase-\pi/3 search
algorithm but much better average-case behavior. Furthermore the new
algorithm gives \epsilon^{2q+1} convergence
for all integral q,
whereas the Phase-\pi/3 search
algorithm requires q to
be (3^{n}-1)/2 with n a
positive integer. In the new algorithm, the operations are controlled by
two ancilla qubits, and fixed point behavior is achieved by irreversible
measurement operations applied to these ancillas. It is an example of
how measurement can allow us to bypass some restrictions imposed by
unitarity on quantum computing.
Key words:
ancilla, fixed point, limit cycle, measurement, quantum search algorithm |