# Adiabatic quantum counting by geometric phase estimation

Adiabatic quantum counting by geometric phase estimation We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, α, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a Berry phase 2πα. By estimating the Berry phase, we can approximate α, and solve the problem. For an error bound $${\epsilon}$$ , the algorithm can solve the problem with cost of order $${(\frac{1}{\epsilon})^{3/2}}$$ , which is not as good as the optimal algorithm in the quantum circuit model, but better than the classical random algorithm. Moreover, since the Berry phase is a purely geometric feature, the result may be robust to decoherence and resilient to certain noise. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Adiabatic quantum counting by geometric phase estimation

, Volume 9 (3) – Sep 24, 2009
15 pages

Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-009-0132-y
Publisher site
See Article on Publisher Site

### References

• Quantum summation with an application to integration
Heinrich, S.
• Path integration on a quantum computer
Traub, J.F.; Wozniakowski, H.

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