Quantum Phase
Estimation using
Multivalued Logic
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Quantum Phase - Quantum Computing - Lecture Slides, Slides of Computer Science
These are the Lecture Slides of Quantum Computing which includes Classical Computers, Quantum Computers, Significantly Faster, Factorization Problems, Exponential, Classical Computers, Non Polynomial Problems, Unstructured Search, Circuit Level Representation etc. Key important points are: Quantum Phase, Estimation, Multivalued Logic, Importance of Quantum Phase Estimation, Binary Logic, Performance Requirements, Salient Features, Conclusion, Abrams, Lloyd Algorithm
Typology: Slides
2012/2013
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Quantum Phase
Estimation using
Multivalued Logic
Agenda
- Importance of Quantum Phase Estimation (QPE)
- QPE using binary logic
- QPE using MVL
- Performance Requirements
- Salient features
- Conclusion
Abstract
- We generalize the Quantum Phase Estimation algorithm to MVL logic.
- We show the quantum circuits for QPE using qudits.
- We derive the performance requirements of the QPE to achieve high probability of success.
- We show how this leads to logarithmic decrease in the number of qudits and exponential decrease in error probability of the QPE algorithm as the value of the radix d increases.
General
Controlled
Gates
Another new concept – we use controlled powers of some Unitary Matrix U
REMINDER OF
EIGENVALUES AND
EIGENVECTORS
Basic Math
for Binary
Phase
Estimation
Finding the eigenvalue is the same as finding its phase φ Docsity.com
Target register
Index register to store the eigenvalue
Unitary operator for which we calculate phase of eigenvalue using phase kickback
we measure the phase
We initialize to all states
Formulas for
the phase
estimation
algorithm
This is the input to QFT
( )
We found phase
Assume k an integer
Number of bits
Concluding, we can calculate phase
Agenda
- Importance of Quantum Phase Estimation (QPE)
- QPE using binary logic
- QPE using MVL
- Performance Requirements
- Salient features
- Conclusion
ISMVL 2011, 23-25 May 2011, Tuusula, Finland Docsity.com
Abstract
- We generalize the Quantum Phase Estimation algorithm to MVL logic.
- We show the quantum circuits for QPE using qudits.
- We derive the performance requirements of the QPE to achieve high probability of success.
- We show how this leads to logarithmic decrease in the number of qudits and exponential decrease in error probability of the QPE algorithm as the value of the radix d increases.
ISMVL 2011, 23-25 May 2011, Tuusula, Finland Docsity.com