Properties of The Discrete Sinc Quantum State and Applications to
Measurement Interpolation
- URL: http://arxiv.org/abs/2207.00564v1
- Date: Fri, 1 Jul 2022 17:29:18 GMT
- Title: Properties of The Discrete Sinc Quantum State and Applications to
Measurement Interpolation
- Authors: Charlee Stefanski, Vanio Markov, Constantin Gonciulea
- Abstract summary: We provide and analyze several alternative estimators for extracting the outcome of a quantum computation.
The Ratio-Based Estimator uses a closed form expression for the decimal part of the encoded value using the ratio of the two most frequent outcomes.
The Coin Approximation Estimator relies on the fact that the decimal part of the encoded value is very well approximated by the parameter of the Bernoulli process represented by the magnitudes of the largest two amplitudes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Extracting the outcome of a quantum computation is a difficult task. In many
cases, the quantum phase estimation algorithm is used to digitally encode a
value in a quantum register whose amplitudes' magnitudes reflect the discrete
sinc function. In the standard implementation the value is approximated by the
most frequent outcome, however, using the frequencies of other outcomes allows
for increased precision without using additional qubits. One existing approach
is to use Maximum Likelihood Estimation, which uses the frequencies of all
measurement outcomes. We provide and analyze several alternative estimators,
the best of which rely on only the two most frequent measurement outcomes. The
Ratio-Based Estimator uses a closed form expression for the decimal part of the
encoded value using the ratio of the two most frequent outcomes. The Coin
Approximation Estimator relies on the fact that the decimal part of the encoded
value is very well approximated by the parameter of the Bernoulli process
represented by the magnitudes of the largest two amplitudes. We also provide
additional properties of the discrete sinc state that could be used to design
other estimators.
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