Quantum Phase Estimation Distribution
Resolve an eigenphase into a finite measurement distribution and expose wraparound ties.
Free theory articleResolve an eigenphase into a finite measurement distribution and expose wraparound ties.
Concept & interpretation
Let's calculate the outcome distribution for an eigenphase of 1/3 measured with a 3-bit register (giving 8 possible outcomes).
Experiment: Resolving Eigenphases
Follow these steps to observe how phase estimation resolves an eigenphase into a distribution:
- Open the module at https://riano.app/module/quantum-phase-estimation-distribution.
- Set the Eigenphase to
1/4and Register bits to3. - Notice that the peak probability becomes exactly 1.0 at outcome 2, because 2/8 = 1/4 exactly matches the eigenphase.
- Change the Eigenphase to
1/3. Since 1/3 cannot be represented exactly with 3 bits, the probability distribution spreads, with a peak probability of 0.687... at outcome 3. - Increase the Register bits to
4. The peak probability outcome shifts to 5 (decoded as 5/16 = 0.3125), and the circular error decreases.