Selecting efficient phase estimation with constant-precision phase shift operators

We investigate the cost of three phase estimation procedures that require only constant-precision phase shift operators. The cost is in terms of the number of elementary gates, not just the number of measurements. Faster phase estimation requires the minimal number of measurements with a logarithmic factor of reduction when the required precision $$n$$n is large. The arbitrary constant-precision approach (ACPA) requires the minimal number of elementary gates with a minimal factor of 14 of reduction in comparison with Kitaev’s approach. The reduction factor increases as the precision gets higher in ACPA. Kitaev’s approach is with a reduction factor of 14 in comparison with the faster phase estimation in terms of elementary gate counts.

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