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2

Earlier on that paper, they state that the input to the adders (or subtracters) will have an extra qubit than the ones needed to represent the numerical input. For example, if you want to input $8$, you need $4$ qubits since $8$ in binary is $1000$. So, you will input $5$ qubits to the gates. They use this extra qubit to look out for overflow. For example if ...


2

The iterative Quantum Phase Estimation(IQPE) procedure tries to measure the phase associated with a unitary matrix one bit at a time. While the idea of phase kickback used in the original QPE algorithm is used in IQPE too, one crucial aspect of the circuit is the classically controlled rotations. Since we use the measurement values of the previously ...


3

The idea here is essentially as follows: We classify the pairs $(j, k)$ produced by the quantum algorithm as either good or bad. For a good pair, it holds that $| \{ dj + 2^m k \}_{2^{\ell + m}} | \le 2^{m-2}$. We lower-bound the probability of the quantum algorithm producing a good pair when run. We show that given $s$ good pairs, we can solve for the ...


3

The circuits for the QFT where $N$ is a power of 2 are simpler than circuits where $N$ is an arbitrary number. They get just-as-good results with lower cost. Power of 2 sizes also enable important optimizations like qubit recycling, which allow you to only store one exponent qubit at a time, which is a substantial space savings. It sounds to me like you ...


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