Logarithmic-depth quantum circuits for Hamming weight projections
Logarithmic-depth quantum circuits for Hamming weight projections
A pure state of fixed Hamming weight is a superposition of computational basis states such that each bitstring in the superposition has the same number of ones. Given a Hilbert space of the form $\mathcal{H}={({\mathbb{C}}_{2})}^{\ensuremath{\bigotimes}n}$, or an $n$-qubit system, the identity operator can be decomposed as a sum of projectors …