Fig. 8: AKLT state preparation protocol.
From: An architecture for two-qubit encoding in neutral ytterbium-171 atoms
a Within each ququart, there are two qubits (optical and nuclear). Starting from a chain of singlets between optical and nuclear qubits across different sites, we project each ququart onto the spin-1 subspace. The projected wavefunction is the exact ground state of the AKLT Hamiltonian. b If the i-th ququart is projected onto the spin-0 subspace instead, the “o”-qubit of the (i − 1)-th ququart and “n”-qubit of the (i + 1)-th ququart automatically forms a maximally entangled singlet. c The quantum circuit of the actual experimental procedure consists of three steps. (i) Initialize the system into the product state of a particular pattern, which is followed by the intra-ququart SWAP and inter-ququart CNOT to create a chain of singlets. (ii) Apply individual qubit rotations and intra-ququart gates to rotate \(\left\vert 01\right\rangle -\left\vert 10\right\rangle\) into \(\left\vert 00\right\rangle\), measure \(\left\vert 00\right\rangle\), and then apply the reverse operation. This sequence effectively performs singlet/triplet projections. (iii) After the measurement, ququarts projected onto the spin-1 subspace automatically form the AKLT state, while spin-0 ququarts completely disentangle. One can rearrange neutral atoms to throw away spin-0 ququarts.
