The Power of Power-of-SWAP: Postselected Quantum Computation with the Exchange Interaction
This work defines Exchange Quantum Polynomial Time (XQP) circuits using only computational basis SPAM and the isotropic Heisenberg exchange interaction, excluding singlet states. It shows that XQP is an intermediate complexity class between BPP and BQP. Key results include proving postselected XQP(pi/4) is universal for quantum computation and suggesting that simulating XQP efficiently would collapse the polynomial hierarchy.