The Power of Power-of-SWAP: Postselected Quantum Computation with the Exchange Interaction

Abstract:We introduce Exchange Quantum Polynomial Time (XQP) circuits, which comprise quantum computation using only computational basis SPAM and the isotropic Heisenberg exchange interaction. Structurally, this restricted model captures decoherence-free subspace computation without access to singlet states. We prove that XQP, as well as its constrained family consisting solely of $\sqrt{\mathrm{SWAP}}$ gates, is universal for quantum computation under polynomial overheads in circuit depth and size. This establishes the universality of the $\sqrt{\mathrm{SWAP}}$ gate on its own under a logical encoding of qubits. We further prove that circuits generated by $\sqrt{\mathrm{SWAP}}$ gates are semi-universal, and thus generate $t$-designs for the uniform distribution over SU(2)-invariant unitaries. Finally, we study additional properties of the XQP model, including its relation to the six-vertex and Potts model in statistical physics. Our findings suggest that XQP circuits are naturally suited to near-term hardware and provide a simple platform for experimental demonstrations of quantum advantage.

arXiv:2603.28527 [quant-ph]

(or arXiv:2603.28527v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.28527 Focus to learn more arXiv-issued DOI via DataCite

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