#QuantumComplexity

Exchange Quantum Polynomial Time (XQP): Limited Interactions Rival Full Quantum Power

Oxford researchers define XQP, a new complexity class using only Heisenberg exchange interactions and √SWAP gates. Efficient simulation would collapse the polynomial hierarchy to PH⊆P³, bridging BPP and BQP without complex singlet states.

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Quadratic Bosonic Hamiltonian Simulation Complexity: BQP-Completeness and PostBQP-Hardness

Simulating inertially coupled bosons (unifying quantum walks & classical oscillators) is BQP-complete. Extending to general quadratic Hamiltonians is PostBQP-hard, revealing a sharp complexity transition in bosonic quantum simulation.

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