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

arXiv:2603.26561 · quant-ph, cs.CC · Submitted 2026-03-27 · Read on arXiv

quant-ph, cs.CC

Submitted: 2026-03-27

Updated: 2026-09-24

Comments: 6+11 pages, 1 figure

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• BQP — 30× in this paper · explained in 2 episodes
• BQP-complete — 14× in this paper · explained in 2 episodes
• BQP-Completeness — 7× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Unitary Dynamics — 3× in this paper · explained in 2 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Quantum Physics — 2× in this paper · explained in 10 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Effective Hamiltonian — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Redundancy — 1× in this paper · explained in 2 episodes

Sources

• Shadow Hamiltonian Simulation
• A simple quantum algorithm to efficiently prepare sparse states
• Direct Equivalence between Dynamics of Quantum Walks and Coupled Classical Oscillators
• Quantum Computing, Postselection, and Probabilistic Polynomial-Time

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