Encoding universal quantum computation into quantized Berry phases: Hardness results and classical algorithms

arXiv:2609.37199 · quant-ph · Submitted 2026-09-29 · Read on arXiv

quant-ph

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Spectral Gap — 35× in this paper · explained in 5 episodes
• BQP — 26× in this paper · explained in 2 episodes
• BQP-complete — 6× in this paper · explained in 2 episodes
• Effective Hamiltonian — 5× in this paper · explained in 2 episodes
• Adiabatic Evolution — 4× in this paper · explained in 2 episodes
• BQP-Completeness — 3× in this paper · explained in 2 episodes
• Fidelity — 3× in this paper · explained in 2 episodes
• Quantization — 3× in this paper · explained in 12 episodes
• Topological Order — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Ancilla Qubits — 2× in this paper · explained in 1 episode
• Entanglement — 2× in this paper · explained in 3 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Berry Curvature — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Adiabatic Error Cancellation in Berry Phase Estimation
• Computational complexity of Berry phase estimation in topological phases of matter
• Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians
• Locality in Quantum Systems
• A Simple Proof that Toffoli and Hadamard are Quantum Universal
• Quasi-adiabatic Continuation for Disordered Systems: Applications to Correlations, Lieb-Schultz-Mattis, and Hall Conductance
• Hardness of recognizing phases of matter
• On the Computational Complexity of Guided Berry Phase Estimation
• Classical Algorithms for Hamiltonian Dynamics Mean Value and Guided Local Hamiltonian Problem
• A Dequantized Algorithm for the Guided Local Hamiltonian Problem

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