Sublinear-depth Quantum Simulation of Electrons with Atomic Orbitals

arXiv:2610.00950 · quant-ph · Submitted 2026-10-01 · Read on arXiv

quant-ph

Submitted: 2026-10-01

Updated: 2026-10-01

Terminology

• Fast Multipole Method — 5× in this paper
• Sparsity — 3× in this paper · explained in 4 episodes
• Ancilla Qubits — 2× in this paper · explained in 1 episode
• Quantization — 2× in this paper · explained in 12 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Block Encoding — 1× in this paper · explained in 4 episodes
• Chebyshev Polynomials — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Hubbard Model — 1× in this paper · explained in 3 episodes

Sources

• Low-gate-count block encodings for second-quantized fermionic Hamiltonians
• A Denser Planar Surface Code
• Hamiltonian Simulation in the Interaction Picture
• First-Quantized Quantum Simulation of Non-Relativistic QED with Emergent Topologically Protected Coulomb Interactions
• Quantum simulation of electronic structure via quantum fast multipole method
• Decay properties of spectral projectors with applications to electronic structure
• A Quantum Algorithm with Polylogarithmic Depth per Trotter Step for the Extended Hubbard Model
• Low-depth fermion routing without ancillas
• Fast simulation of fermions with reconfigurable qubits

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• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity