Optimal Query Complexity for Ground-State Preparation

arXiv:2609.35668 · quant-ph, cs.CC, cs.DS · Submitted 2026-09-28 · Read on arXiv

quant-ph, cs.CC, cs.DS

Submitted: 2026-09-28

Updated: 2026-10-01

Terminology

• Trace — 23× in this paper · explained in 2 episodes
• Accuracy — 17× in this paper · explained in 1 episode
• Trace Distance — 14× in this paper · explained in 3 episodes
• Hilbert Space — 7× in this paper · explained in 2 episodes
• Ancilla Qubits — 6× in this paper · explained in 1 episode
• Block Encoding — 5× in this paper · explained in 4 episodes
• Query Complexity — 5× in this paper · explained in 2 episodes
• Spectral Gap — 3× in this paper · explained in 5 episodes
• Frustration — 2× in this paper · explained in 2 episodes
• Ab Initio — 1× in this paper · explained in 1 episode
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes

Sources

• Variations on Quantum Adversary
• Fast quantum algorithms for traversing paths of eigenstates
• A new quantum ripple-carry addition circuit
• Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla
• Dissipative ground state preparation and the Dissipative Quantum Eigensolver
• Multi-level quantum signal processing with applications to ground state preparation using fast-forwarded Hamiltonian evolution
• Optimal Ground-State Preparation with a Guiding State
• Quantum Algorithms for Ground-State Preparation and Green's Function Calculation
• Optimal Lower Bound for Ground-State Energy Estimation with a Guiding State
• Sharp Remez inequality
• Trade-offs between Quantum and Classical Resources in the Linear Combination of Unitaries
• Randomized Quantum Singular Value Transformation

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