DQC1-completeness of normalized trace estimation for functions of log-local Hamiltonians

arXiv:2604.01519 · quant-ph, cs.CC · Submitted 2026-04-02 · Read on arXiv

quant-ph, cs.CC

Submitted: 2026-04-02

Updated: 2026-09-23

Project page: https://changpeng-shao.github.io/DQC1_trace_estimation_

Terminology

• Trace — 41× in this paper · explained in 2 episodes
• Query Complexity — 13× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• BQP — 5× in this paper · explained in 2 episodes
• Block Encoding — 3× in this paper · explained in 4 episodes
• BQP-Completeness — 2× in this paper · explained in 2 episodes
• Entanglement — 2× in this paper · explained in 3 episodes
• Objective Function — 2× in this paper · explained in 2 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Unified Framework — 2× in this paper · explained in 5 episodes
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Alternation — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Annual ACM Symposium on Theory of Computing — 1× in this paper
• BQP-complete — 1× in this paper · explained in 2 episodes
• Chebyshev Polynomials — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes

Sources

• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Dequantization and Hardness of Spectral Sum Estimation
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• A quantum algorithm for estimating the determinant
• DQC1-hardness of estimating correlation functions
• Quantum Complexity: restrictions on algorithms and architectures
• Quantum space-depth tradeoffs for coherent block encodings

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