Copy-scarce learning of ground states

arXiv:2609.38513 · quant-ph · Submitted 2026-09-29 · Read on arXiv

quant-ph

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Trace — 23× in this paper · explained in 2 episodes
• Spectral Gap — 17× in this paper · explained in 5 episodes
• Benchmark — 13× in this paper · explained in 2 episodes
• Block Encoding — 12× in this paper · explained in 4 episodes
• Shadow Tomography — 11× in this paper · explained in 4 episodes
• Trace Distance — 10× in this paper · explained in 3 episodes
• Fidelity — 7× in this paper · explained in 2 episodes
• Ancilla Qubits — 6× in this paper · explained in 1 episode
• Accuracy — 4× in this paper · explained in 1 episode
• Annual ACM-SIAM Symposium on Discrete Algorithms — 4× in this paper
• Decode — 4× in this paper · explained in 2 episodes
• Entanglement — 4× in this paper · explained in 3 episodes
• Query Complexity — 3× in this paper · explained in 2 episodes
• Stabilizer States — 3× in this paper · explained in 2 episodes
• Gibbs State — 2× in this paper · explained in 2 episodes
• Heisenberg Scaling — 2× in this paper · explained in 4 episodes
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes

Sources

• Mixed state tomography reduces to pure state tomography
• Trade-offs between Quantum and Classical Resources in the Linear Combination of Unitaries
• Catalytic Tomography of Ground States
• Optimal high-precision shadow estimation
• Dimension-Free Polylogarithmic Quantum Shadow Tomography
• Optimal lower bounds for quantum state tomography
• Classical shadows of fermions with particle number symmetry
• Provably Efficient Learning of Fermionic Correlations under Particle-Number Symmetry
• Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach
• Efficiently estimating quantum thermal properties from exponentially fewer samples
• Quantum Amplitude Amplification and Estimation
• Near-Heisenberg-limited parallel amplitude estimation with logarithmic depth circuit
• Lower Bounds on Quantum Query Complexity
• Quantum Computing: Lecture Notes
• Hamiltonian Simulation by Uniform Spectral Amplification
• Improved constant factors for qubitized Hamiltonian simulation

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