Estimating quantum relative entropies on quantum computers

arXiv:2501.07292 · quant-ph, cs.IT, cs.LG, cs.NA, math.IT, math.NA · Submitted 2025-01-13 · Read on arXiv

quant-ph, cs.IT, cs.LG, cs.NA, math.IT, math.NA

Submitted: 2025-01-13

Updated: 2025-10-01

Comments: comments are welcome; v2: added more numerical experiments and application in quantum channel capacity

Journal ref: Communications Physics volume 9, Article number: 231 (2026)

DOI: 10.1038/s42005-026-02655-y

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Loss Function — 32× in this paper · explained in 2 episodes
• Superadditivity — 20× in this paper · explained in 2 episodes
• Quantum Circuits — 10× in this paper · explained in 2 episodes
• Trace — 9× in this paper · explained in 2 episodes
• Fidelity — 8× in this paper · explained in 2 episodes
• Verification — 6× in this paper · explained in 2 episodes
• Trace Distance — 5× in this paper · explained in 3 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Entanglement — 3× in this paper · explained in 3 episodes
• Query Complexity — 3× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adaptive Strategy — 1× in this paper · explained in 1 episode
• Computational overhead — 1× in this paper · explained in 2 episodes
• Kullback-Leibler (KL) Divergence — 1× in this paper · explained in 3 episodes
• Parameter Shift Rule — 1× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes

Sources

• Distributional property testing in a quantum world
• Rational approximations of operator monotone and operator convex functions
• Bounds on Petz-R'enyi Divergences and their Applications for Device-Independent Cryptography
• Quantum Generative Training Using R'enyi Divergences
• Smooth relaxation preserving Turing machines
• Semidefinite programming lower bounds on the squashed entanglement
• PennyLane: Automatic differentiation of hybrid quantum-classical computations
• Sample-Efficient Estimation of Nonlinear Quantum State Functions

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