Verifiable quantum advantage based on polynomials with planted structures

arXiv:2609.39918 · quant-ph, cs.CC, cs.CR, cs.DS · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.CC, cs.CR, cs.DS

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Verification — 29× in this paper · explained in 2 episodes
• Hypergraph — 22× in this paper · explained in 2 episodes
• Verifier — 16× in this paper · explained in 2 episodes
• Quantum Circuits — 10× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Anticoncentration — 3× in this paper · explained in 1 episode
• Entanglement — 3× in this paper · explained in 3 episodes
• Unbalanced Oil and Vinegar — 3× in this paper
• Benchmarking — 2× in this paper · explained in 3 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Analyzer — 1× in this paper · explained in 1 episode
• Annual ACM-SIAM Symposium on Discrete Algorithms — 1× in this paper
• Annual Symposium on Foundations of Computer Science — 1× in this paper
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes

Sources

• Complexity-Theoretic Foundations of Quantum Supremacy Experiments
• On the Classical Hardness of Spoofing Linear Cross-Entropy Benchmarking
• A polynomial-time classical algorithm for noisy random circuit sampling
• On verifiable quantum advantage with peaked circuit sampling
• From independent sets and vertex colorings to isotropic spaces and isotropic decompositions
• Spoofing Linear Cross-Entropy Benchmarking in Shallow Quantum Circuits
• A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device
• Quantum Amplitude Amplification and Estimation
• Characterizing Quantum Supremacy in Near-Term Devices
• Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
• Simpler Proofs of Quantumness
• Partition Rank and Algebraic Circuit Lower Bounds
• Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations
• Efficiently verifiable quantum advantage using error correction
• Solving Polynomial Equations Over Finite Fields
• How to factor 2048 bit RSA integers with less than a million noisy qubits
• Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage
• Planting Undetectable Backdoors in Machine Learning Models
• Computational advantage of quantum random sampling
• Bell sampling from quantum circuits

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• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
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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