Path-Finding, Orbit State Preparation, and the Security of Invariant Quantum Money

arXiv:2609.39774 · cs.CR · Submitted 2026-09-30 · Read on arXiv

cs.CR

Submitted: 2026-09-30

Updated: 2026-10-02

Terminology

• Verification — 37× in this paper · explained in 2 episodes
• Verifier — 13× in this paper · explained in 2 episodes
• Trace — 11× in this paper · explained in 2 episodes
• Spectral Gap — 9× in this paper · explained in 5 episodes
• Trace Distance — 6× in this paper · explained in 3 episodes
• BQP — 3× in this paper · explained in 2 episodes
• Approximate Counting — 2× in this paper · explained in 1 episode
• Abstraction — 1× in this paper · explained in 1 episode
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Computational Complexity Conference — 1× in this paper
• Entanglement — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Fingerprinting — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes

Sources

• Quantum money from knots
• Breaking and making quantum money: toward a new quantum cryptographic protocol
• Another Round of Breaking and Making Quantum Money: How to Not Build It from Lattices, and More
• Quantum Money from Modular Forms
• A General Quantum Duality for Representations of Groups with Applications to Quantum Money, Lightning, and Fire
• Public-Key Quantum Fire and Key-Fire From Classical Oracles
• Component mixers and a hardness result for counterfeiting quantum money
• Creating superpositions that correspond to efficiently integrable probability distributions
• The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes

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