Exact Non-Identity Check and Gate-Teleportation-Based Indistinguishability Obfuscation are NP-hard for Low-T-Depth Quantum Circuits

arXiv:2511.17856 · quant-ph · Submitted 2025-11-22 · Read on arXiv

quant-ph

Submitted: 2025-11-22

Updated: 2026-09-24

Terminology

• Quantum Circuits — 15× in this paper · explained in 2 episodes
• Non-Identity Check — 9× in this paper
• Exact Non-Identity Check — 5× in this paper
• BQP — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Decode — 1× in this paper · explained in 2 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• On Quantum Obfuscation
• Constructions for Quantum Indistinguishability Obfuscation
• Optimal T depth quantum circuits for implementing arbitrary Boolean functions
• Non-Identity Check Remains QMA-Complete for Short Circuits
• Quantum boolean functions
• Quantum circuit for multi-qubit Toffoli gate with optimal resource
• Hardness of approximating the weight enumerator of a binary linear code
• Quantum Indistinguishable Obfuscation via Quantum Circuit Equivalence

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