Pragmatic Obfuscation of Factoring in Hamiltonian Simulation and Ground State Estimation

The advent of large-scale quantum computers promises transformative advances across various fields including optimization, materials science, and cryptography. However, this also poses a threat to traditional cryptography, due to Shor’s algorithm, which efficiently factors large integers, and finds discrete logarithms. The existence of this algorithm undermines widely-used cryptographic protocols based on the hardness of these problems. Even with Post-Quantum Cryptography, attacks of the "save now, decrypt later" type can compromise the confidentiality of long-term secrets. Keeping this mind, we would like to develop quantum systems that are designed specifically for benign applications such as Hamiltonian Simulation or Ground State Estimation – which could be of importance to the industries such as the pharmaceutical industry. However, it cannot be taken for granted that even such a system is secure from malicious users attempting to run Shor’s Algorithm. In this note we propose the idea of using known circuit-to-Hamiltonian mappings to hide Shor’s algorithm in Hamiltonian simulation and Ground state estimation circuits. We provide the resource estimates for these mappings, and also propose some methods to potentially reduce these overhead costs.