Efficient Quantum-Safe Homomorphic Encryption for Quantum Computer Programs
Ben Goertzel
TL;DR
The paper proposes a quantum-safe homomorphic encryption framework (MLWE+BNSF) for outsourcing quantum computations while preserving data and circuit confidentiality. It generalizes classical categorical HE to quantum programs via bounded natural super functors, introducing a depolarizing mask and a QC-bridge to securely couple quantum and classical data flows. A formal security argument (qIND-CPA/CCA) is provided alongside practical considerations: noise budgeting, circuit privacy, KB-based reasoning with encrypted axiom capsules, and distributed orchestration using the ρ-calculus. The authors present a concrete teleportation toy-example, a prototype Dirac3 photonic QPU path, and a roadmap toward private QML, KB-relative inference, and multi-party evolutionary program synthesis, arguing the approach is feasible on near-term hardware with standard post-quantum assumptions. Overall, this work lays a detailed foundation for scalable, private quantum computation in cloud environments, with a concrete path to near-term demonstrations and long-term scalable deployments.
Abstract
We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order groups with Module Learning-With-Errors (MLWE) lattices and by generalizing polynomial functors to bounded natural super functors (BNSFs). A secret depolarizing BNSF mask hides amplitudes, while each quantum state is stored as an MLWE ciphertext pair. We formalize security with the qIND-CPA game that allows coherent access to the encryption oracle and give a four-hybrid reduction to decisional MLWE. The design also covers practical issues usually left open. A typed QC-bridge keeps classical bits produced by measurements encrypted yet still usable as controls, with weak-measurement semantics for expectation-value workloads. Encrypted Pauli twirls add circuit privacy. If a fixed knowledge base is needed, its axioms are shipped as MLWE "capsules"; the evaluator can use them but cannot read them. A rho-calculus driver schedules encrypted tasks across several QPUs and records an auditable trace on an RChain-style ledger. Performance analysis shows that the extra lattice arithmetic fits inside today's QPU idle windows: a 100-qubit, depth-10^3 teleportation-based proof runs in about 10 ms, the public key (seed only) is 32 bytes, and even a CCA-level key stays below 300 kB. A photonic Dirac-3 prototype that executes homomorphic teleportation plus knowledge-base-relative amplitude checks appears feasible with current hardware. These results indicate that fully homomorphic, knowledge-base-aware quantum reasoning is compatible with near-term quantum clouds and standard post-quantum security assumptions.