Quantum computing promises immense power, but outsourcing sensitive quantum computations to cloud-based Quantum Processing Units (QPUs) raises critical security concerns: How can you run a program on someone else's quantum computer without revealing the program itself or the data it processes? A groundbreaking new paper by Ben Goertzel introduces a potential solution: an efficient, quantum-safe homomorphic encryption scheme specifically designed for quantum computer programs.

Published on arXiv (2504.21235), the research tackles the dual challenge of securing quantum computations against future quantum adversaries and enabling meaningful computation on encrypted data and programs – a feat known as homomorphic encryption (HE). While classical HE exists, extending it securely and efficiently to the quantum realm is notoriously difficult.

The Quantum-Safe Core: Lattices and Functors

The core innovation replaces vulnerable composite-order group cryptography, susceptible to Shor's algorithm, with Module Learning-With-Errors (MLWE) lattices – a leading candidate for post-quantum cryptography. To handle the unique structure of quantum states and operations, the scheme employs Bounded Natural Super Functors (BNSFs). These mathematical constructs generalize polynomial functors used in classical HE:

  • Secret Depolarizing BNSF Mask: Hides the complex amplitudes of quantum states.
  • MLWE Ciphertext Pairs: Store the encrypted quantum state information.

The formal security proof utilizes a qIND-CPA game, specifically designed to allow coherent quantum access to the encryption oracle, and reduces security to the hardness of the decisional MLWE problem – a well-studied assumption in post-quantum cryptography.

Bridging Theory and Practice: Solving Real-World Hurdles

Beyond the core encryption, the paper addresses critical practical issues often omitted in theoretical proposals:

  1. Handling Measurements: A Typed QC-Bridge allows classical bits resulting from measurements to remain encrypted but still usable as controls in subsequent quantum operations. It employs weak-measurement semantics, crucial for expectation-value calculations common in algorithms like VQE.
  2. Circuit Privacy: Encrypted Pauli Twirls are applied to the encrypted program, preventing the QPU owner from learning information about the underlying quantum circuit.
  3. Secure Knowledge Integration: If a program requires a fixed knowledge base (e.g., axioms for reasoning), these are encrypted as MLWE "capsules". The evaluator (QPU) can utilize them computationally but cannot decrypt and read their contents.
  4. Orchestration & Audit: A rho-calculus driver schedules encrypted tasks across potentially multiple QPUs. Crucially, it records an auditable execution trace on a ledger inspired by RChain, providing transparency and verifiability without compromising privacy.

Feasibility for Near-Term Quantum Clouds

The performance analysis is particularly striking, suggesting this isn't just theoretical:

  • A 100-qubit quantum proof (like a teleportation-based verification) with depth 1000 is estimated to run in about 10 milliseconds.
  • Public keys are remarkably compact (a mere 32-byte seed).
  • Even keys providing CCA-level security (resisting chosen-ciphertext attacks) stay under 300 kB.
  • The authors argue that a photonic Dirac-3 prototype capable of executing homomorphic teleportation combined with knowledge-base-relative amplitude checks is feasible with current hardware.

Implications: Unlocking Secure Quantum Outsourcing

This work represents a significant leap towards practical secure quantum cloud computing. It provides a potential blueprint for:

  • Protecting Proprietary Quantum Algorithms: Companies could run sensitive IP on third-party QPUs without fear of theft.
  • Securing Quantum Data Processing: Sensitive data (e.g., financial, pharmaceutical) processed on quantum hardware could remain confidential.
  • Enabling Verifiable Quantum Services: The ledger-based audit trail allows clients to verify correct execution without learning internal details.

"These results indicate that fully homomorphic, knowledge-base-aware quantum reasoning is compatible with near-term quantum clouds and standard post-quantum security assumptions," Goertzel concludes. If the performance claims hold under real-world implementation and scrutiny, this scheme could become a foundational technology for the emerging quantum computing ecosystem, providing the essential 'Fort Knox' security layer quantum applications desperately need.

Source: Goertzel, Ben. "Efficient Quantum-Safe Homomorphic Encryption for Quantum Computer Programs." arXiv preprint arXiv:2504.21235 (2025).