Half-Blind Quantum Computation

• Half-blind quantum computation is a model that delegates tasks by selectively encrypting only the sensitive portions of a quantum circuit.
• It segments operations into protected and public regions, using MBQC and one-time pad encryption to maintain seamless quantum-classical interfaces.
• The approach reduces quantum resource overhead while ensuring security and correctness, integrating quantum homomorphic encryption for practical cloud deployments.

Half-blind quantum computation refers to delegated quantum computation protocols in which blindness (the server’s ignorance of certain computational details) is enforced selectively, rather than globally. This approach is motivated by the practical observation that, for most quantum algorithms, only specific subroutines or regions of the circuit contain sensitive information requiring cryptographic protection, while the remainder can be left exposed to optimize resource overhead. By introducing selective blindness—protecting only critical circuit components—half-blind quantum computation achieves a tradeoff between privacy and efficiency that is favorable for near-term quantum cloud services and large-scale delegated quantum algorithms.

1. Selective Blind Quantum Computation: Motivation and Concept

Traditional Blind Quantum Computation (BQC) protocols guarantee full blindness: all computational details, including inputs, operations, and outputs, are concealed from the remote server via universal schemes such as Universal Blind Quantum Computation (UBQC) based on measurement-based models and the quantum one-time-pad. However, this uniform application incurs substantial quantum resource and communication overhead, especially for circuits where the majority of operations are not security-critical.

Half-blind quantum computation—also termed "partial blind quantum computation" (Lee et al., 13 Mar 2025)—selectively applies BQC protocols only to those subcircuits that process sensitive data, while the remainder is executed without cryptographic protection. The critical insight is that in algorithms such as Grover's search, only the oracle requires privacy; the Grover diffusion operator is typically known and public. By isolating BQC to sensitive routines and efficiently “gluing” the protected and unprotected regions, this approach delivers substantial reductions in quantum overheads while retaining strong cryptographic guarantees where needed.

2. Protocol Structure and Mechanisms

The half-blind approach segments the full quantum circuit into protected (BQC-enabled) and non-protected sections. The key requirement is to maintain a seamless interface between the encrypted output states of BQC-protected subcircuits and the rest of the computation.

Quantum One-Time Pad Encryption

Each BQC subcircuit generates output states of the form: $|\psi'\rangle = X^{S_X} Z^{S_Z}|\psi\rangle$ where $S_X$ and $S_Z$ are classical bit-strings (one-time pad keys) tracking the cumulative Pauli frame correction induced during the MBQC protocol. These keys are maintained by the client. To connect such encrypted output qubits with the adjoining non-protected circuit regions, classical $X$ and $Z$ correction gates (parameterized by $S_X$ and $S_Z$) are applied, either physically or virtually.

Type 1 and Type 2 Connections

The framework defines two interfaces between BQC circuits and the unprotected circuit:

• Type 1 (Protected $\rightarrow$ Unprotected): The BQC segment outputs a quantum one-time padded state. Prior to its use in unprotected regions, the client (or a trusted agent) applies $X$ and $Z$ corrections based on $(S_X, S_Z)$, recovering the plaintext quantum register.
• Type 2 (Unprotected $\rightarrow$ Protected): When a one-time padded state—possibly emerging from a previous BQC-protected region—must serve as input to a subsequent BQC-protected circuit, the brickwork MBQC protocol [BFK09] is adjusted by adapting the measurement angle for the original input, specifically

$$\phi'_{0,y} = (-1)^{m \oplus a}\,\phi_{0,y} + \pi b$$

where $(a, b)$ are the classical one-time pad keys carried with the input and $m$ is a measurement outcome flag. This modification allows seamless chaining of BQC-protected components without revealing plaintext states to the server.

Integration with Quantum Homomorphic Encryption (QHE)

At the boundary between blind and non-blind components, the protocol borrows gate-by-gate correction techniques from quantum homomorphic encryption (QHE), leveraging the fact that the output of a BQC segment is Pauli-encrypted. The downstream circuit must be compatible with the propagation of these Pauli keys, which is always the case for Clifford gates or for protocols implementing careful Pauli frame updates and corrections for non-Clifford layers.

3. Security Analysis: Universality, Correctness, and Blindness

The selective BQC protocol (Lee et al., 13 Mar 2025) provides universality, correctness, and blindness in the following sense:

• Universality is preserved, as the framework is based on the MBQC brickwork model, which can simulate arbitrary quantum circuits. Selectivity in blindness is orthogonal to universality; only the coverage of privacy is reduced.
• Correctness holds because all byproduct Pauli corrections are fully tracked and compensated by the client’s classical key registers. When BQC outputs are used as inputs to further subcircuits (including other BQC-protected regions), the measurement angles and stabilizer frame updates are correctly computed as:

$$\phi'_{1,y} = (-1)^{s^X_{1,y} \oplus a_y}\, \phi_{1,y} + \pi\, (s^Z_{1,y} \oplus b_y)$$

where $s^X_{1,y}$ and $s^Z_{1,y}$ denote the previous MBQC correction chains, and $(a_y, b_y)$ are active QHE keys.

• Blindness is preserved in all BQC-protected components, meaning that the server remains ignorant of the client’s data, algorithm logic, and output within those sections. This is guaranteed via standard MBQC security arguments: quantum states are uniformly sampled on the Bloch sphere and measurement angles are one-time padded with client-side secrets, ensuring the server’s partial trace is maximally mixed and classical instructions do not correlate with private data [BFK09]. The blindness guarantee is formally inherited by the selective protocol.

4. Practical Examples and Resource Optimization

An explicit application is provided for Grover’s search algorithm. In this context, only the black-box oracle is encapsulated within a BQC-protected region, while the fixed structured diffuser is executed as a public circuit. Simulated implementations (via Qiskit) confirm that the selective protocol correctly manages encryption key updates, measurement bases, and quantum-classical boundaries, leading to correct logical outcomes with reduced overhead.

The mechanism allows recycling of physical qubits: after measurement and key update, spent qubits can be reinitialized and reused elsewhere in the protocol. This enables further compaction of resource usage—a critical feature for NISQ-era and early fault-tolerant quantum computers.

5. Comparison to Fully-Blind and Traditional Approaches

Compared with standard fully-blind protocols, half-blind quantum computation reduces the total number of qubits, gates, and measurements subject to cryptographic protection, significantly reducing communication overheads, classical bookkeeping, and quantum resource requirements. It also broadens the applicability to circuits with modular or hybrid-sensitive components.

Unlike naive “semi-blind” methods, where sensitive information might leak via interface states, the constructed protocol ensures that the transition across protected/unprotected boundaries is always mediated by explicit Pauli frame correction or the QHE/MBQC interface, so the server never observes plaintext sensitive data at any stage.

6. Future Directions and Theoretical Implications

Possible extensions of the half-blind framework include dynamic or adaptive BQC protection where sensitivity is determined according to real-time client logic, and optimizations for generic hybrid quantum-classical algorithms where privacy levels for subroutines might evolve. The interface between QHE and selective MBQC protocols may also lead to new cryptographic primitives or verification schemes allowing efficient auditing of delegated computations for correctness and privacy.

Potential open problems involve tighter lower bounds for quantum resource savings under selective blindness, quantitative analysis of privacy risk for various partitionings, and composability of the protocol in composable cryptography frameworks. Further, this direction paves the way for secure delegated algorithms in cloud quantum computing infrastructures where minimization of quantum client requirements and bandwidth is paramount.

7. Summary Table: Comparison of Selective and Global BQC

Attribute	Full BQC	Half-Blind (Selective) BQC (Lee et al., 13 Mar 2025)
Privacy coverage	Entire circuit	Sensitive subcircuits only
Resource overhead	High	Reduced
Universality	Yes	Yes
Practical implementation	Expensive	More efficient
Pauli frame management	Global	Localized per protected region
MBQC brickwork usage	Full circuit	Interface and protected segments
QHE integration	Optional	Essential for interface

This approach, introduced in (Lee et al., 13 Mar 2025), demonstrates that efficient secure delegated computation is possible by targeting cryptographic resources to regions of true sensitivity, integrating QHE and MBQC frameworks, and providing systematic interface protocols for maintaining correctness and security guarantees at all circuit boundaries.