Blind Quantum Computing

Blind Quantum Computing

Blind quantum computing (BQC) is a protocol where a client with limited quantum resources can delegate a quantum computation to a powerful server, without the server learning the computation or its result. This is a capability with no classical analog: in classical computing, any server that executes your computation necessarily sees your data.

The Impossibility in Classical Computing

In classical computing, a server running a computation must have access to the program instructions and data. Homomorphic encryption allows computation on encrypted data, but the server must still run the program in plaintext. There is no way for a classical server to execute an unknown computation on unknown data and return an encrypted result: the server must know the function it is computing.

Quantum mechanics provides an escape: through a quantum channel, the client can encode both the data and the computation into quantum states that the server manipulates without decoding.

Measurement-Based Quantum Computing in Brief

BQC protocols do not use the circuit model directly. They rely on measurement-based quantum computing (MBQC), a different but equally powerful way to run quantum algorithms. Since MBQC has not appeared earlier in this curriculum, here is the essential picture.

Cluster states. A cluster state is a grid of qubits prepared in a fixed entangled pattern: every qubit starts in $|+⟩=(|0⟩+|1⟩)/\sqrt{2}$, and a CZ (controlled-Z) gate is applied between every pair of neighboring qubits in the grid. The result is a highly entangled blank canvas. It contains no information about any particular algorithm, and the same cluster state can serve as the substrate for any computation.

Computing by measuring. In the circuit model, you drive a computation by applying gates. In MBQC, the cluster state is prepared first, and the computation then proceeds by measuring qubits one at a time, each in a chosen basis. The typical choice is a basis in the X-Y plane at some angle $\theta$, namely $\{|{+}_{\theta }⟩,|{-}_{\theta }⟩\}$ with $|{\pm }_{\theta }⟩=(|0⟩\pm e^{i\theta }|1⟩)/\sqrt{2}$. The measurement angles play the role that gates play in a circuit: choosing a sequence of angles across the grid carves a specific algorithm out of the generic entanglement.