Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions

####Server generates following superposition sampled over random distribution D\sqrt{D(\mu,r)}|\mu,r\rangle</math>

#### Servers entangles above superposition and <math>\psi</math> with a third register for function output as follows:</br><math>\sum_{a,b,\mu\in\{0,1\},r}\alpha_{ab}\sqrt{D(\mu,r)}|a,b\rangle|\mu,r\rangle|f_a(r)\rangle</math>, such that</br>  <math>f_0=\mathrm{AltHE.Enc}_{pk}()</math>;</br><math>f_1(\mu_1,r_1)=f_0 (\mu_0,r_0)\oplus_H \hat{c}=\mathrm{AltHE.Enc}_{pk}(\mu_0,r_0)\oplus_H <math>\mathrm{AltHE.Enc}_{pk}(s)</math>  

####Server performs Hadamard on second register and measures it to get a string d such that first register of input quantum state is reduced to the following ideal state:</br><math>(Z^{d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1))}\otimes X^{\mu_0})\textrm{CNOT}_{1,2}^s|\psi\rangle</math> </br>where <math>(\mu_0,r_0)=(\mu_1,r_1)\oplus_H s</math> as <math>\oplus_H</math> is the homomorphic XOR operation.

####The server uses <math>pk_{i+1}</math> to compute HE.Enc<math>_{pk_{i+1}}(c_{x,z,pk_i})</math> and <math>\mathrm{HE.Enc}_{pk_{i+1}}(\hat{c},y,d)</math>.