Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions

Classical Fully Homomorphic Encryption for Quantum Circuits (edit)

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 *Output:  Updated encryption of pad key <math>\tilde{z},\tilde{x}</math> (and Quantum One time Padded Output State <math>X^{\tilde {x}}Z^{\tilde{z}}C|\psi\rangle</math> in case of quantum output, where C is the quantum circuit)
 **'''Circuit Evaluation (FHE.Eval())'''
-#Server creates a quantum superposition state for the encrypted classical message.</br> <math>Z^zX^x|\psi\rangle</math> represents quantum superposition state of <math>l</math>,</br> <math>|\psi\rangle=\sigma_{a,b\epsilon\{0,1\}}|a,b\rangle</math> represents the two qubits superposition state for classical message m,</br> <math>Z^zX^x</math> represents quantum one time pad. </br>
+#Server creates a quantum superposition state for the encrypted classical message.</br> <math>Z^zX^x|\psi\rangle</math> represents quantum superposition state of <math>l</math>,</br> <math>|\psi\rangle=\sum_{a,b\epsilon\{0,1\}}|a,b\rangle</math> represents the two qubits superposition state for classical message m,</br> <math>Z^zX^x</math> represents quantum one time pad. </br>
 # For all i, Server applies gate <math>c_i</math> on qubit l and the <math>l_{th}</math> bits of pad key <math>(\tilde {x}^{[l]},\tilde{z}^{[l]})</math> are updated to <math>(\tilde {x}'^{[l]},\tilde{z}'^{[l]})</math> as follows.
 ##	 If <math>c_i=\{P,H,CNOT\}</math>, a Clifford gate then <div class="floatright">//(<math>c_iZ^{z^{[l]}}X^{x^{[l]}}|\psi\rangle=Z^{z'^{[l]}}X^{x'^{[l]}}c_i|\psi\rangle</math>)</div>