Editing Classical Fully Homomorphic Encryption for Quantum Circuits (section)

== Notation ==
*<math>m</math>: classical data of client's required quantum input states
*<math>\lambda</math>: security parameter
* <math>k</math>: security parameter
* <math>\tilde{x}</math>: encrypted pad key
*<math>s</math>: concatenated pad key elements
*<math>c=HE.Enc_{pk}(s)</math> Encryption of s using public key <math>pk</math> via classical HE encryption step.
*<math>\hat{c}</math>: converted c using classical HE in order to use it with <math>AltHE</math>
* <math>\tilde{x}^{[l]}</math>: <math>l^{th}</math> bit of encrypted pad key
* <math>L_c</math>: depth of a layer of circuit where each layer contains Clifford gates and Toffoli gates
* <math>L</math>: depth of the circuit (no. of layers in the circuit)
* <math>\{pk_i, sk_i, evk_i, t_{sk_i}\}</math>: <math>i_{th}</math> homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, trapdoor information required for randomness recovery from secret texts.
* <math>y</math>: measurement outcome of third register
* <math>(\mu_0,r_0) (\mu_1,r_1)</math>: random claw for pair, for given y
* <math>d</math>: measurement outcome of the second register