Measurement-Only Universal Blind Quantum Computation: Difference between revisions

Measurement-Only Universal Blind Quantum Computation (edit)

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-The [https://journals.aps.org/pra/abstract/10.1103/PhysRevA.87.050301 example protocol] achieves the functionality of [[Secure Client- Server Delegated Computation|Delegated Computation]] which is the task of assigning quantum computation to an untrusted device while maintaining privacy of the computation. It can be done via [[Secure Client- Server Delegated Computation#Protocols|classical online/offline]] and [[Secure Client- Server Delegated Computation|quantum online/offline]] communication. Following description deals with a method which involves quantum online and classical online communication, called Blind Quantum Computation. It comes with the properties of correctness i.e. if both parties follow the protocol the final outcome is correct, blindness i.e. the Client to have Server carry out a quantum computation for her (Client) such that the Client’s inputs, outputs and circuit used for computation remain perfectly private from the Server and Universality i.e. the following protocol can implement any quantum computation.</br></br>
+The [https://journals.aps.org/pra/abstract/10.1103/PhysRevA.87.050301 example protocol] achieves the functionality of [[Secure Client-Server Delegated Computation|Delegated Computation]] which is the task of assigning quantum computation to an untrusted device while maintaining the privacy of the computation. It can be done via [[Secure Client-Server Delegated Computation#Protocols|classical online/offline]] and [[Secure Client-Server Delegated Computation|quantum online/offline]] communication. Following description deals with a method which involves quantum online and classical online communication, called Blind Quantum Computation. It comes with the properties of correctness i.e. if both parties follow the protocol the final outcome is correct, blindness i.e. the Client to have Server carry out a quantum computation for her (Client) such that the Client’s inputs, outputs, and circuit used for computation remain perfectly private from the Server and Universality i.e. the following protocol can implement any quantum computation.</br></br>
 '''Tags:''' [[Category: Two Party Protocols]] [[:Category: Two Party Protocols|Two Party]], [[Category: Universal Task]][[:Category: Universal Task|Universal Task]], [[Category: Quantum Functionality]] [[:Category: Quantum Functionality|Quantum Functionality]], Quantum Online communication, Classical Online communication, [[Supplementary Information#Measurement Based Quantum Computation|Measurement Based Quantum Computation (MBQC)]],
 [[Prepare and Send-Universal Blind Quantum Computation|Prepare and Send-UBQC]], [[Measurement-Only Verifiable Universal Blind Quantum Computation|Measurement Only Verifiable UBQC]], [[Quantum Key Distribution|QKD]], [[Quantum Teleportation]].
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 ==Pseudocode==
-*Unless given specific mention in [.], following steps apply to both protcols
+*Unless given specific mention in [.], following steps apply to both protocols
-*'''Input:''' Server: Dimeonsions of Resource State (m,n,o)
+*'''Input:''' Server: Dimensions of Resource State (m,n,o)
 *'''Output:''' Client: Final Outcome
 #Server’s preparation
@@ Line 42: / Line 42: @@
 #Interaction and Computation For i= 1 →m, j= 1 →n, k= 1 →o
 ##[Protocol 1a]
-###Server directly sends the qubit |ψi,j,ki to Client
+###Server directly sends the qubit <math>|\psi\rangle_{i,j,k}</math> to Client
 ###Client measures his qubit in the measurement basis according to the measurement pattern
 ##[Protocol 1b]
 ###Server creates Bell pair
-###Server sends one half (|Φ2i) of the Bell pair to Client
+###Server sends one half (<math>|\phi_2\rangle</math>) of the Bell pair to Client
 ###Client tells her response to Server if she received the sent qubit or not iv. If she didn’t, Server repeats the previous two processes, otherwise
-###Client measures her share of entangled qubit (|Φ2i) in measurement basis {|0i ± eθ |1i} determined by measurement pattern.   in case of Clifford gates while {π/4} in case of non-Clifford gates.
+###Client measures her share of entangled qubit (<math>|\phi_2\rangle</math>) in measurement basis {<math>|0\rangle</math> &plusmn; <math>e^{i\theta}|1\rangle</math>} determined by measurement pattern.   in case of Clifford gates while {<math>\pi/4</math>} in case of non-Clifford gates.
 ###Server uses gate teleportation to apply this unknown gate on the qubit of resource state as follows
-####He entangles his share of Bell pair with the qubit of the resource state |ψi,j,ki by performing CZ
+####He entangles his share of Bell pair with the qubit of the resource state <math>|\psi\rangle_{i,j,k}</math> by performing CZ
-####He measures the qubit in the register, |ψi,j,ki in X basis ({|+i,|−i}) and communicates the outcome to the Client. This applies the required measurement on the qubit of the resource state with some correction depending on the outcome
+####He measures the qubit in the register, <math>|\psi\rangle_{i,j,k}</math> in X basis ({<math>|+\rangle,|-\rangle</math>}) and communicates the outcome to the Client. This applies the required measurement on the qubit of the resource state with some correction depending on the outcome
 ####Client records Server’s outcome and uses it when computing the final result or measurement angles for further qubits
 *Interaction and Computation steps are repeated until all the qubits of resource state are measured.
 <div style='text-align: right;'>''*contributed by Shraddha Singh''</div>