Prepare-and-Send Universal Blind Quantum Computation: Difference between revisions

'''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 Offline communication, Classical Online communication, [[Supplementary Information#Measurement Based Quantum Computation|Measurement Based Quantum Computation (MBQC)]], [[Measurement-Only Universal Blind Quantum Computation|Measurement Only UBQC]], [[Pseudo-Secret Random Qubit Generator (PSQRG)]], [[Prepare-and-Send Verifiable Universal Blind Quantum Computation|Prepare and Send Verifiable Universal Blind Quantum Computation (VUBQC)]].

The following Universal Blind Quantum Computation (UBQC) protocol uses the unique feature of Measurement Based Quantum Computation [[Supplementary Information#Measurement Based Quantum Computation (MBQC)|(MBQC)]] that separates the classical and quantum parts of a computation. MBQC requires a set of initial entangled states, called graph states for computation. Here, we shall use a special family of graph states, [[Supplementary Information#Brickwork States|brickwork states]] which are universal (can implement any quantum operation) for X-Y measurements and do not leak any specific data about the computation during preparation. The protocol can be divided into three stages: preparation, computation and output correction.<br/>

Preparation stage includes a partially quantum Client preparing and sending quantum states to the Server who constructs the required brickwork state. Computation stage involves interaction. Output Correction involves retrieval of correct output from the results sent by the Server. We shall discuss below three protocols with different attributes but same functionality. All UBQC protocols discussed below require Client to prepare the required quantum states for computation and send those to the Server, hence the name ''Prepare and Send UBQC''. Protocol 1a deals with a partially quantum Client capable of preparing initial quantum states for the construction of brickwork state with classical input/output computation. Protocols 1b and 1c are extensions to accommodate quantum inputs and quantum outputs, respectively.

* '''Interaction and Measurement''' Client and Server interact to perform operations needed for computation. For a given computation and graph state, MBQC provides a measurement angle and some extra Pauli X, Z corrections, for each qubit. The correction sets (also called Dependency sets), unique for every graph state are based on previous measurement outcomes and can be obtained from '''[[Supplementary Information#Flow Construction-Determinism|flow construction]]'''. Also, as Client’s input state has random local phase, the same should be added to the measurement angle for computation along with Pauli Corrections to get the correct outcome. Now, in order to hide the output, Client randomly chooses to add a π rotation or not. The final measurement angle includes all the above parameters and hence, is sent to the Server. When Server returns the classical outcome, Client gets the correct outcome by taking into account the random π rotation and then uses it to calculate measurement angle for for the next qubit. The step is repeated until every qubit has been measured. Server returns measurement outcomes for the last column to Client. Client deciphers this outcome to get the final result. This ends the computation stage.

*(m,n) define dimensions of the brickwork state

*This protocol is secure/blind in every setting (universal)

*''Blindness'' The protocol is blind while leaking at most (m,n) to the Server

== Pseudocode==

[https://github.com/cgmcintyr/SimulaQron/tree/develop/examples/ubqc <u>click here for SimulaQron code</u>]