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

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* '''Server’s preparation''' Server prepares brickwork state of m rows and n columns. It entangles all the received qubits as per Client’s instructions. Thus, ends preparation stage.
* '''Server’s preparation''' Server prepares brickwork state of m rows and n columns. It entangles all the received qubits as per Client’s instructions. Thus, ends preparation stage.
* '''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.
* '''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.
==Notations==
**<math>\phi</math>, measurement angle for given MBQC pattern to implement the required computation
**<math>\phi_0</math>, measurement angle including Pauli X,Z corrections
**<math>s_X,s_Z</math> Dependency sets for Pauli X and Pauli Z corrections, respectively (obtained from flow construction).
**<math>\theta</math>, randomly chosen angles by Client in order to hide classical input
** r <math>\epsilon_R\{0,1\}</math>, randomly chosen parameter for <math>\pi</math> rotation in order to hide classical output
**<math>\delta</math>, final measurement angle


==Requirements==
==Requirements==
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