Editing Prepare-and-Send Universal Blind Quantum Computation
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The [https://arxiv.org/abs/0807.4154 example protocol] achieves the functionality | The [https://arxiv.org/abs/0807.4154 example protocol] achieves the functionality assigning universal quantum computation to an untrusted device while maintaining privacy of the input, output and computation of the client. Following description deals with a method which involves quantum offline and classical online communication, called Blind Quantum Computation. | ||
</br> </br> | </br> </br> | ||
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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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*Quantum offline channel | *Quantum offline channel | ||
*Classical online channel | *Classical online channel | ||
*Server should | *Server should have a quantum device with storage technology for quantum states. | ||
[[File:Prepare-and-Send Universal Blind Quantum Computation.png|center|Prepare-and-Send Universal Blind Quantum Computation]] | |||
==Properties== | ==Properties== | ||
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*[[Secure Client- Server Delegated Quantum Computation#Properties|Blindness]] The protocol is blind while leaking at most (m,n) to the Server. | *[[Secure Client- Server Delegated Quantum Computation#Properties|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>] | [https://github.com/cgmcintyr/SimulaQron/tree/develop/examples/ubqc <u>click here for SimulaQron code</u>] | ||
==='''Stage 1:''' Preparation=== | ==='''Stage 1:''' Preparation=== | ||
*Input: Client: Dimensions of Brickwork State (m,n), Input States ( | *Input: Client: Dimensions of Brickwork State (m,n), Input States (ψ0,y) [Protocol 1b only], Auxilliary Input States (ψx,y) | ||
*Output: Server: Brickwork State <math>G_{\text{mxn}}</math> | *Output: Server: Brickwork State <math>G_{\text{mxn}}</math> | ||
**'''Client’s preparation''' | **'''Client’s preparation''' | ||
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###Client computes <math>\phi '_{x,y}</math> where <math>s^X_{0,y}=s^Z_{0,y}=0</math> <br/> | ###Client computes <math>\phi '_{x,y}</math> where <math>s^X_{0,y}=s^Z_{0,y}=0</math> <br/> | ||
###Client chooses <math>r_{x,y} \epsilon_R {0,1}</math> and computes <math>\delta_{x,y}=\phi '_{x,y}+\theta_{x,y}+\pi r_{x,y}</math>. | ###Client chooses <math>r_{x,y} \epsilon_R {0,1}</math> and computes <math>\delta_{x,y}=\phi '_{x,y}+\theta_{x,y}+\pi r_{x,y}</math>. | ||
###Client transmits <math>\delta_{x,y}</math> to Server. Server measures in the basis | ###Client transmits <math>\delta_{x,y}</math> to Server. Server measures in the basis \{|+δx,yi,|−δx,yi\}. | ||
###Server transmits the result | ###Server transmits the result sx,y ∈ {0,1} to Client. | ||
###If | ###If rx,y = 1 above, Client flips sx,y; otherwise she does nothing. | ||
**'''Output Correction [only for quantum outputs]''' | **'''Output Correction [only for quantum outputs]''' | ||
#Server sends to Client all qubits in the last layer. | #Server sends to Client all qubits in the last layer. | ||
#Client performs the final Pauli corrections . | #Client performs the final Pauli corrections . | ||
<div style='text-align: right;'>''*contributed by Shraddha Singh''</div> | <div style='text-align: right;'>''*contributed by Shraddha Singh''</div> |