Editing Measurement-Only Verifiable Universal Blind Quantum Computation
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This protocol allows the client to verify the correctness of the blind delegated quantum computing with high probability. Here, the server prepares and sends a universal resource quantum state to the client, and the client only performs measurements to carry out the quantum computation. Using this method, it is easy to verify with high probability whether the server is honest. The computation here remains perfectly private from the server and this protocol can implement any quantum computation. | |||
</br> | </br> | ||
'''Tags''' [[ | '''Tags''' [[Two Party Protocols|Two Party]], [[Universal Task|Universal Task]], [[Quantum Functionality|Quantum Functionality]], [[Secure Delegated Quantum Computation|Secure Delegated Quantum Computation]], Quantum Online communication, Classical Online communication, [[Supplementary Information#Measurement Based Quantum Computation|Measurement Based Quantum Computation (MBQC)]], [[Verifiable Secure Delegated Quantum Computation|Verification of Quantum computers]]. | ||
==Assumptions== | ==Assumptions== | ||
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==Outline== | ==Outline== | ||
This protocol is based on MBQC and is mainly derived from Measurement- | This protocol is based on MBQC and is mainly derived from Measurement Only-Universal Blind Quantum Computation. In this protocol, the server prepares and sends the resource state to the client, whereas the client performs measurements on the received states. The server is considered to be a general adversary and any computational deviations can be detected in this method by the client. | ||
<br></br> | <br></br> | ||
By performing measurements, the client creates the final state to be a mixture of resource state and trap qubits, in a random distribution. If the measurement of all the trap qubits | By performing measurements, the client creates the final state to be a mixture of resource state and trap qubits, in a random distribution. If the measurement of all the trap qubits match the expected outcome, then it shows with high probability that the server is honest and has not deviated from the protocol. | ||
<br></br> | <br></br> | ||
This protocol is dived into two stages: Servers' preparation and Client's measurement. | This protocol is dived into two stages: Servers' preparation and Client's measurement. | ||
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==Notation== | ==Notation== | ||
* <math>m\times n</math>: Resource state size | * <math>m\times n</math>: Resource state size | ||
* <math>|\psi\rangle_P</math>: <math>P(|R\rangle\otimes |+\rangle^{\otimes \frac{N}{3}} \otimes |0\rangle^{\otimes \frac{N}{3}})</math>, this is the | * <math>|\psi\rangle_P</math>: <math>P(|R\rangle\otimes |+\rangle^{\otimes \frac{N}{3}} \otimes |0\rangle^{\otimes \frac{N}{3}})</math>, this is the $n$-qubit state left with the server which contains the trap qubits (<math>|0\rangle</math>, <math>|+\rangle</math>) and resource state. | ||
* <math>|R\rangle</math>: <math>\frac{n}{3}</math>-qubit resource state | * <math>|R\rangle</math>: <math>\frac{n}{3}</math>-qubit resource state | ||
* <math>P</math>: <math>n</math>-qubit permutation, which keeps the order of qubits in <math>|R\rangle</math> | * <math>P</math>: <math>n</math>-qubit permutation, which keeps the order of qubits in <math>|R\rangle</math> | ||
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* <math>\sigma_q</math>: <math>\bigotimes^n_{j=1}X^{x_j}_jZ^{z_j}_j</math> | * <math>\sigma_q</math>: <math>\bigotimes^n_{j=1}X^{x_j}_jZ^{z_j}_j</math> | ||
==Requirements== | ==Hardware Requirements== | ||
* Quantum computation resources for the server. | * Quantum computation resources for the server. | ||
* A quantum channel from the server to the client to transfer the quantum states. | * A quantum channel from the server to the client to transfer the quantum states. | ||
* Measurement device for the client. | * Measurement device for the client. | ||
* No channel is required from client to the server. | * No channel is required from client to the server. | ||
==Properties== | ==Properties== | ||
* This protocol detects a cheating server with high probability. | * This protocol is detects a cheating server with high probability. | ||
* Universality: This protocol is universal in nature. The resource state used is universal and thus can implement any quantum computation. | * Universality: This protocol is universal in nature. The resource state used is universal and thus can implement any quantum computation. | ||
* Correctness: The correctness of the protocol is implied | * Correctness: The correctness of the protocol is implied form the measurement based quantum computing used. | ||
* Blindness: As there exists no quantum channel from the client to the server, the | * Blindness: As there exists no quantum channel from the client to the server, the no-signalling theorem ensures that no information about the states is sent to the server using just the measurements. | ||
* The security of this protocol is device independent | * The security of this protocol is device independent. | ||
== | ==Pseudocode== | ||
'''Stage 1''': Server's preparation </br> | '''Stage 1''': Server's preparation </br> | ||
'''Input''': Dimensions of the resource state. | '''Input''': Dimensions of the resource state. | ||
* Server creates the resource state <math>G_{m\times n}</math> and sends each qubit to Client | |||
* Server creates <math>G_{m\times n}</math> and sends each qubit to Client | |||
</br> | </br> | ||
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* For <math>i = 1, 2, ... m-1</math>: | * For <math>i = 1, 2, ... m-1</math>: | ||
** For <math>j = 1, 2, ...n</math>: | ** For <math>j = 1, 2, ...n</math>: | ||
*** Client receives resource state qubit <math>|\psi\rangle_{i,j,0}</math> from server. | *** Client receives the resource state qubit <math>|\psi\rangle_{i,j,0}</math> from the server. | ||
*** | *** The client performs the measurement on the qubit according to the measurement pattern. | ||
** Through the measurements, Client creates the state <math>\sigma_q|\psi\rangle_P</math> in the server's possession, where | ** Through the measurements, Client creates the state <math>\sigma_q|\psi\rangle_P</math> in the server's possession, where | ||
<div style="text-align: center;"><math> |\psi\rangle_P = P(|R\rangle\otimes |+\rangle^{\otimes \frac{N}{3}} \otimes |0\rangle^{\otimes \frac{N}{3}}) </math></div> | <div style="text-align: center;"><math> |\psi\rangle_P = P(|R\rangle\otimes |+\rangle^{\otimes \frac{N}{3}} \otimes |0\rangle^{\otimes \frac{N}{3}}) </math></div> | ||
* For <math>i = 1, 2, ...n</math>: (for every qubit of <math>\sigma_q|\psi\rangle_P</math>) | * For <math>i = 1, 2, ...n</math>: (for every qubit of <math>\sigma_q|\psi\rangle_P</math>) | ||
** Client receives <math>\sigma_q{|\psi\rangle_P}_i</math> from the server. | ** Client receives <math>\sigma_q{|\psi\rangle_P}_i</math> $\sigma_q\ket{\psi_P}_i$ from the server. | ||
** Measurement is done after applying the correction <math>\sigma^{\dagger}_q</math> on the qubit received. | ** Measurement is done after applying the correction <math>\sigma^{\dagger}_q</math> on the qubit received. | ||
** If result obtained is <math>|1\rangle</math> (for trap qubit <math>|0\rangle</math>) or <math>|-\rangle</math>(for trap qubit <math>|+\rangle</math>): | ** If result obtained is <math>|1\rangle</math> (for trap qubit <math>|0\rangle</math>) or <math>|-\rangle</math>(for trap qubit <math>|+\rangle</math>): | ||