# Classical Verification of Quantum Computations

@article{Mahadev2018ClassicalVO, title={Classical Verification of Quantum Computations}, author={Urmila Mahadev}, journal={2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)}, year={2018}, pages={259-267} }

We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum prover as a trusted measurement device. The protocol forces the prover to behave as follows: the prover must construct an n qubit state of his choice, measure each qubit in the Hadamard or standard basis as directed by the verifier, and report the measurementâ€¦Â

## 136 Citations

On Information-Theoretic Classical Verification of Quantum Computers

- Computer Science, Mathematics
- 2021

A family of protocols which seem natural for verifying quantum computations and generalizes such known protocols, namely those of [AAV13,AG17], showing that any protocol from this family is bound to require an extremely powerful prover, much like the classical protocols of [LFKN92] and [Sha92].

A simple protocol for fault tolerant verification of quantum computation

- Computer ScienceQuantum Science and Technology
- 2018

This paper presents a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions, based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input.

Robust verification of quantum computation

- Computer Science
- 2018

This work considers a single-prover verification protocol developed by Fitzsimons and Kashefi and shows that this protocol is indeed robust with respect to deviations on the quantum state prepared by the verifier, and proves a rigidity result for a type of quantum correlations known as steering correlations.

Verification of independent quantum devices

- Physics, Computer Science
- 2019

This work presents a scalable verification technique that exploits the principles of measurement-based quantum computing to link quantum circuits of different input size, depth, and structure, and enables consistency checks of quantum computations within a device, as well as between independent devices.

Cross-Verification of Independent Quantum Devices

- Physics, Computer SciencePhysical Review X
- 2021

This work presents a verification technique that exploits the principles of measurement-based quantum computation to link quantum circuits of different input size, depth, and structure, and enables consistency checks of quantum computations within a device, as well as between independent devices.

A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device

- Computer Science, MathematicsJ. ACM
- 2021

The authors' solution relies on the existence of a new cryptographic primitive for constraining the power of an untrusted quantum device: post-quantum secure trapdoor claw-free functions that must satisfy an adaptive hardcore bit property.

A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device

- Computer Science, Mathematics2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018

The randomness protocol can be used as the basis for an efficiently verifiable "quantum supremacy" proposal, thus answering an outstanding challenge in the field.

On the Possibility of Classical Client Blind Quantum Computing

- Computer Science, MathematicsCryptogr.
- 2021

Using the functionality of delegated pseudo-secret random qubit generator (PSRQG), a classical client can instruct the preparation of a sequence of random qubits at some distant party, one could achieve a purely classical-client computational secure verifiable delegated universal quantum computing (also referred to as verifiable blind quantum computation).

Computationally-Secure and Composable Remote State Preparation

- Mathematics, Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

The implementation of "random remote state preparation with verification", a functionality first defined in (Dunjko and Kashefi 2014), is expected to be useful for removing the need for quantum communication in such protocols while keeping functionality.

Rational proofs for quantum computing

- Computer ScienceQuantum Inf. Comput.
- 2020

This paper shows that the client can be completely classical if the server is rational (i.e., economically motivated), following the ``rational proofs" framework of Azar and Micali.

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