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Quantum Engineering

Parallel self‐testing for device‐independent verifiable blind quantum computation

Qingshan Xu, Xiaoqing Tan, Rui Huang, Xiaodan Zeng

Published Jul 24, 2020• 11 citations
Publisher

Abstract

With advances in experimental quantum computing, the requirement for verifying the correctness of quantum computation is urgent. The recent protocols of device-independent verifiable blind quantum computation provide a fruitful solution. However, all existing approaches have relatively high overhead. In this paper, we present a parallel self-testing technology to extract the presence of tensor products of Pauli observables on maximally entangled state. We then utilize our parallel self-testing to propose a device-independent verification protocol. Finally, compared to other existing protocols, our scheme has a lower overhead, which costs Bell pairs, where n is the size of original computation.

DOI
10.1002/que2.51

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With advances in experimental quantum computing, the requirement for verifying the correctness of quantum computation is urgent. The recent protocols of device-independent verifiable blind quantum computation provide a fruitful solution. However, all existing approaches have relatively high overhead. In this paper, we present a parallel self-testing technology to extract the presence of tensor products of Pauli observables on maximally entangled state. We then utilize our parallel self-testing to propose a device-independent verification protocol. Finally, compared to other existing protocols, our scheme has a lower overhead, which costs Bell pairs, where n is the size of original computation.
As progress on experimental quantum processors continues to advance, the problem of verifying the correct operation of such devices is becoming a pressing concern. The recent discovery of protocols for verifying computation performed by entangled but non-communicating quantum processors holds the promise of certifying the correctness of arbitrary quantum computations in a fully device-independent manner. Unfortunately, all known schemes have prohibitive overhead, with resources scaling as extremely high degree polynomials in the number of gates constituting the computation. Here we present a novel approach based on a combination of verified blind quantum computation and Bell state self-testing. This approach has dramatically reduced overhead, with resources scaling as only O(m4ln⁡m)O(m^4\ln m)O(m4lnm) in the number of gates.
We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension 2n{2}^{n}2n for $n\ensuremath{\in}\mathbb{N}$. This provides self-tests of sets of informationally complete measurements in arbitrarily high dimension. We then show that this can be used for the device-independent certification of the entanglement of all bipartite entangled states by exploiting a connection to measurement-device-independent entanglement witnesses and quantum networks. This work extends a more compact parallel work on the same subject [Bowles et al., Phys. Rev. Lett. 121, 180503 (2018)] and provides all the required technical proofs.
We introduce a device-independent two-prover scheme in which a classical verifier can use a simple untrusted quantum measurement device (the client device) to securely delegate a quantum computation to an untrusted quantum server. To do this, we construct a parallel self-testing protocol to perform device-independent remote state preparation of n qubits and compose this with the unconditionally secure universal verifiable blind quantum computation (VBQC) scheme of Fitzsimons and Kashefi []. Our self-test achieves a multitude of desirable properties for the application we consider, giving rise to practical and fully device-independent VBQC. It certifies parallel measurements of all cardinal and intercardinal directions in the X Y plane as well as the computational basis, uses few input questions (of size logarithmic in n for the client and a constant number communicated to the server) and requires only single-qubit measurements to be performed by the client device.
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of NNN EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 111 by an honest quantum device using poly(N)(N)(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most εεε must be poly(N,ε)(N,ε)(N,ε)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed measurement statistics. However, existing self-testing methods for generic nnn-partite states face a scalability barrier, requiring exponentially many samples in the system size. In this work, we overcome this barrier by introducing a protocol that robustly self-tests almost all nnn-qubit states with only polynomial sample complexity. The key ingredient is an efficient scheme for device-independently evaluating multipartite Pauli measurements, which can be implemented using only a linear number of ancillary Bell pairs together with standard projective and Bell measurements, well within the reach of current quantum technology. Beyond self-testing states, our scheme provides a general framework for implementing a wide range of learning and certification protocols in the device-independent setting, thereby opening a scalable route to device-independent quantum information processing in large-scale quantum networks.