Resource-efficient verification of quantum computing using Serfling’s bound

Takeuchi, Yuki; Mantri, Atul; Morimae, Tomoyuki; Mizutani, Akihiro; Fitzsimons, Joseph F.

doi:10.1038/s41534-019-0142-2

Cited by 59 publications

(67 citation statements)

References 54 publications

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“…Our theorem 2 shows that our protocol requires reducing the error rates of single-qubit gates with the size of the target circuit. This requirement is similar to that found in other works [29,38,41], and is a known obstacle towards scalable quantum computing. A strategy that has been exploited in previous works is to incorporate fault-tolerance into the existing protocols [29,41].…”

Section: Discussionsupporting

confidence: 82%

“…In the mesothetic protocol the verifier requires an n-qubit memory and the ability to execute single-qubit gates. This protocol ismore demanding than several existing cryptographic protocols [27][28][29][30][31][32][33][34][35][36][37][38] requiring single-qubit memory for the verifier. An interesting question is whether a mesothetic protocol can be devised that only requires single-qubit gates and single-qubit memory for the verifier.…”

Section: Discussionmentioning

confidence: 99%

“…In the first two theorems the number ε is replaced by the soundness cr e (see definition 4 in appendix D.2), namely the probability that Alice accepts a wrong output for the target when Bob is cheating. Our mesothetic verification protocol is different from prepare-and-send [26][27][28][29][30][31][32][33] or receive-and-measure [34][35][36][37][38] cryptographic protocols in that Alice encrypts the computation through the QOTP during the actual implementation of the circuits, and not before or after the implementation. To do this, she must possess an nqubit quantum memory and be able to execute single-qubit gates.…”

Section: Mesothetic Verification Protocolmentioning

confidence: 99%

“…Inspired by cryptographic protocols [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], our accreditation protocol is trap-based, meaning that the target circuit being accredited is implemented together with a number v of classically simulable circuits (the 'trap' circuits) able to detect all types of noise subject to conditions N1 and N2 above. A single run of our protocol requires implementing the target circuit being accredited and v trap circuits.…”

Section: Introductionmentioning

confidence: 99%

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Accrediting outputs of noisy intermediate-scale quantum computing devices

2019

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We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upperbound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementing quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our accreditation protocol assumes that single-qubit gates have bounded probability of error. We allow for arbitrary spatial and temporal correlations in the noise affecting state preparation, measurements, single-qubit and two-qubit gates. We describe how to implement our protocol on real-world devices, and we also present a novel cryptographic protocol (which we call 'mesothetic' protocol) inspired by our accreditation protocol. measure [34-38] single qubits, however recently a protocol for a fully classical verifier was devised that relies on the widely believed intractability of a computational problem for quantum computers [39]. Other protocols for classical verifiers have also been devised, but they require interaction with multiple entangled and noncommunicating provers [40][41][42][43][44]. Cryptographic protocols show that with minimal assumptions, verification of the outputs of quantum computations of arbitrary size can be done efficiently, in principle.In practice, implementing cryptographic protocols in experiments remains challenging, especially in the near term. In experiments all the operations are noisy, as in figure 1(b), and the verifier does not possess noiseless quantum devices. Thus, the verifiability of protocols requiring noiseless devices for the verifier is not guaranteed. Moreover, the concept of scalability, which is of primary interest in cryptographic protocols, is not equivalent to that of practicality, which is essential for experiments. For instance, suppose that the target circuit contains a few hundred qubits and a few hundred gates. Cryptographic protocols require implementing this circuit on a large cluster state containing thousands of qubits and entangling gates [26][27][28][29][30][31]34] or on two spatially-separated devices sharing thousands of copies of Bell states [40,41]; or appending several teleportation gadgets to the target circuit (one for each T-gate in the circuit and six for each Hadamard gate) [33]; or building Feynman-Kitaev clock states, which require entangling the system with an auxiliary qubit per gate in the target circuit [35,39,43]. These protocols are scalable, as they require a number of additional qubits, gates and measurements growing linearly with the size of the target circuit, yet they remain impractical for NISQ devices.In this paper we present an accreditation protocol that provides an upper-bound on the variation distance between noisy and noiseless probability di...

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Section: Discussionsupporting

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Mesothetic Verification Protocolmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accrediting outputs of noisy intermediate-scale quantum computing devices

2019

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“…Similarly, Ref. [34] derives an efficient method to verify the production of graph states by measuring all but one copy of the state. In contrast, we measure all available states and only aim to make a statement about all the created states (after the fact).…”

Section: Relation To Other Workmentioning

confidence: 99%

Witnessing entanglement in experiments with correlated noise

Dirkse

Pompili

Hanson

et al. 2020

Quantum Sci. Technol.

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The purpose of an entanglement witness experiment is to certify the creation of an entangled state from a finite number of trials. The statistical confidence of such an experiment is typically expressed as the number of observed standard deviations of witness violations. This method implicitly assumes that the noise is well-behaved so that the central limit theorem applies. In this work, we propose two methods to analyze witness experiments where the states can be subject to arbitrarily correlated noise. Our first method is a rejection experiment, in which we certify the creation of entanglement by rejecting the hypothesis that the experiment can only produce separable states. We quantify the statistical confidence by a p-value, which can be interpreted as the likelihood that the observed data is consistent with the hypothesis that only separable states can be produced. Hence a small pvalue implies large confidence in the witnessed entanglement. The method applies to general witness experiments and can also be used to witness genuine multipartite entanglement. Our second method is an estimation experiment, in which we estimate and construct confidence intervals for the average witness value. This confidence interval is statistically rigorous in the presence of arbitrary noise. The method applies to general estimation problems, including fidelity estimation. To account for systematic measurement and random setting generation errors, our model takes into account device imperfections and we show how this affects both methods of statistical analysis. Finally, we illustrate the use of our methods with detailed examples based on a simulation of NV centers.

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

Tan

Huang

et al. 2020

Quantum Engineering

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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 Ofalse(n11lognfalse) Bell pairs, where n is the size of original computation.

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Resource-efficient verification of quantum computing using Serfling’s bound

Cited by 59 publications

References 54 publications

Accrediting outputs of noisy intermediate-scale quantum computing devices

Accrediting outputs of noisy intermediate-scale quantum computing devices

Witnessing entanglement in experiments with correlated noise

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

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