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arXiv:2103.06603 · Physical Review A

Experimental accreditation of outputs of noisy quantum computers

Samuele Ferracin, Seth Merkel, David C. McKay, Animesh Datta

Published Oct 11, 2021• 19 citations
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Abstract

We provide and experimentally demonstrate an accreditation protocol that upper bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of 24 quantum circuits executed on programmable superconducting hardware, ranging from depth-9 circuits on 10 qubits to depth-21 circuits on 4 qubits. Our protocol requires implementing the ``target'' quantum circuit along with a number of random Clifford circuits and subsequently postprocessing the outputs of these Clifford circuits. Importantly, the number of Clifford circuits is chosen to obtain the bound with the desired confidence and accuracy and is independent of the size and nature of the target circuit. We thus demonstrate a practical and scalable method of ascertaining the correctness of the outputs of arbitrary-sized noisy quantum computers---the ultimate arbiter of the utility of the computer itself.

DOI
10.1103/physreva.104.042603

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We provide and experimentally demonstrate an accreditation protocol that upper bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of 24 quantum circuits executed on programmable superconducting hardware, ranging from depth-9 circuits on 10 qubits to depth-21 circuits on 4 qubits. Our protocol requires implementing the ``target'' quantum circuit along with a number of random Clifford circuits and subsequently postprocessing the outputs of these Clifford circuits. Importantly, the number of Clifford circuits is chosen to obtain the bound with the desired confidence and accuracy and is independent of the size and nature of the target circuit. We thus demonstrate a practical and scalable method of ascertaining the correctness of the outputs of arbitrary-sized noisy quantum computers---the ultimate arbiter of the utility of the computer itself.
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 upper-bound 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.
We develop a family of quantum accreditation protocols for quantum circuits with non-Clifford two-qubit gates. The latter includes families of gates such as the fSim and XY families of gates, native to existing hardwares. We provide practical and scalable protocols that upper-bound the total variation distance between the probability distributions of error-free and erroneous quantum computations. We also establish the robustness of our protocols to small perturbations and generalize Pauli twirling to non-Pauli single-qubit bases, which may be of independent interest.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
Random circuit sampling is a leading approach to demonstrating quantum computational advantage, but benchmarking noisy implementations through linear cross-entropy requires costly calculations of ideal output probabilities. We propose a metrological benchmark based on the response to controlled perturbations, characterized by quantum Fisher information (QFI). A relation between QFI and out-of-time-order correlators enables protocols with local or global control. For Haar-random circuits, the average QFI approaches its maximal value in the local protocol and grows linearly with the number of qubits under collective control. In contrast, Clifford circuits yield zero QFI despite extensive operator spreading, showing that the response probes dynamical properties beyond spreading alone. A butterfly protocol further uses system size to enhance sensitivity, yielding a mean inverse sensitivity proportional to the number of qubits with single-qubit readout. Its fluctuations distinguish the Haar and Clifford ensembles despite their identical mean responses. For noisy implementations, we derive an exact relation between the noisy and ideal QFI within a global white-noise model, providing a quantitative reference for the degradation of the benchmark. These protocols enable metrological benchmarking of noisy random quantum circuits without computing ideal output probabilities.
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable OOO, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data { X i noisy , X i exact } via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where X i noisy and X i exact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.