Error-Mitigation

Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers. However, today’s quantum computers are noisy, posing challenges to obtaining accurate results. Here, we explore the impact of noise on quantum computing, focusing on the challenges in sampling bit strings from noisy quantum computers and the implications for optimization and machine learning. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the conditional value at risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on real quantum computers involving up to 127 qubits. The results show strong alignment with theoretical predictions. ...

Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens the question to what extent inaccuracy in the error model impacts the performance of error mitigation. In this work, we develop a methodology to efficiently compute upper bounds on the impact of error-model inaccuracy in error mitigation. Our protocols require no additional experiments, and instead rely on comparisons between the error model and the error-learning data from which the model is generated. We demonstrate the efficacy of our methodology by deploying it on an IBM Quantum superconducting qubit quantum processor, and through numerical simulation of standard error models. We show that our estimated upper bounds are typically close to the worst observed performance of error mitigation on random circuits. Our methodology can also be understood as an operationally meaningful metric to assess the quality of error models, and we further extend our methodology to allow for comparison between error models. Finally, contrary to what one might expect we show that observable error in noisy layered circuits of sufficient depth is not always maximized by a Clifford circuit, which may be of independent interest. ...

Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal with noise that can be applied to these algorithms. Recent work introduced a technique for mitigating expectation values against correlated measurement errors that can be applied to measurements of 10s of qubits. We apply these techniques to VQAs and demonstrate its effectiveness in improving estimates to the cost function. Moreover, we use the data resulting from this technique to experimentally characterize measurement errors in terms of the device connectivity on devices of up to 20 qubits. These results should be useful for better understanding the near-term potential of VQAs as well as understanding the correlations in measurement errors on large, near-term devices. ...