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Register a new userGeneral error mitigation for quantum circuits
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Added by
Manpreet Singh Jattana
Publication date
2020
fields
Physics
and research's language is
English
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A general method to mitigate the effect of errors in quantum circuits is outlined. The method is developed in sight of characteristics that an ideal method should possess and to ameliorate an existing method which only mitigates state preparation and measurement errors. The method is tested on different IBM Q quantum devices, using randomly generated circuits with up to four qubits. A large majority of results show significant error mitigation.
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Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, these approximations can be vastly improved by error mitigation, for the computation of expectation values, as shown by small-scale experimental demonstrations. However, the practical scaling of these methods to larger system sizes remains unknown. Here, we demonstrate the utility of zero-noise extrapolation for relevant quantum circuits using up to 26 qubits, circuit depths of 60, and 1080 CNOT gates. We study the scaling of the method for canonical examples of product states and entangling Clifford circuits of increasing size, and extend it to the quench dynamics of 2-D Ising spin lattices with varying couplings. We show that the efficacy of the error mitigation is greatly enhanced by additional error suppression techniques and native gate decomposition that reduce the circuit time. By combining these methods, we demonstrate an accuracy in the approximate quantum simulation of the quench dynamics that surpasses the classical approximations obtained from a state-of-the-art 2-D tensor network method. These results reveal a path to a relevant quantum advantage with noisy, digital, quantum processors.
Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring $M$ copies of a noisy state $rho$. This enables us to estimate expectation values with respect to a state with dramatically reduced error, $rho^M/ mathrm{Tr}(rho^M)$, without explicitly preparing it, hence the name virtual distillation. As $M$ increases, this state approaches the closest pure state to $rho$, exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of $rho$). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.
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.
If NISQ-era quantum computers are to perform useful tasks, they will need to employ powerful error mitigation techniques. Quasi-probability methods can permit perfect error compensation at the cost of additional circuit executions, provided that the nature of the error model is fully understood and sufficiently local both spatially and temporally. Unfortunately these conditions are challenging to satisfy. Here we present a method by which the proper compensation strategy can instead be learned ab initio. Our training process uses multiple variants of the primary circuit where all non-Clifford gates are substituted with gates that are efficient to simulate classically. The process yields a configuration that is near-optimal versus noise in the real system with its non-Clifford gate set. Having presented a range of learning strategies, we demonstrate the power of the technique both with real quantum hardware (IBM devices) and exactly-emulated imperfect quantum computers. The systems suffer a range of noise severities and types, including spatially and temporally correlated variants. In all cases the protocol successfully adapts to the noise and mitigates it to a high degree.
We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the number of measurements to be performed on the target quantum circuit, without additional experimental overhead. We demonstrate through numerical simulations and experiments on IBM Quantum hardware that the proposed scheme significantly increases the accuracy of cost functions evaluations within the framework of variational quantum algorithms, thus leading to improved ground-state calculations for quantum chemistry and physics problems beyond state-of-the-art results.
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