Error mitigation extends the computational reach of a noisy quantum processor

Abstract

Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems [1]. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction [2, 3]. However, recent theoretical work [4, 5] has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single-and two-qubit experiments and then extend its application to the variational optimization [6][7][8] of Hamiltonians for quantum chemistry and magnetism [9]. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of nearterm quantum computing hardware.Quantum computation can be extended indefinitely if decoherence and inaccuracies in the implementation of gates can be brought below an error-correction threshold [2, 3]. However, the resource requirements for a fullyfault tolerant architecture lie beyond the scope of nearterm quantum hardware [10]. In the absence of quantum error correction, the dominant sources of noise in current hardware are unitary gate errors and decoherence, both of which set a limit on the size of the computation that can be carried out. In this context, hybrid-quantum algorithms [7, 8, 11] with short-depth quantum circuits have been designed to perform computations within the available coherence window, while also demonstrating some robustness to coherent unitary errors [9, 12]. However, even when restricting to short depth circuits, the effect of decoherence already becomes evident for small experiments [9]. The recently proposed zero-noise extrapolation method [4, 5, 13] presents a route to mitigating incoherent errors and significantly improving the accuracy of the computation. It is important to note that, unlike quantum error-correction this technique does not allow for an indefinite extension of the computation time, and only provides corrections to expectation values, without correcting for the full statistical behavior. However, since it does not require any additional quantum resources, the technique is extremely well suited for practical implementations with near-term hardware.We shall first briefly describe the proposal of [4] and discuss important...

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