Error mitigation for short-depth quantum circuits (1612.02058v3)

Abstract: Two schemes are presented that mitigate the effect of errors and decoherence in short depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates of the expectation values of observables used to evaluate the noisy circuit. The two schemes we discuss are deliberately simple and don't require additional qubit resources, so to be as practically relevant in current experiments as possible. The first method, extrapolation to the zero noise limit, subsequently cancels powers of the noise perturbations by an application of Richardson's deferred approach to the limit. The second method cancels errors by resampling randomized circuits according to a quasi-probability distribution.

• The paper introduces error mitigation methods—zero-noise extrapolation and probabilistic error cancellation—that enhance the reliability of quantum circuits.
• The zero-noise extrapolation technique uses scaling of noise parameters to achieve orders-of-magnitude precision improvements without extra quantum resources.
• Probabilistic error cancellation employs quasi-probability distributions derived from full noise characterization to improve estimation of quantum circuit outcomes.

Error Mitigation for Short-Depth Quantum Circuits: An Analytical Perspective

In the field of quantum computing, error and noise mitigation is a critical challenge that must be addressed to achieve reliable quantum computations. The paper "Error mitigation for short-depth quantum circuits" by Temme, Bravyi, and Gambetta, presents two practical techniques that offer solutions to these challenges for near-term quantum devices. Spanning approaches that exploit both coherent and incoherent noise models, this work tackles error mitigation in short-depth quantum circuits—a class of circuits most relevant for today's quantum simulators and near-term quantum applications.

Summary of Techniques

The paper introduces two primary error mitigation techniques: extrapolation to the zero-noise limit and probabilistic error cancellation using quasi-probability distributions.

1. Extrapolation to the Zero Noise Limit: This method is relatively simple, relying on Richardson's deferred approach to the zero noise limit. By manipulating the noise level through system control, multiple data points can be sampled for the expectation value of a quantum observable. The authors use a series expansion involving the noise parameter, where successive coefficients can be systematically canceled in the computational zeroth order. Remarkably, this technique doesn't necessitate additional quantum resources, making it attractive for current quantum experiments. The implementation requires a precise adjustment of the system's dynamics according to scaling coefficients, reflecting different noise rates.
2. Probabilistic Error Cancellation via Quasi-Probability: The authors present a method that uses a probabilistic framework to counter the effect of noise in quantum circuits, especially when characterized by Markovian dynamics. This involves constructing a quasi-probability distribution that represents the ideal quantum circuit in terms of its noisy counterparts. The solution draws on classical techniques of simulating quantum circuits; it involves quasi-probability representations of ideal circuits, derived as mixtures of noisy circuits. This allows an estimation of expectation values by resampling the noisy circuits appropriately. A primary requirement for this technique is a full characterization of the noise model, which can be realized through extensive tomography.

Implications and Numerical Results

The authors provide a detailed analysis of their error mitigation techniques with significant numerical demonstrations. For example, the extrapolation method demonstrates effective noise reduction across multiple noise paradigms, achieving precision improvements to the order of $10^{-6}$ - $10^{-11}$ under low-noise conditions. In the context of probabilistic error cancellation, simulation outcomes on random Clifford+$T$ circuits showcase a marked improvement in estimating output probabilities—a critical element for simulations on noisy quantum devices.

Both methodologies harbor the potential to blend seamlessly into near-term quantum experiments without incurring substantial quantum resource overheads, which is vital considering current hardware constraints. For instance, the paper notes that probabilistic error cancellation can enable the simulation of ideal circuits with a substantial length, under realistic error rates commonly encountered in practice.

Future Prospects

The developed techniques add a layer to the theoretical toolkit available for enhancing quantum circuits’ reliability. As quantum processors evolve, these schemes may serve both as stand-alone protocols and as parts of more complex error correction architectures. There is an evident potential for integrating these methods with classical optimization algorithms and using them as supplements in hybrid quantum-classical computational frameworks.

Additionally, the methodologies could provide an essential stepping stone toward genuinely fault-tolerant quantum computation. As quantum technology advances, further refinement and adaptation of these techniques could substantially bridge the gap between noisy intermediate-scale quantum (NISQ) devices and fully scalable quantum hardware.

By laying the groundwork for error mitigation in near-term, practical quantum computation scenarios, this paper contributes significantly to the ongoing efforts to transition theoretical quantum computing models to tangible, experimentally realizable technologies.