Practical Quantum Error Mitigation for Near-Future Applications (1712.09271v2)

Abstract: It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation [Li2017,Temme2017] and quasi-probability decomposition [Temme2017]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localised Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation of up to 19 qubits in the context of a `SWAP test' circuit. Our optimised methods dramatically reduce the circuit's output error without increasing the qubit count or time requirements.

• The paper introduces a protocol using error extrapolation and quasi-probability decomposition to mitigate noise on near-term quantum devices.
• The exponential extrapolation method significantly reduces computed errors compared to traditional linear techniques.
• Numerical simulations on up to 19 qubits validate that these methods yield unbiased estimates without increasing circuit complexity.

Practical Quantum Error Mitigation for Near-Future Applications

The paper "Practical Quantum Error Mitigation for Near-Future Applications" addresses the critical challenge of minimizing errors in quantum computations executed on near-term quantum devices that cannot utilize full quantum fault tolerance. The authors, Suguru Endo, Simon C. Benjamin, and Ying Li, introduced a protocol to implement error mitigation strategies in realistic scenarios, considering the inevitable imperfections in an experimenter's knowledge of the noise models affecting quantum systems.

Overview and Techniques

The paper focuses on two primary methods for quantum error mitigation (QEM): error extrapolation and quasi-probability decomposition. These methods were previously introduced but require precise knowledge about the error model, which poses a challenge in real experimental conditions. This paper expands these techniques to address this limitation and offers a practical solution for their implementation:

1. Error Extrapolation: This method relies on running quantum circuits with boosted noise levels and using the measurement results to extrapolate back to the error-free case. The authors introduced an exponential variant of this method, offering improved accuracy over the traditional linear extrapolation approach.
2. Quasi-Probability Decomposition: This technique involves modifying quantum operations according to a quasi-probability distribution, effectively simulating an error-free operation. The paper introduces a protocol using single-qubit Clifford gates and measurements, which allows the complete mitigation of local Markovian errors.

Numerical Simulations

The researchers conducted numerical simulations involving up to 19 qubits, particularly focusing on the SWAP Test circuit, frequently used for estimating state overlaps in quantum algorithms. To evaluate the aforementioned QEM techniques, the authors performed intensive simulations under various noise models, validating the effectiveness of their QEM methods in reducing computational errors.

Results

Significant findings include:

• The implementation of the exponential extrapolation method effectively reduced the output error compared to linear extrapolation.
• Quasi-probability decomposition, when paired with realistic noise assumptions and gate-set tomography, achieved unbiased estimates of the ideal observable, albeit with variance amplification.
• The authors demonstrated that the mitigation methods could be deployed without increasing the qubit count or the time complexity of the circuits.

Implications and Future Directions

The implications of these findings are substantial for the development of quantum computing applications in the near term. By making efficient error mitigation techniques practically implementable, the paper paves the way for leveraging hybrid quantum algorithms, particularly those with shallow circuits relevant in areas such as quantum chemistry.

Future exploration might involve refining these techniques further to account for more complex noise models involving correlated errors or extending them for applications across different quantum computing architectures. The demonstration of these techniques on actual quantum hardware could also mark the next phase of research to firmly establish their practicality and scalability.

This research is crucial as it provides a stepping stone towards achieving practical quantum supremacy, particularly for quantum devices operating within the noisy intermediate-scale quantum (NISQ) era. By focusing on error mitigation instead of error correction, these methods align well with the current capabilities and constraints of quantum hardware.