Learning-based quantum error mitigation (2005.07601v2)

Abstract: 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.

• The paper proposes a learning-based quantum error mitigation strategy for NISQ devices that avoids exhaustive noise model reconstruction by optimizing coefficients via training with classically simulable circuits.
• The methodology uses Clifford circuits to learn error-mitigating Pauli configurations, transforming the problem into a statistical estimation and showing resilience to correlated errors.
• Results from simulations and hardware tests demonstrate the method significantly outperforms traditional techniques and shows potential for scalability and practical implementation in noisy quantum systems.

Learning-based Quantum Error Mitigation

The paper "Learning-based quantum error mitigation" proposes a novel error mitigation strategy for quantum computations in noisy intermediate-scale quantum (NISQ) devices, leveraging a learning approach that obviates the need for exhaustive noise model reconstructions. This work is pivotal in the current era where quantum computers are transitioning from theoretical constructs to devices capable of executing tasks beyond classical reach, albeit limited by noise and error rates that are too high for practical error correction. Instead of traditional quantum error correction, which is resource-intensive, error mitigation strategies present a more feasible alternative for NISQ devices.

Methodology

The authors introduce a learning-based protocol where quasi-probability distributions are optimized through a training process involving Clifford circuits. These circuits, which are efficiently simulatable on classical computers, allow the protocol to assess the error-correcting coefficients without necessitating a full characterization of the noise affecting a system. This approach circumvents the need for gate set tomography, which can be impractical due to its requirement for numerous qubit measurements and configurations, especially given the presence of correlated errors.

The central approach is based on transforming a quantum computation into a statistical estimation problem. The paper outlines how error-mitigating Pauli gates are interspersed with computing gates in a quantum circuit, allowing errors to be symmetrized via Pauli twirling. The mitigation thus relies on a computed optimal configuration of these gates, learned from a set of training circuits.

Results and Analysis

The protocol has been verified using both classical simulations and real quantum hardware. Simulations were performed for circuits up to 8 qubits with variational circuits and realistic noise models, including spatially and temporally correlated errors. The learning-based mitigation was shown to significantly outperform traditional error mitigation methods based purely on initial tomography, demonstrating resilience against previously underestimated noise types.

Key results demonstrate that the learning-based approach adapts dynamically to error severities and types, such as spatial crosstalk and temporal correlations, which can be prevalent in practical quantum hardware. Error mitigation even exceeded physical fidelity levels reported in some trapped-ion systems, reflecting the method's robustness and effectiveness.

Implications and Future Directions

This method presents a significant stride toward practical error mitigation for NISQ devices by leveraging the intrinsic variability and configurability of quantum circuits without a prohibitive overhead. The approach is scalable and adaptable, suggesting feasibility for larger systems beyond the immediate demonstration. Consequently, this work implies that current noise levels in quantum computers might not be as substantial a barrier as previously thought, provided such learning-based error mitigation protocols are effectively implemented.

Furthermore, the paper suggests combining learning-based error mitigation with other methods like symmetry-based post-selection or noise extrapolation could yield further advancements in error control, forming a comprehensive toolkit for quantum computation in the NISQ era.

Conclusion

This research opens a practical pathway for improving the utility of NISQ devices, highlighting a new paradigm where learning processes adaptively optimize error-mitigating strategies. This flexibility, coupled with the protocol's significant empirical performance, underscores its potential role in advancing quantum computation towards more meaningful and complex applications—paving the way for more reliable quantum computation in noisy environments. As such, it provides a foundation for future exploration and combination with other error mitigation techniques, ultimately promoting a more integrated and robust approach to mitigating quantum computational errors.