Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors (2201.09866v2)

Abstract: Noise in pre-fault-tolerant quantum computers can result in biased estimates of physical observables. Accurate bias-free estimates can be obtained using probabilistic error cancellation (PEC), which is an error-mitigation technique that effectively inverts well-characterized noise channels. Learning correlated noise channels in large quantum circuits, however, has been a major challenge and has severely hampered experimental realizations. Our work presents a practical protocol for learning and inverting a sparse noise model that is able to capture correlated noise and scales to large quantum devices. These advances allow us to demonstrate PEC on a superconducting quantum processor with crosstalk errors, thereby providing an important milestone in opening the way to quantum computing with noise-free observables at larger circuit volumes.

• The paper presents a new probabilistic error cancellation strategy that employs sparse Pauli-Lindblad models to achieve bias-free estimates on noisy quantum processors.
• It demonstrates algorithmic scalability by efficiently learning and inverting noise channels in multi-qubit systems, validated on superconducting processors.
• The authors establish rigorous theoretical bounds on sample complexity and fidelity, ensuring consistent noise mitigation even in correlated quantum circuits.

Probabilistic Error Cancellation with Sparse Pauli-Lindblad Models on Noisy Quantum Processors

The paper, "Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors," presents a significant contribution to the field of quantum computing, specifically in addressing the critical challenge of error mitigation in pre-fault-tolerant quantum processors. The authors explore probabilistic error cancellation (PEC) techniques to obtain accurate, bias-free estimates of physical observables, even under the detrimental effects of noise inherent in current quantum hardware.

Main Contributions

The authors propose a scalable and efficient protocol for designing and manipulating sparse noise models that capture correlated noise in large quantum circuits. This paper introduces a method based on sparsely populated Pauli-Lindblad error models, allowing them to learn and invert noise channels efficiently. The key advances that the paper discusses are:

1. Algorithmic Efficiency and Scalability: The methodology scales linearly with the number of qubits, a considerable improvement over previous models. The protocol effectively captures noise correlations across multiple qubits and forms a compact representation from which inversions and sampling become tractable.
2. Experimental Demonstration: The paper illustrates the application of this model to superconducting quantum processors, notably those with noise channels affected by crosstalk errors. PEC is demonstrated experimentally, removing noise-induced bias in the estimation of observables over circuits involving larger volumes.
3. Complexity and Learning Guarantees: The paper includes rigorous theoretical frameworks that underlie the noise-model learning. Sample complexity and fidelity bounds are established, ensuring that the sparse model can be learned consistently, even in systems with considerable noise.

Numerical Results and Claims

• Mitigation Accuracy: Through experiments on systems with up to 20 qubits, the proposed method exhibited significant noise reduction, improving the fidelity of measured observables.
• Scalable Application: The model was efficiently learned and applied to 20-qubit systems maintaining low sampling overheads, which is indicative of the method's scalability.
• Theoretical Reliability: The reliability of the sparse noise model in reconstructing channel parameters aligns with theoretical predictions, portraying convergence and consistency in mitigating errors.

Implications and Future Directions

The research proposes a critical step toward practical quantum computations, enabling experiments and computation on larger circuits by mitigating hardware limitations due to noise. The sparse modeling and PEC technique could facilitate the exploration of quantum algorithms and simulations that were previously impractical on near-term machines.

Future work may delve into further optimizing the sampling overhead and extending the methodology to a more diverse set of quantum hardware architectures beyond superconducting qubits. Additionally, integrating this approach with other noise mitigation strategies could further enhance its applicability in various quantum-information-processing tasks.

In conclusion, this paper outlines a robust approach to error mitigation via sparse modeling and probabilistic strategies. The advancements offer a near-term solution for enhancing the computational capability of quantum processors, paving the way for more complex quantum algorithms to be explored despite current technological imperfections.