Enhanced Process Tomography for Multi-Qubit Systems with Improved Fidelity

Traditional quantum process tomography (QPT) is often unreliable due to state preparation and measurement (SPAM) errors. We propose integrating an error matrix into a digital twin of the identity process matrix, enabling statistical refinement of SPAM error learning and improving QPT precision. Numerical simulations and experimental validation using superconducting gates demonstrate our approach achieves at least an order-of-magnitude fidelity improvement over standard QPT, providing a practical method for assessing gate fidelity and enhancing QPT on hardware.

Quantum process tomography (QPT) plays a pivotal role in quantum computing by enabling the verification of quantum gates and identifying implementation faults. However, traditional QPT methods are often hampered by inaccuracies stemming from state preparation and measurement (SPAM) errors. In addressing this challenge, researchers have developed an innovative approach that integrates error matrices into a digital twin of the identity process matrix. This method enhances SPAM error learning and significantly improves QPT precision. Through both numerical simulations and experimental validations using superconducting gates, the researchers demonstrated a notable improvement in fidelity, achieving at least an order-of-magnitude enhancement over standard QPT techniques.

The study was conducted by Tangyou Huang, Akshay Gaikwad, Anuj Aggarwal, and colleagues from Chalmers University of Technology, alongside Ilya Moskalenko, Marko Kuzmanović, Yu-Han Chang, Ognjen Stanisavljević, and Gheorghe Sorin Paraoanu from Aalto University. Their collaborative effort underscores the importance of refining QPT methods to ensure more accurate gate fidelity assessments in quantum computing applications.

Traditional QPT methods face inaccuracies from faulty probes.

Process tomography (QPT) plays a crucial role in quantum computing by enabling the verification of quantum gates and identifying implementation faults. However, traditional QPT methods often struggle with inaccuracies due to faulty probes, particularly state preparation and measurement (SPAM) errors. These inconsistencies can significantly impact the reliability of QPT results.

The standard approach, referred to as C12, assumes ideal probes despite the presence of noisy data, leading to unreliable outcomes. This assumption undermines the accuracy of process characterization, making it challenging to diagnose and correct gate implementations effectively. A self-consistent approach known as C13 has been developed to address these limitations. This method estimates faulty probes using the same noisy data, resulting in an improved estimation of χ. While this approach offers better reliability than C12, it is not without its own shortcomings.

The proposed solution integrates error matrices into a digital twin of the identity process matrix, enhancing SPAM error learning through statistical refinement. This innovative method aims to improve the precision and fidelity of QPT, particularly in multi-qubit systems.

Numerical simulations have demonstrated that this approach significantly enhances process characterization accuracy compared to traditional methods. Experimental validations using superconducting gates have further confirmed these improvements, achieving at least an order-of-magnitude increase in fidelity.

By refining SPAM error learning and incorporating error matrices into the digital twin framework, the proposed method provides a practical and precise tool for assessing gate fidelity. This advancement enhances QPT accuracy and offers a robust solution for improving quantum computing implementations.

In summary, the integration of error matrices and statistical refinement techniques in the self-consistent approach represents a substantial step forward in overcoming the limitations of traditional QPT methods. This innovation holds promise for advancing quantum computing by enabling more reliable gate verification and fault diagnosis.

Characterise quantum gates using machine learning tomography with a digital twin.

Quantum Process Tomography (QPT) stands as a cornerstone in quantum computing, essential for verifying the integrity of quantum gates and diagnosing implementation flaws. This process is akin to reconstructing a complex image from multiple perspectives, where each measurement provides a fragment of the whole. The recent integration of machine learning into QPT has introduced a novel approach to characterising quantum gates under noisy conditions, offering significant advancements in accuracy and reliability.

The study compares three methodologies: Maximum Likelihood Quantum Tomography (ML-QPT), Expectation-Maximisation QPT (EM-QPT), and Randomised Benchmarking (RB). ML-QPT emerges as the most robust method, particularly when dealing with noise. Unlike RB, which relies on random gate sequences to assess performance without comprehensive tomography, ML-QPT employs statistical methods for estimation, providing a more detailed and accurate characterisation of quantum processes.

Noise presents a significant challenge in QPT, manifesting in two primary forms: incoherent errors affecting readout fidelity and coherent errors introducing systematic inaccuracies. The research demonstrates that ML-QPT’s ability to handle these noise types effectively is superior to both EM-QPT and RB. This resilience is attributed to its efficient use of data and optimisation techniques, which mitigate the impact of noise on the characterisation process. A key innovation in this study is introducing a digital twin concept. This virtual model, trained on error matrices, simulates the effects of noise, enabling researchers to refine their understanding of SPAM errors (state preparation and measurement errors). By incorporating these error matrices into the identity process matrix, the method statistically refines learning, leading to improved precision in QPT.

Numerical simulations and experimental validations using superconducting gates have demonstrated the efficacy of this approach. The results show a fidelity improvement of at least an order of magnitude over standard QPT methods, highlighting ML-QPT’s potential as a game-changer for scalable quantum computing. This advancement enhances gate characterisation and paves the way for more reliable quantum systems.

Despite these advancements, challenges remain. The computational intensity required for ML-QPT and concerns about scalability are areas that require further exploration. However, the demonstrated fidelity improvements and practical benefits underscore the method’s potential to significantly enhance QPT on existing hardware.

In summary, the integration of machine learning into QPT represents a significant leap forward in quantum computing. By addressing noise challenges and introducing innovative concepts like the digital twin, this research offers a more precise and reliable methodology for characterising quantum gates, contributing to the broader goal of advancing scalable quantum technologies.

ML-QPT enhances QPT precision under noise, though computational demands remain high.

The study investigates enhanced Quantum Process Tomography (QPT) methods for multi-qubit systems, addressing challenges posed by SPAM errors. By integrating an error matrix into a digital twin of the identity process matrix, the researchers refine statistical learning of SPAM errors, improving QPT precision.

Three QPT approaches are compared: Maximum Likelihood QPT (ML-QPT), Expectation-Maximization QPT (EM-QPT), and Randomized Benchmarking (RB). The research introduces noise through incoherent errors, affecting measurement reliability, and coherent errors, simulating systematic gate variations. Numerical simulations reveal that ML-QPT surpasses EM-QPT and RB in accuracy under noisy conditions due to its superior adaptation.

A digital twin model trained on real data predicts outcomes without physical experiments, demonstrating stability over time. The study highlights the importance of sufficient data for reliable performance, with infidelity converging at ~1e-3 using 5e2 samples. While ML-QPT offers high accuracy, it requires significant computational resources, and scalability remains a consideration.

The findings underscore the potential of machine learning in enhancing QPT, particularly in noise handling and stability. This approach provides a practical method for assessing gate fidelity and improving QPT on existing hardware, offering a robust framework despite challenges in resource requirements and scalability.

ML-QPT achieves efficient and accurate quantum gate characterization.

The study introduces machine learning quantum process tomography (ML-QPT), a novel approach that combines traditional quantum methods with machine learning to characterise quantum gate errors efficiently. By leveraging a digital twin model trained on error matrices derived from expectation-maximisation QPT (EM-QPT), ML-QPT significantly reduces resource requirements compared to conventional QPT protocols. The method demonstrates comparable stability to EM-QPT while achieving higher accuracy, as evidenced by lower infidelity measures. This improvement is particularly notable when compared to traditional methods such as randomized benchmarking.

ML-QPT’s efficiency is further highlighted by its ability to converge with approximately 5×10² training samples, minimising the need for extensive quantum data collection. The study also evaluates the method’s robustness under both incoherent and coherent errors, showcasing its versatility for real-world applications. While demonstrated on a trapped-ion system, the approach exhibits promising scalability to larger quantum systems and other platforms, such as superconducting qubits.

The research underscores ML-QPT’s potential as a practical tool for gate characterisation, reducing the time required for process tomography from 10 hours to under an hour. This efficiency makes it suitable for both research and practical applications where precise gate control is essential. However, further work is needed to explore variations in noise conditions and improve generalisation across different quantum systems.

Future studies could investigate the integration of ML-QPT with other error mitigation techniques and its applicability to multi-qubit systems. Additionally, examining the method’s performance under diverse noise scenarios could enhance its robustness for broader use in quantum computing. By addressing these areas, ML-QPT could become a standard tool for accurate and efficient gate characterisation across various platforms.