[Paper Review] Extending the Computational Reach of a Superconducting Qutrit Processor

Noah Goss, Samuele Ferracin+6 more|arXiv (Cornell University)|May 25, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper introduces and experimentally demonstrates noise tailoring and error mitigation techniques for superconducting qutrit processors, using randomized compiling (RC) to convert coherent errors into stochastic noise and combining it with noise-optimized XEB (NOX) and readout error mitigation (RCAL). The method achieves up to 3× improvement in fidelity for multipartite entanglement and random circuit sampling, marking the first successful error mitigation experiment on qudits and significantly extending the computational reach of current qudit hardware.

ABSTRACT

Quantum computing with qudits is an emerging approach that exploits a larger, more-connected computational space, providing advantages for many applications, including quantum simulation and quantum error correction. Nonetheless, qudits are typically afflicted by more complex errors and suffer greater noise sensitivity which renders their scaling difficult. In this work, we introduce techniques to tailor and mitigate arbitrary Markovian noise in qudit circuits. We experimentally demonstrate these methods on a superconducting transmon qutrit processor, and benchmark their effectiveness for multipartite qutrit entanglement and random circuit sampling, obtaining up to 3x improvement in our results. To the best of our knowledge, this constitutes the first ever error mitigation experiment performed on qutrits. Our work shows that despite the intrinsic complexity of manipulating higher-dimensional quantum systems, noise tailoring and error mitigation can significantly extend the computational reach of today's qudit processors.

Motivation & Objective

• To address the challenge of increased noise sensitivity and complex error profiles in qudit-based quantum computing, especially in superconducting qutrit processors.
• To extend the computational reach of near-term qudit processors by developing practical error mitigation techniques tailored to qudit-specific noise.
• To demonstrate that noise tailoring via randomized compiling (RC) can effectively convert coherent errors into stochastic noise, enabling classical post-processing to recover noiseless expectation values.
• To benchmark the effectiveness of the proposed error mitigation framework on two key quantum tasks: multipartite entanglement and random circuit sampling.

Proposed method

• The authors implement randomized compiling (RC) to twirl arbitrary Markovian noise in multi-qutrit gate cycles into stochastic noise channels, effectively converting coherent errors into noise that can be corrected via post-processing.
• They combine RC with noise-optimized randomized benchmarking (NOX) and readout error mitigation (RCAL) to calibrate and correct for both gate and measurement errors in a unified framework.
• The method leverages the coherent-decoherent polar decomposition of quantum channels, where the process fidelity is expressed as a product of coherent and decoherent error contributions, enabling precise quantification of error types.
• A key innovation is the use of the McWeeny purification formula to verify that RC successfully converts coherent errors into decoherent ones, as evidenced by improved state fidelity after purification.
• The experimental setup uses three capacitively coupled, fixed-frequency transmon qutrits, with full characterization of single-qutrit confusion matrices to enable accurate readout error correction.
• Classical post-processing combines RC, NOX, and RCAL to extract noiseless expectation values, significantly improving the fidelity of quantum circuits without additional hardware.

Experimental results

Research questions

• RQ1 Can randomized compiling (RC) effectively tailor coherent errors in qudit systems into stochastic noise, enabling classical error mitigation?
• RQ2 To what extent can noise-optimized randomized benchmarking (NOX) and readout error mitigation (RCAL) improve the fidelity of qudit circuits in the presence of complex, multi-level noise?
• RQ3 Does the combination of RC, NOX, and RCAL lead to measurable improvements in benchmarking tasks such as multipartite entanglement and random circuit sampling on a real qutrit processor?
• RQ4 Can the coherent-decoherent decomposition of quantum channels be used to quantify and verify the success of noise tailoring in qudits?
• RQ5 What is the maximum fidelity improvement achievable in practice for qudit circuits using this error mitigation framework?

Key findings

• The proposed error mitigation framework—combining RC, NOX, and RCAL—achieves up to a 3× improvement in fidelity for both multipartite qutrit entanglement and random circuit sampling experiments.
• State purification using the McWeeny formula shows a fidelity increase from 0.912 (bare) to 0.998 (with RC), providing strong evidence that RC successfully converts coherent errors into stochastic noise.
• The method enables the first experimental demonstration of error mitigation in qudit systems, marking a critical step toward scalable qudit-based quantum advantage.
• The coherent-decoherent polar decomposition analysis confirms that the dominant error contribution shifts from coherent (angle) errors to decoherent (amplitude) errors after RC, making errors amenable to post-processing correction.
• The framework is experimentally validated on a real superconducting qutrit processor, demonstrating practical feasibility and scalability potential for near-term qudit hardware.
• The results show that despite the intrinsic complexity of qudits, noise tailoring and error mitigation can significantly extend the computational reach of current qudit processors.