Compressive gate set tomography

Abstract

Flexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. Obtaining such a detailed picture of the experimental implementation is associated with high requirements on the number of sequences and their design, making gate set tomography a challenging task even for only two qubits. In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them randomly. Such tomographic information is needed for the crucial task of dealing with coherent noise. To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem. We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics by using second-order geometrical optimization methods on the complex Stiefel manifold. Besides the reduction in sequences, we demonstrate numerically that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography. Therefore, it is more flexible than traditional approaches. We also demonstrate how coherent errors in shadow estimation protocols can be mitigated using estimates from gate set tomography.

14+12 pages, several figures and diagrams; v2: An error in our interface to pyGSTi has been corrected and Sections IV.A and IV.B have been reworked; v3: Added a new section on noise mitigation for shadow estimation with compressive GST, a corresponding appendix, an improved runtime table and various clarifications

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• Learning logical Pauli noise in quantum error correction
• Tensor network noise characterization for near-term quantum computers
• Benchmarking universal quantum gates via channel spectrum
• SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments
• Stability of classical shadows under gate-dependent noise
• Gradient-descent methods for fast quantum state tomography
• Machine learning of quantum channels on NISQ devices
• Robust ultra-shallow shadows
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Classical certification of quantum gates under the dimension assumption
• Bosonic randomized benchmarking with passive transformations
• A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network
• Benchmarking Single-Qubit Gates on a Neutral Atom Quantum Processor
• Quantum Process Tomography with Digital Twins of Error Matrices