PyGSTi is an implementation of Gate Set Tomography in the python programming language. Gate Set Tomography (GST) is a theory and protocol for simultaneously estimating the state preparation, gate operations, and measurement effects of a physical system of one or many quantum bits (qubits). These estimates are based entirely on the statistics of experimental measurements, and their interpretation and analysis can provide a detailed understanding of the types of errors/imperfections in the physical system. In this way, GST provides not only a means of certifying the "goodness" of qubits but also a means of debugging (i.e. improving) them.
PyGSTi is an implementation of Gate Set Tomography in the python programming language. Gate Set Tomography (GST) is a theory and protocol for simultaneously estimating the state preparation, gate operations, and measurement effects of a physical system of one or many quantum bits (qubits). These estimates are based entirely on the statistics of experimental measurements, and their interpretation and analysis can provide a detailed understanding of the types of errors/imperfections in the physical system. In this way, GST provides not only a means of certifying the "goodness" of qubits but also a means of debugging (i.e. improving) them.
PyGSTi is a Python package for modeling and characterizing noise (errors) in small quantum information processors. In addition to being a basic framework for describing quantum circuits and noise models, it implements mainstream quantum characterization, verification, and validation (QCVV) protocols such as Gate Set Tomography (GST), Randomized Benchmarking (RB), Robust Phase Estimation, and Idle Tomography. It also implements prototype protocols used for timeseries analysis and crosstalk detection, all of which have the goal of better understanding the noise found in existing as-built experimental devices. The central protocol of pyGSTi (from where it derives its name) is Gate Set Tomography. GST is a theory and protocol for simultaneously estimating the state preparation, gate operations, and measurement effects of a physical system of one or many quantum bits (qubits). These estimates are based entirely on the statistics of experimental measurements, and their interpretation and analysis can provide a detailed understanding of the types of errors/imperfections in the physical system. In this way, GST provides not only a means of certifying the “goodness” of qubits but also a means of debugging (i.e. improving) them. The other protocols follow this similar pattern in that they use statistical inference and analysis of experimental data to estimate one or more properties of the noise in a device.
Quantum error correction (QEC) can strongly suppress noise, but predicting whether a computation succeeds requires understanding not only how much effective noise persists after QEC, but what form that noise takes. To thoroughly characterize this noise, we introduce logical gate set tomography (``logical GST''). Logical GST produces detailed representations of noisy logical operations that can be used to derive higher-level metrics, such as gate fidelity and diamond distance, and to test for non-Markovian and coherent logical errors. We use logical GST to obtain the first full, self-consistent characterization of a universal single-qubit logical gate set, implemented in the seven-qubit Steane code using Quantinuum System Model H1, a 20-qubit trapped-ion quantum processor. In the experimental data from H1, logical GST identified predominantly logical Pauli-stochastic errors, found no evidence of logical non-Markovianity, and detected weak potential signatures of coherent logical error. By contrast, higher-shot datasets generated with Quantinuum's detailed system emulator, identify mechanisms for weak but statistically significant logical non-Markovianity and strong evidence of coherent logical error. Finally, we use logical GST to perform error attribution with the system emulator, revealing how specific physical error sources shape logical error mechanisms.
Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is calibration-free . GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a gate set simultaneously and self-consistently, relative to each other. Long sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. In this paper, we cover GST's intellectual history, the techniques and experiments used to achieve its intended purpose, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. Our focus is fundamental mathematical aspects of GST, rather than implementation details, but we touch on some of the foundational algorithmic tricks used in the pyGSTi implementation.
Quantum gate set tomography (GST) has emerged as a promising method for the full characterization of quantum logic gates. In contrast to quantum process tomography (QPT), GST self-consistently and correctly accounts for state preparation and measurement (SPAM) errors. It therefore provides significantly more accurate estimates than QPT as gate fidelities increase into the fault-tolerant regime. We give a detailed review of GST and provide a self-contained guide to its implementation. The method is presented in a step-by-step fashion and relevant mathematical background material is included. Our goal is to demonstrate the utility of GST as both an accurate characterization technique and a simple and effective diagnostic tool. As an illustration, we compare the output of GST and QPT using simulated example data for a single qubit. In agreement with the original literature, we find that coherent errors are poorly estimated by QPT near quantum error correction thresholds, while GST is accurate in this regime.
Gate set tomography (GST) characterizes the process matrix of quantum logic gates, along with measurement and state preparation errors in quantum processors. GST typically requires extensive data collection and significant computational resources for model estimation. We propose a more efficient GST approach for qudits, utilizing the qudit Hadamard and virtual Z gates to construct fiducials while assuming virtual Z gates are error-free. Our method reduces the computational costs of estimating characterization results, making GST more practical at scale. We experimentally demonstrate the applicability of this approach on a superconducting transmon qutrit.
Abstract Engineering quantum devices requires reliable characterization of the quantum system, including qubits, quantum operations (also known as instruments) and the quantum noise. Recently, quantum gate set tomography (GST) has emerged as a powerful technique for self-consistently describing quantum states, gates, and measurements. However, non-Markovian correlations between the quantum system and environment impact the reliability of GST. To address this, we propose a self-consistent operational framework called instrument set tomography (IST) for non-Markovian GST. Based on the stochastic quantum process, the instrument set describes instruments and system-environment (SE) correlations. We introduce a linear inversion IST (LIST) to describe instruments and SE correlations without physical constraints. The disharmony of linear relationships between instruments is detected. Furthermore, we propose a physically constrained statistical method based on the maximum likelihood estimation for IST (MLE-IST) with adjustable dimensions. MLE-IST shows significant flexibility in adapting to different types of devices, such as noisy intermediate-scale quantum (NISQ) devices, by adjusting the model and constraints. Experimental results demonstrate the effectiveness and necessity of simultaneously describing instruments and SE correlations. Specifically, the LIST and MLE-IST obtains significant improvement on average square error reduction in the imperfect implemented simulations by orders of −23.77 and −6.21, respectively, compared to their comparative methods. Remarkably, real-chip experiments indicate that a polynomial number of parameters with respect to the Markovian order are sufficient to characterize non-Markovian quantum noise in current NISQ devices. Consequently, IST provides an essential and self-consistent framework for characterizing, benchmarking, and developing quantum devices in terms of the instrument set.