Abstract To progress in the characterization of noise for quantum computers, gate set tomography (GST) has emerged as a self-consistent protocol that accurately estimates noisy gates, state preparations, and measurements. In its original incarnation, GST improves estimation precision by applying gates sequentially, assuming the noise yields fixed completely-positive and trace-preserving (CPTP) maps independent of prior gate history. This ‘Markovian’ assumption can conflict with experiments, where time-correlated noise may induce non-Markovian dynamics, or slow drifts and cumulative calibration errors introduce context dependence, causing CP-divisible maps to vary with circuit depth. In this work, we address this issue for trapped-ion devices with phonon-mediated two-qubit gates. Using detailed microscopic modeling of high-fidelity light-shift gates, we tailor GST to capture the main source of context dependence: motional degrees of freedom. Rather than invalidating GST, context dependence can be incorporated into the gate-set parametrization, reducing sampling cost. Our results identify a promising research avenue that might be applicable to other platforms where microscopic modeling can be incorporated: the development of a context-aware GST.
Abstract To progress in the characterization of noise for quantum computers, gate set tomography (GST) has emerged as a self-consistent protocol that accurately estimates noisy gates, state preparations, and measurements. In its original incarnation, GST improves estimation precision by applying gates sequentially, assuming the noise yields fixed completely-positive and trace-preserving (CPTP) maps independent of prior gate history. This ‘Markovian’ assumption can conflict with experiments, where time-correlated noise may induce non-Markovian dynamics, or slow drifts and cumulative calibration errors introduce context dependence, causing CP-divisible maps to vary with circuit depth. In this work, we address this issue for trapped-ion devices with phonon-mediated two-qubit gates. Using detailed microscopic modeling of high-fidelity light-shift gates, we tailor GST to capture the main source of context dependence: motional degrees of freedom. Rather than invalidating GST, context dependence can be incorporated into the gate-set parametrization, reducing sampling cost. Our results identify a promising research avenue that might be applicable to other platforms where microscopic modeling can be incorporated: the development of a context-aware GST.
Abstract Gate set tomography (GST) allows for a self-consistent characterization of noisy quantum information processors (QIPs). The standard device-agnostic approach treats the QIPs as black boxes that are only constrained by the laws of physics, attaining full generality at aconsiderable resource cost: numerous circuits built from the gate set must be run in order to amplify each of the gate set parameters. In this work, we show that a microscopic parametrization of quantum gates under time-correlated noise on the driving phase, motivated by recent experiments with trapped-ion gates, reduces the required resources enabling a more efficient version of GST. By making use of the formalism of filter functions over the noise spectral densities, we discuss the minimal parametrizations of the gate set that include the effect of finite correlation times and non-Markovian quantum evolutions during the individual gates. We compare the estimated gate sets obtained by our method and the standard long-sequence GST, discussing their accuracies in terms of established metrics, as well as showcasing the advantages of the parametrized approach in terms of the sampling complexity for specific examples.
The efficiency of Quantum Characterisation, Verification, and Validation (QCVV) protocols highly hinges on the agreement between the assumed noise model and the underlying error mechanisms. As a matter of fact, errors in Quantum Processing Units (QPUs) incorporate various aspects of context-dependability which are overlooked by the majority of the commonly used QCVV protocols. As QCVV protocols are indispensable when it comes to characterizing and evaluating quantum operations, there is a serious need for a detailed characterization taking into account such aspects. In this work, we address these shortcomings by designing a context-aware version of the gate set tomography (GST) protocol. Our experiment selection approach is based on a polynomial quantification of the accumulation of errors within the designed circuits. Using simulated QPUs, we show that this technique enables a characterization with an inaccuracy reaching 10−5. Furthermore, we use our proposed protocol to experimentally infer context-dependent errors, namely crosstalk and memory effects, in a publicly accessible cloud-based superconducting qubits platform. Our results show that when the GST is upgraded to include such features of context-awareness, a large coherence in the errors is observed. These findings open up possibilities of drastically reducing the errors within the currently demonstrated QPUs.
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.
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.
Quantum-system characterization techniques represent the front line in the identification and mitigation of noise in quantum computing but can be expensive in terms of quantum resources and time to repeatedly employ. Another challenging aspect is that the parameters governing the performance of various operations tend to drift over time and monitoring these is hence a difficult task. One of the most promising characterization techniques, gate-set tomography (GST), provides a self-consistent estimate of the completely positive trace-preserving (CPTP) maps for a complete set of gates, as well as preparation and measurement operators. We develop a method for performance optimization seeded by tomography (POST), which couples the power of GST with a classical optimization routine to achieve a consistent gate improvement in just a short number of steps within a given calibration cycle. By construction, the POST procedure finds the best available gate operation given the hardware and is therefore robust to the effects of drift. Further, in comparison to other quantum error-mitigation techniques, it builds upon a one-time application of GST. To demonstrate the performance of this method on a real quantum computer, we map out the operations of six qubit pairs on the superconducting ibmq_poughkeepsie quantum device. Under the restriction of logical-only control, we monitor the performance of the POST approach on a chosen controlled-not (cnot) gate over a period of six weeks. In this time, we achieve a consistent improvement in gate fidelity, averaging a fidelity increase of 21.1% as measured by randomized benchmarking. The POST approach should find wide applicability as it is hardware agnostic and can be applied at the upper logical level or at a deeper pulse-control level.
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.