The field of quantum technologies has experienced explosive growth in the past decade. As hardware capabilities have advanced, quantum computing has exhibited a scaling trend analogous to Moore's law, often referred to as Rose's law, where the number of coherently controlled qubits roughly doubles every two years. Associated with such rapid growth is an equally growing need for benchmarking tools and error handling. While advancements in quantum hardware and software have mainly concentrated on enhancing gate fidelity and qubit connectivity, the progress in addressing readout errors has been relatively limited during the same period. This thesis tries to close this gap by advancing and developing new tools for information extraction in quantum systems. We do this in two different ways: In Part II, we focus on mitigating the effect of general readout errors in quantum systems. We developed a comprehensive protocol for readout-error-mitigated state tomography (REMST) and implemented it on a superconducting qubit system. The REMST protocol was designed to mitigate not only classical readout errors but also more challenging coherent and correlated readout errors. The protocol uses only a deterministic application of single-qubit readout, making it one of the most experimentally friendly approaches available. We developed a scalable version of the REMST protocol and showed numerically that it is suitable for systems with more than 100 qubits, matching the size of current state-of-the-art systems. The REMST protocol was applied to superconducting qubit experiments, where we saw an improvement in reconstruction accuracy by a factor of up to 30. In Part III, we move our focus to optimal measurement strategies. Adaptive measurement strategies promise a quadratic improvement in the statistical fluctuation of pure and close-to-pure state reconstruction by dynamically optimizing measurement settings during sampling. We investigated whether these adaptive measurement strategies were viable in realistic experimental settings. We demonstrated both analytically and in numerical simulations that going from ideal readout to noisy readout disproportionally deteriorates the quality of the adaptive measurement strategy, to a point where no asymptotic benefit exists for adaptive measurements. These results not only deepen our understanding of readout processes in superconducting qubits but also provide concrete implementations of more robust quantum measurement and tomography protocols, offering clearer insight into the interplay between readout noise and information extraction.
The field of quantum technologies has experienced explosive growth in the past decade. As hardware capabilities have advanced, quantum computing has exhibited a scaling trend analogous to Moore's law, often referred to as Rose's law, where the number of coherently controlled qubits roughly doubles every two years. Associated with such rapid growth is an equally growing need for benchmarking tools and error handling. While advancements in quantum hardware and software have mainly concentrated on enhancing gate fidelity and qubit connectivity, the progress in addressing readout errors has been relatively limited during the same period. This thesis tries to close this gap by advancing and developing new tools for information extraction in quantum systems. We do this in two different ways: In Part II, we focus on mitigating the effect of general readout errors in quantum systems. We developed a comprehensive protocol for readout-error-mitigated state tomography (REMST) and implemented it on a superconducting qubit system. The REMST protocol was designed to mitigate not only classical readout errors but also more challenging coherent and correlated readout errors. The protocol uses only a deterministic application of single-qubit readout, making it one of the most experimentally friendly approaches available. We developed a scalable version of the REMST protocol and showed numerically that it is suitable for systems with more than 100 qubits, matching the size of current state-of-the-art systems. The REMST protocol was applied to superconducting qubit experiments, where we saw an improvement in reconstruction accuracy by a factor of up to 30. In Part III, we move our focus to optimal measurement strategies. Adaptive measurement strategies promise a quadratic improvement in the statistical fluctuation of pure and close-to-pure state reconstruction by dynamically optimizing measurement settings during sampling. We investigated whether these adaptive measurement strategies were viable in realistic experimental settings. We demonstrated both analytically and in numerical simulations that going from ideal readout to noisy readout disproportionally deteriorates the quality of the adaptive measurement strategy, to a point where no asymptotic benefit exists for adaptive measurements. These results not only deepen our understanding of readout processes in superconducting qubits but also provide concrete implementations of more robust quantum measurement and tomography protocols, offering clearer insight into the interplay between readout noise and information extraction.
Assumption-free reconstruction of quantum states from measurements is essential for benchmarking and certifying quantum devices, but it remains difficult due to the extensive measurement statistics and experimental resources it demands. An approach to alleviating these demands is provided by adaptive measurement strategies, which can yield up to a quadratic improvement in reconstruction accuracy for pure states by dynamically optimizing measurement settings during data acquisition. A key open question is whether these asymptotic advantages remain in realistic experiments, where readout is inevitably noisy. In this work, we analyze the impact of readout noise on adaptive quantum state tomography with readout-error mitigation, focusing on the challenging regime of reconstructing pure states using mixed-state estimators. Using analytical arguments based on Fisher information optimization and extensive numerical simulations using Bayesian inference, we show that any nonzero readout noise eliminates the asymptotic quadratic scaling advantage of adaptive strategies. We numerically investigate the behavior for finite measurement statistics for single- and two-qubit systems with exact readout-error mitigation and find a gradual transition from ideal to sub-optimal scaling. We furthermore investigate realistic scenarios where detector tomography is performed with a limited number of state copies for calibration, showing that insufficient detector characterization leads to estimator bias and limited reconstruction accuracy. Although our result imposes an upper bound on the reconstruction accuracy that can be achieved with adaptive strategies, we nevertheless observe numerically a constant-factor gain in reconstruction accuracy, which becomes larger as the readout noise decreases. This indicates potential practical benefits in using adaptive measurement strategies in well-calibrated experiments.
Abstract Quantum technologies rely heavily on accurate control and reliable readout of quantum systems. Current experiments are limited by numerous sources of noise that can only be partially captured by simple analytical models and additional characterization of the noise sources is required. We test the ability of readout error mitigation to correct noise found in systems composed of quantum two-level objects (qubits). To probe the limit of such methods, we designed a beyond-classical readout error mitigation protocol based on quantum state tomography (QST), which estimates the density matrix of a quantum system, and quantum detector tomography (QDT), which characterizes the measurement procedure. By treating readout error mitigation in the context of state tomography the method becomes largely readout mode-, architecture-, noise source-, and quantum state-independent. We implement this method on a superconducting qubit and evaluate the increase in reconstruction fidelity for QST. We characterize the performance of the method by varying important noise sources, such as suboptimal readout signal amplification, insufficient resonator photon population, off-resonant qubit drive, and effectively shortened T1 and T2 coherence. As a result, we identified noise sources for which readout error mitigation worked well, and observed decreases in readout infidelity by a factor of up to 30.
Quantum simulation, the study of strongly correlated quantum matter using synthetic quantum systems, has been the most successful application of quantum computers to date. It often requires determining observables with high precision, for example when studying critical phenomena near quantum phase transitions. Thus, readout errors must be carefully characterized and mitigated in data postprocessing, using scalable and noise-model agnostic protocols. We present a readout error-mitigation protocol that uses only single-qubit Pauli measurements and avoids experimentally challenging randomized measurements. The proposed approach captures a very broad class of correlated noise models and is scalable to large qubit systems. It is based on a complete and efficient characterization of few-qubit correlated positive operator-valued measures, using overlapping detector tomography. To assess the effectiveness of the protocol, observables are extracted from simulations involving up to 100 qubits employing readout errors obtained from experiments with superconducting qubits.
The accurate measurement of quantum two-level objects (qubits) is crucial for developing quantum computers. Over the last decade, the measure of choice for benchmarking readout routines for superconducting qubits has been assignment fidelity; however, this method only focuses on the preparation of computational basis states and therefore does not provide a complete characterization of the readout. Here, we expand the focus to the use of detector tomography to fully characterize multiqubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum-state reconstruction infidelity as a proxy. The results are then compared with assignment fidelities, showing good agreement for separable two-qubit states. We therefore propose the rate of infidelity convergence as a validation tool for assignment fidelity and a more comprehensive benchmark for single- and multiqubit readout optimization. To make the best use of experimental resources, we investigate the most efficient distribution of a limited shot budget between detector tomography and state reconstruction within the context of single- and two-qubit experiments. To address the growing interest in three-qubit gates and test the scalability of the validation tool, we perform three-qubit quantum-state tomography that goes beyond conventional readout-error-mitigation methods and find a factor-of-30 reduction in quantum infidelity. Our results demonstrate that qubit readout correlations are not induced by a significantly reduced state distinguishability. Consequently, correlation coefficients can serve as a valuable tool in qubit readout optimization.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.
In Phys. Rev. A 108, L060402 (2023), we introduced a Bayesian measurement error mitigation algorithm, which leveraged complete information from the readout signal, and validated the protocol on a quantum device with five superconducting qubits. Here, we present an improved algorithm's implementation, tailored for multiqubit experiments on near-term superconducting qubit quantum devices. In particular, we provide a detailed algorithm workflow, from calibrating the detector response functions to the postprocessing of measurement outcomes, offering a computationally efficient solution for the output size typical of current quantum computing devices. We show how the numerical representation of the noise function affects the performance of the error mitigation algorithm and test the convergence criteria. We benchmark our protocol on actual quantum computers with superconducting qubits, where the readout signal encodes the measurement information as unprocessed analog data before qubit state assignment. Finally, we compare the performance of our algorithm against other measurement error mitigation methods, such as iterative Bayesian unfolding and the Mthree method, and show how our method can be integrated on top of other readout error mitigation protocols.