We consider the problem of reproducing one quantum measurement given the ability to perform another. We give a general framework and specific protocols for this problem. For example, we show how to use available “imperfect” devices a small number of times to implement a target measurement with average error that drops off exponentially with the number of imperfect measurements used. We hope that could be useful in near-term applications as a type of lightweight error mitigation of the measuring devices. As well as the view to practical applications, we consider the question from a general theoretical perspective in the most general setting where both the available and target measurements are arbitrary generalized quantum measurements. We show that this general problem in fact reduces to the ability to reproduce the statistics of (complete) von Neumann measurements, and that in the asymptotic limit of infinitely many uses of the available measurement, a simple protocol based upon “classical cloning” can perfectly achieve this task. We show that asymptotically any nontrivial quantum measurement can reproduce any other. We also study optimal protocols for a fixed number of uses of the available measurement. This includes, but is not limited to, improving both noisy and lossy quantum measurements. Furthermore, we show that, in a setting where we perform multiple measurements in parallel, we can achieve finite-rate measurement reproduction, by using block-coding techniques from classical information theory. Finally, we show that advantages can also be gained by making use of probabilistic protocols.
We consider the problem of reproducing one quantum measurement given the ability to perform another. We give a general framework and specific protocols for this problem. For example, we show how to use available “imperfect” devices a small number of times to implement a target measurement with average error that drops off exponentially with the number of imperfect measurements used. We hope that could be useful in near-term applications as a type of lightweight error mitigation of the measuring devices. As well as the view to practical applications, we consider the question from a general theoretical perspective in the most general setting where both the available and target measurements are arbitrary generalized quantum measurements. We show that this general problem in fact reduces to the ability to reproduce the statistics of (complete) von Neumann measurements, and that in the asymptotic limit of infinitely many uses of the available measurement, a simple protocol based upon “classical cloning” can perfectly achieve this task. We show that asymptotically any nontrivial quantum measurement can reproduce any other. We also study optimal protocols for a fixed number of uses of the available measurement. This includes, but is not limited to, improving both noisy and lossy quantum measurements. Furthermore, we show that, in a setting where we perform multiple measurements in parallel, we can achieve finite-rate measurement reproduction, by using block-coding techniques from classical information theory. Finally, we show that advantages can also be gained by making use of probabilistic protocols.
Quantum states and measurements are two central physical objects in the theory of quantum mechanics. The preparation, control and measurement of quantum states lies at the heart of modern quantum information processing protocols ranging from secure communication to quantum computation and precision sensing. And yet, the reliable operation of these advanced protocols ultimately rests on a far more essential prerequisite - our ability to calibrate, certify and benchmark the quantum states we prepare and the quantum measurements we perform. Quantum information theory provides a natural framework for these tasks, meaningfully connecting the resources we expend for characterisation with the accuracy and precision we can expect in return. While decades of advances in quantum information have refined our understanding of quantum characterisation and sharpened our practical ability to calibrate with enhanced precision, important questions about the fundamental limits of quantum characterisation remain unanswered. Although incorporating entanglement at the measurement stage is known to enhance the estimation of unknown quantum states, the extent of this improvement remains poorly understood. This leaves open a fundamental question on the utility of complex entangling measurement strategies, impeding progress towards bridging the significant gap between practically achievable precision and the ultimate theoretical quantum limit. Complementary to quantum state estimation, which is relatively well-established in theory and practice, the characterisation of quantum measurements lacks a rigorous information-theoretic foundation, leading to a dearth of principled benchmarks and provably optimal strategies despite growing experimental interest. This thesis develops and applies information-theoretic tools to answer questions in quantum characterisation, with an eye to enabling practical improvements beyond current techniques in the field. First, we introduce a computable measure of entanglement enhancement for quantum state estimation and study its variation across general multi-parameter estimation problems for higher-dimensional quantum states. We show that the entanglement enhancement is maximised for full qudit state tomography but grows only linearly with system dimension even when allowing an asymptotically large number of entangling operations. Our proposed tight upper bound to entanglement enhancement therefore constitutes a strong limitation on the utility of such entangling measurements. Next, we formulate the dual problem of quantum detector estimation, developing a comprehensive framework for maximally precise calibration centred around a newly introduced quantity - the detector quantum Fisher information. This information-theoretic measure stipulates the ultimate precision attainable for measurement calibration and identifies the optimal input states that achieve this precision. Further, our framework enables the first provably optimal detector estimation experiment and reveals the scope for entanglement-based enhancements, thereby placing measurement characterisation on equal footing with state characterisation. Considered together, these results suggest two contrasting conclusions about quantum characterisation. On the one hand, they show that for quantum state estimation, increasingly powerful entangling measurements offer only diminishing returns at the ultimate precision limit. On the other hand, they highlight practical quantum advantages available for detector estimation by providing a framework that can improve calibration performance and guide future experimental design. More broadly, these results complete and advance the triad of state, process, and detector characterisation, positioning quantum information measures as not merely abstract bounds, but practical guides for deciding when complex quantum resources are genuinely worth deploying and where near-term quantum advantages are most likely to be realised.
Variational Quantum Algorithms (VQA) are one of the most promising candidates for near-term quantum advantage. Traditionally, these algorithms are parameterized by rotational gate angles whose values are tuned over iterative execution on quantum machines. The iterative tuning of these gate angle parameters make VQAs more robust to a quantum machine's noise profile. However, the effect of noise is still a significant detriment to VQA's target estimations on real quantum machines - they are far from ideal. Thus, it is imperative to employ effective error mitigation strategies to improve the fidelity of these quantum algorithms on near-term machines.While existing error mitigation techniques built from theory do provide substantial gains, the disconnect between theory and real machine execution characteristics limit the scope of these improvements. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine.We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters -by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements - a mean of over 3x across a variety of VQA applications, run on IBM Quantum machines.More importantly, while we study two specific error mitigation techniques, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a priori. Integrating more mitigation techniques into the VAQEM framework in the future can lead to further formidable gains, potentially realizing practically useful VQA benefits on today's noisy quantum machines.
We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about $1\ensuremath{\rightarrow}2$ learning of the measurement, otherwise the task is called $1\ensuremath{\rightarrow}2$ cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension d of the Hilbert space. For $1\ensuremath{\rightarrow}2$ cloning we also propose a simple quantum network that achieves the optimal fidelity. The optimal fidelity for $1\ensuremath{\rightarrow}2$ learning just slightly outperforms the estimate and prepare strategy in which one first estimates the unknown measurement and depending on the result suitably prepares the duplicate.
We study measurements on various subsystems of the output of a universal $\stackrel{\ensuremath{\rightarrow}}{1}2$ cloning machine, and establish a correspondence between these measurements at the output and effective measurements on the original input. We show that one can implement sharp effective measurement elements by measuring only two out of the three output systems. Additionally, certain complete sets of sharp measurements on the input can be realized by measurements on the two clones. Furthermore, we introduce a scheme that allows us to restore the original input in one of the output bits, by using measurements and classical communication---a protocol that resembles teleportation.
Variational Quantum Algorithms (VQA) are one of the most promising candidates for near-term quantum advantage. Traditionally, these algorithms are parameterized by rotational gate angles whose values are tuned over iterative execution on quantum machines. The iterative tuning of these gate angle parameters make VQAs more robust to a quantum machine’s noise profile. However, the effect of noise is still a significant detriment to VQA’s target estimations on real quantum machines — they are far from ideal. Thus, it is imperative to employ effective error mitigation strategies to improve the fidelity of these quantum algorithms on near-term machines.While existing error mitigation techniques built from theory do provide substantial gains, the disconnect between theory and real machine execution characteristics limit the scope of these improvements. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine.We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters -by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements — a mean of over 3x across a variety of VQA applications, run on IBM Quantum machines.More importantly, while we study two specific error mitigation techniques, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a priori. Integrating more mitigation techniques into the VAQEM framework in the future can lead to further formidable gains, potentially realizing practically useful VQA benefits on today’s noisy quantum machines.
Quantum computing offers exponential advantages for problems in cryptography, optimization, and quantum simulation, yet the practicality of current Noisy Intermediate-Scale Quantum (NISQ) devices is severely constrained by decoherence, gate imperfections, and measurement noise. Conventional quantum error correction (QEC) codes such as Steane and surface codes impose large qubit overheads and require high-fidelity logical operations, making them unsuitable for near-term hardware. To address this gap, this work introduces ML-QEM, an adaptive quantum error mitigation framework that employs machine learning to identify and correct dominant Pauli error patterns in real time using only 3–5 ancillary qubits. By integrating Qiskit Aer noise modeling with a lightweight TensorFlow-based classifier, ML-QEM learns device-specific noise characteristics and applies targeted recovery operations with minimal latency. Evaluations across depolarizing, amplitude damping, and thermal relaxation noise models demonstrate a 28.4% average fidelity improvement, 60–84% lower overhead than Steane and surface codes, and a classical processing delay of only 21.7 ms. ML-QEM thus provides an effective and resource-efficient pathway toward enhancing quantum computation fidelity in the NISQ era.