Quantum computing has holds considerable potential for accelerating computational tasks beyond the capabilities of classical computation. However, a major obstacle arises from the delicate nature of quantum hardware, where quantum gates and qubits, the fundamental components of a quantum circuit (QC), are vulnerable to external interference. Consequently, even a simple QC can produce significantly noisy output. This noise introduces uncertainty, making it difficult to ascertain whether the output represents meaningful computation or merely random noise. This uncertainty raises questions regarding the fidelity of a QC and the extent to which we can rely on its output. Existing classification-based approaches for output estimation have limitations, including the potential for incorrect results due to misclassification or the requirement for a large number of measurements, which can be expensive. To circumvent this, in this paper, we propose QuEST, which introduces an efficient technique for estimating the output of a QC by analyzing probability distributions of post-measurement data. Specifically, the QuEST framework employs Gaussian distribution functions to compare the measured distribution of a circuit with a pre-trained distribution obtained from a training circuit dataset. Moreover, we reformulate this problem by leveraging the properties of sequential time series, thereby deriving a straightforward and intuitive metric to measure the confidence of the QC output. By utilizing this metric, the QuEST framework monitors fidelity evolution over time as the QC interacts with its external environment, enabling the system to preemptively halt QC execution upon reaching a specified confidence threshold. When evaluated against state-of-the-art benchmark quantum circuits, our proposed QuEST framework accurately estimates the output of
100% of the benchmark circuits, while significantly achieving speedup up to
58.3× compared to a standard QC execution. These results highlight the efficiency of our framework and its potential for practical quantum computing applications.
We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum nondemolition. Despite several claims of “measuring noncommuting observables” in the physics literature, we show that we are always measuring commuting processes. Our main interest is in the notion of quantum smoothing, or retrodiction. In particular, we examine proposals to estimate the result of an external measurement made on an open quantum systems during a period where it is also undergoing continuous monitoring. A full analysis shows that the nondemolition principle is in place, and so a well-posed statistical inference problem can be formulated. We extend the formalism to consider multiple independent external measurements made on the system over the course of a continual period of monitoring.
Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric Rényi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric Rényi relative entropy for the interval α∈ (0 , 1) of the Rényi parameter α. In channel estimation, these results imply a condition for the unattainability of Heisenberg scaling, while in channel discrimination, they lead to improved bounds on error rates in the Chernoff and Hoeffding error exponent settings. More generally, we introduce the amortized quantum Fisher information as a conceptual framework for analyzing general sequential protocols that estimate a parameter encoded in a quantum channel. We then use this framework, beyond the aforementioned application, to show that Heisenberg scaling is not possible when a parameter is encoded in a classical–quantum channel. We then identify a number of other conceptual and technical connections between the tasks of estimation and discrimination and the distinguishability measures involved in analyzing each. As part of this work, we present a detailed overview of the geometric Rényi relative entropy of quantum states and channels, as well as its properties, which may be of independent interest.