QuEST: Quantum Circuit Output Estimation using Gaussian Distribution Analysis

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 $58.3 \times$ compared to a standard QC execution. These results highlight the efficiency of our framework and its potential for practical quantum computing applications.