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Design, Automation, and Test in Europe

Quantum Measurement Discrimination using Cumulative Distribution Functions

Zachery Utt, Daniel Volya, Prabhat Mishra

Published Apr 1, 2023• 6 citations
Publisher

Abstract

Quantum measurement is one of the critical steps in quantum computing that determines the probabilities associated with qubit states after conducting several circuit ex-ecutions and measurements. As a mesoscopic quantum system, real quantum computers are prone to noise. Therefore, a major challenge in quantum measurement is how to correctly inter-pret the noisy results of a quantum computer. While there are promising classification based solutions, they either produce incorrect results (misclassify) or require many measurements (expensive). In this paper, we present an efficient technique to estimate a qubit's state through analysis of probability distributions of post-measurement data. Specifically, we estimate the state of a qubit using cumulative distribution functions to compare the measured distribution of a sample with the distributions of basis states$\vert 0\rangle$and$\vert 1\rangle$. Our experimental results demonstrate a drastic reduction (78%) in single qubit readout error. It also provides significant reduction (12%) when used to boost existing multi-qubit discriminator models.

DOI
10.23919/date56975.2023.10136989

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Quantum measurement is one of the critical steps in quantum computing that determines the probabilities associated with qubit states after conducting several circuit ex-ecutions and measurements. As a mesoscopic quantum system, real quantum computers are prone to noise. Therefore, a major challenge in quantum measurement is how to correctly inter-pret the noisy results of a quantum computer. While there are promising classification based solutions, they either produce incorrect results (misclassify) or require many measurements (expensive). In this paper, we present an efficient technique to estimate a qubit's state through analysis of probability distributions of post-measurement data. Specifically, we estimate the state of a qubit using cumulative distribution functions to compare the measured distribution of a sample with the distributions of basis states∣0⟩\vert 0\rangle∣0⟩and∣1⟩\vert 1\rangle∣1⟩. Our experimental results demonstrate a drastic reduction (78%) in single qubit readout error. It also provides significant reduction (12%) when used to boost existing multi-qubit discriminator models.
Interpreting the results of a quantum computer can pose a significant challenge due to inherent noise in these mesoscopic quantum systems. Quantum measurement, a critical component of quantum computing, involves determining the probabilities linked with quantum states post-multiple circuit computations based on quantum readout values provided by hardware. While there are promising classification-based solutions, they can either misclassify or necessitate excessive measurements, thereby proving to be costly. This article puts forth an efficient method to discern the quantum state by analyzing the probability distributions of data post-measurement. Specifically, we employ cumulative distribution functions to juxtapose the measured distribution of a sample against the distributions of basis states. The efficacy of our approach is demonstrated through experimental results on a superconducting transmon qubit architecture, which shows a substantial decrease (88%) in single qubit readout error compared to state-of-the-art measurement techniques. Moreover, we report additional error reduction (12%) compared to state-of-the-art measurement techniques when our technique is applied to enhance existing multi-qubit classification techniques. We also demonstrate the applicability of our proposed method for higher dimensional quantum systems, including classification of single qutrits as well as multiple qutrits.
Quantum computers promise a potentially disruptive approach to improving computation in fields such as physics, chemistry, cryptography, optimisation, and machine learning. However, testing quantum computations for faults is currently impractical because of the existence of noise and errors associated with the output. Executing in a quantum system a circuit with only a few valid output states can generate a significant number of implausible states that have zero probability in an ideal computation. Among other sources of noise, readout errors come from the difficulty of discriminating a measurement between 0 and 1 for the different qubits. These issues are affected by readout drift, requiring regular recalibration of the process. In this paper, we provide a novel technique for post-computation analysis of the output probability distributions that permits better discrimination of kerneled data, delaying the need for recalibration. We achieve this by altering the linear discrimination of the final output states by way of a dynamic state selection process that combines Gaussian mixture models with a probability threshold. As an initial assessment of the technique we examine its effect on three to five qubits GHZ states. Our results on almost every one of nine IBM quantum computers show that the number of implausible states is reduced significantly and that the resulting probability distribution is closer to the expected one.
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%100 \%100% of the benchmark circuits, while significantly achieving speedup up to 58.3×58.3 \times58.3× compared to a standard QC execution. These results highlight the efficiency of our framework and its potential for practical quantum computing applications.
Accurate quantum state discrimination is critical for reliable qubit readout in current superconducting quantum processors, as it enables precise measurement outcomes, reduces readout-induced errors, and improves the overall reliability of quantum algorithm execution. Recently, machine learning (ML) techniques have been explored to enhance quantum state discrimination, outperforming traditional methods based on static thresholds. However, these approaches rely on hard-decision schemes that assign binary outcomes without accounting for readout uncertainty, thereby disregarding signal-level variations that can degrade measurement fidelity. This article introduces a measurement-aware classification approach based on Fuzzy C-means (FCM) clustering combined with data filtering, enabling soft-decision readout discrimination through confidence-based shot selection. Experimental validation was conducted on four different real IBM quantum devices, including single- and two-qubit readout scenarios, as well as multi-qubit circuits preparing GHZ and W-state with up to 10 qubits. Results show that the proposed method consistently outperforms state-of-the-art ML-based discriminators in terms of assignment fidelity and state reconstruction accuracy, demonstrating its effectiveness for enhancing readout quality in near-term quantum computing platforms. Quantitatively, the FCM-based discriminator yields 2–3% assignment fidelity improvements in single- and two-qubit readout and statistically significant gains in over 94% of GHZ and 97% of W multi-qubit experiments.
Abstract Measurement errors in quantum computers are very detrimental to quantum computations. The ability to efficiently and accurately readout quantum states is crucial for quantum error correction schemes and quantum algorithms. Readout fidelity is typically limited by a poor signal-to-noise (SNR) ratio between the quantum states we intend to classify, as well as energy relaxation (e.g., T1T_1T1​ decay) from an excited state to a lower state during readout. Superconducting quantum bits (qubit), one of the leading candidates for scalable quantum computing hardware, are particularly limited by energy relaxation due to their relatively short coherence times. While most approaches for classifying the results of readout on superconducting qubits typically utilize clustering algorithms (e.g., a Gaussian mixture model) on integrated readout signals, these cannot distinguish between a quantum bit that was in the ground state prior to measurement from a qubit that decays to the ground state during measurement. For this reason, we instead propose using machine learning (ML) on the raw (non-integrated) analog signal and classification models on the full time series data (i.e., the \emph{trajectory}). We observe that time series classification methods, such as our chosen long short-term memory (LSTM) model, in combination with filtering and feature engineering techniques, consistently outperform clustering models. In particular, we find that the largest improvements come from reclassifying points in the boundary regions between neighboring clusters. These boundary points correspond to measurement records that deviate from the typical cluster, likely due to transient or noisy features in the signal that are not captured when the data is integrated. By retaining temporal information, sequence-aware models such as LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassifications.
Quantum state estimation and discrimination are important tasks not only for many quantum information protocols but also precise measurements. In this paper, we report our recent efforts on this issue. In the first part, we report adoptive quantum state estimation, which provides the most accurate estimation using an optimal measurement basis for each measurement. In the second part, we introduce quantum state data mining where the erroneous states (density matrices) are discriminated from the normal ones efficiently using machine learning method.