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arXiv:2201.07265 · IEEE Transactions on Quantum Engineering

EP-PQM: Efficient Parametric Probabilistic Quantum Memory With Fewer Qubits and Gates

Mushahid Khan, Jean Paul Latyr Faye, Udson C. Mendes, Andriy V. Miranskyy

Published Jan 1, 2022• 8 citations
arXivHTMLPDF

Abstract

Machine learning (ML) classification tasks can be carried out on a quantum computer (QC) using probabilistic quantum memory (PQM) and its extension, parametric PQM (P-PQM), by calculating the Hamming distance between an input pattern and a database of$r$patterns containing$z$features with$a$distinct attributes. For PQM and P-PQM to correctly compute the Hamming distance, the feature must be encoded using one-hot encoding, which is memory intensive for multiattribute datasets with$a>2$. We can represent multiattribute data more compactly by replacing one-hot encoding with label encoding; both encodings yield the same Hamming distance. Implementing this replacement on a classical computer is trivial. However, replacing these encoding schemes on a QC is not straightforward because PQM and P-PQM operate at the bit level, rather than at the feature level (a feature is represented by a binary string of 0’s and 1’s). We present an enhanced P-PQM, called efficient P-PQM (EP-PQM), that allows label encoding of data stored in a PQM data structure and reduces the circuit depth of the data storage and retrieval procedures. We show implementations for an ideal QC and a noisy intermediate-scale quantum (NISQ) device. Our complexity analysis shows that the EP-PQM approach requires$O(z \log _{2}(a))$qubits as opposed to$O(za)$qubits for P-PQM. EP-PQM also requires fewer gates, reducing gate count from$O(rza)$to$O(rz\log _{2}(a))$. For five datasets, we demonstrate that training an ML classification model using EP-PQM requires 48% to 77% fewer qubits than P-PQM for datasets with$a>2$. EP-PQM reduces circuit depth in the range of 60% to 96%, depending on the dataset. The depth decreases further with a decomposed circuit, ranging between 94% and 99%. EP-PQM requires less space; thus, it can train on and classify larger datasets than previous PQM implementations on NISQ devices. Furthermore, reducing the number of gates speeds up the classification and reduces the noise associated with deep quantum circuits. Thus, EP-PQM brings us closer to scalable ML on an NISQ device.

DOI
10.1109/tqe.2022.3169987

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Machine learning (ML) classification tasks can be carried out on a quantum computer (QC) using probabilistic quantum memory (PQM) and its extension, parametric PQM (P-PQM), by calculating the Hamming distance between an input pattern and a database ofrrrpatterns containingzzzfeatures withaaadistinct attributes. For PQM and P-PQM to correctly compute the Hamming distance, the feature must be encoded using one-hot encoding, which is memory intensive for multiattribute datasets witha>2a>2a>2. We can represent multiattribute data more compactly by replacing one-hot encoding with label encoding; both encodings yield the same Hamming distance. Implementing this replacement on a classical computer is trivial. However, replacing these encoding schemes on a QC is not straightforward because PQM and P-PQM operate at the bit level, rather than at the feature level (a feature is represented by a binary string of 0’s and 1’s). We present an enhanced P-PQM, called efficient P-PQM (EP-PQM), that allows label encoding of data stored in a PQM data structure and reduces the circuit depth of the data storage and retrieval procedures. We show implementations for an ideal QC and a noisy intermediate-scale quantum (NISQ) device. Our complexity analysis shows that the EP-PQM approach requiresO(zlog⁡2(a))O(z \log _{2}(a))O(zlog2​(a))qubits as opposed toO(za)O(za)O(za)qubits for P-PQM. EP-PQM also requires fewer gates, reducing gate count fromO(rza)O(rza)O(rza)toO(rzlog⁡2(a))O(rz\log _{2}(a))O(rzlog2​(a)). For five datasets, we demonstrate that training an ML classification model using EP-PQM requires 48% to 77% fewer qubits than P-PQM for datasets witha>2a>2a>2. EP-PQM reduces circuit depth in the range of 60% to 96%, depending on the dataset. The depth decreases further with a decomposed circuit, ranging between 94% and 99%. EP-PQM requires less space; thus, it can train on and classify larger datasets than previous PQM implementations on NISQ devices. Furthermore, reducing the number of gates speeds up the classification and reduces the noise associated with deep quantum circuits. Thus, EP-PQM brings us closer to scalable ML on an NISQ device.
Quantum Machine Learning (QML) is a new domain of Machine Learning (ML) and Quantum Computing (QC) that uses a trainable Variational Quantum Circuit (VQC) to solve various learning problems. Classical data is transformed to the quantum Hilbert space using an embedding scheme and the VQC performs quantum operations on this transformed quantum data using parametric quantum gates. In this work, we present a new embedding scheme using Quantum Random Access Memory (QRAM) that takes address as input, and gives data as the output similar to a classical Random Access Memory (RAM). We propose a basic circuit-based QRAM architecture and its application in, (a) storage for ML usage and, (b) storage of binary data. For ML, we store images of digits dataset into the QRAM and perform binary classification using a Quantum Neural Network (QNN). We observe that QNN driven by the proposed QRAM converges faster (at6th6^{th}6thepoch) with 100% classification accuracy compared to QNN with normal embedding and classical Fully Connected Neural Network (FCNN) setups which converge with same accuracy at around10th10^{th}10thand15th15^{th}15thepochs, respectively. We obtain≈63%\approx 63\%≈63%classification accuracy on real hardware from IBM. For storage of binary data, we measure Hamming Distance (HD) and percentage correct predictions for quality evaluation of the proposed QRAM. We observe that the HD and percentage correct predictions worsens as the number of address lines increases. We propose two techniques to improve the QRAM accuracy namely, (i) clustering of raw data and allocating one QRAM per cluster and, (ii) bit splitting to divide wider data into smaller chunks and allocating one QRAM per split. Clustering provides best results by improving the HD for 9-address QRAM by≈1.95X\approx 1.95\text{X}≈1.95Xthan pure QRAM and≈1.74X\approx 1.74\text{X}≈1.74Ximprovement compared to bit-split (which provides≈1.11X\approx 1.11\text{X}≈1.11Ximprovement than pure QRAM).
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum advantage. In quantum machine learning applications for example, a quantum memory can simplify the data loading process and potentially accelerate the learning task. Quantum memory can also store intermediate quantum state of qubits that can be reused for computation. However, the depth, gate count and compilation time of quantum memories such as, Quantum Read Only Memory (QROM) scale exponentially with the number of address lines making them impractical in state-of-the-art Noisy Intermediate-Scale Quantum (NISQ) computers beyond 4-bit addresses. In this paper, we propose techniques such as, pre-decoding logic and qubit reset to reduce the depth and gate count of QROM circuits to target wider address ranges such as, 8-bits. The proposed approach reduces the number of gates and depth count by at least 2X compared to the naive implementation at only 36% qubit overhead. A reduction in circuit depth and gate count as high as 75X and compilation time by 85X at the cost of a maximum of 2.28X qubit overhead is observed. Experimentally, the fidelity with the proposed pre-decoding circuit compared to existing optimization approach is also higher (as much as 73% compared to 40.8%) under reduced error rates.
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.
Quantum Random Access Memory (QRAM) plays a pivotal role in accelerating quantum algorithms, especially in quantum machine learning. However, its implementation on noisy intermediate-scale quantum (NISQ) computers faces major challenges due to high qubit requirements and large circuit depth. These factors amplify quantum noise, limiting QRAM performance and scalability. In this work, we introduce a gate-pruning strategy that mitigates noise while preserving QRAM functionality. Our approach reduces circuit depth by eliminating small-angle rotation gates which are particularly noise-sensitive on NISQ hardware. This pruning significantly improves QRAM resilience without compromising data-loading efficiency or superposition-based querying. We further show that the pruned QRAM supports a variational quantum classifier capable of parallel training with logarithmic qubit scaling. Experiments on benchmark datasets confirm that our approach enhances noise resilience and classification accuracy, underscoring its potential for practical quantum machine learning in the NISQ era.
When it comes to realizing immediate quantum advantages in practical applications like machine learning and optimization techniques, numerous methods have emerged as a frontrunner technique. Such algorithms often involve quantum circuits for data encoding and the training of Quantum Neural Networks (QNNs) to minimize target functions when applied to tasks involving classical data. Quantum Machine Learning (QML) is a promising area of quantum computing because it may effectively handle difficult learning tasks by taking advantage of the high dimensional Hilbert space to train better representations from limited data. Despite QML's rising popularity, few academic works have addressed the language's security features. There has been a lot of buzz about the promising new discipline of quantum machine learning. Training a parameterized quantum circuit is a common practice in contemporary QML for performing data analysis on classical or quantum datasets. To make accurate predictions on an independent test dataset, state-of-the-art QML techniques first variationally optimize a parameterized quantum circuit using the training dataset. Quantum modeling in QML has also been shown to offer an exponential benefit in sample complexity. In the realms of pattern recognition, machine learning, and data mining, feature dimensionality reduction as a crucial link in the process has become one hot and tough spot. Most academics have gravitated towards this topic because of the difficulty of its studies. The goal of this research is to learn how to implement low loss in the procedure of feature dimension reduction, preserve the integrity of the original data, locate the most effective mapping, and obtain the best possible low-dimensional data. Preliminary findings suggest that QML models may offer advantages over classical models for classical data analysis. In this paper, a thorough investigation into generalization performance in QML is performed. This paper presents a brief survey on Qubits Encoding using Quantum Machine Learning models that help researchers to identify the limitations of the existing models and to design new efficient models for better performance levels.
Machine learning is a powerful tool which, when given the availability of comprehensive datasets, required training iterations and the necessary resources to support them, can achieve impressive results in a variety of classification tasks. In this paper, we put forward a quantum alternative for users that do not posses the ability to gather and store large amounts of data to be used subsequently in lengthy training iterations. A light-weight probabilistic quantum binary classifier can be built by encoding the two chosen class representatives (images) into quantum vectors, such that a Principal Component decomposition can express the differences between them only along one dimension (basis vector). A standard measurement in the computational basis will then project any transformed input sample along one of the two classes. The classifier accepts quantum representations of images as input, which require exponentially fewer number of quantum bits compared with the number of classical bits used to store an image. The technique is illustrated on a "proof of concept" example, in which a quantum character recognizer is built to label any input sample image as either letter {\bf A} or {\bf P}. The quantum classifier can be tuned to "favor" any of the two classes and the measurement probabilities follow closely how far an input sample is from the two class representatives. Despite its relative simplicity, the quantum classifier can distinguish between the standard letter {\bf A} and the standard letter {\bf P} with 98%98\%98% accuracy. In principle, the procedure can be applied to any image classification task, including gray-scale and color images, as well as classification problems in which an input sample is characterized by a collection of properties given by their values.