#QuantumSupportVectorMachine

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Cirq: Google’s Open-Source Python Quantum Circuit Framework

Cirq, what?

Python programming framework Cirq is open-source. With them, you may design, edit, modify, optimise, and activate quantum circuits. Google AI Quantum released Cirq as a public alpha on July 18, 2018. This Apache 2 license allows it to be modified or integrated into any open-source or commercial program.

Goal and Focus

Designed for Noisy Intermediate Scale Quantum computers and algorithms. NISQ computers are noise-sensitive systems with 50–100 qubits and high-fidelity quantum gates, or fewer than a few hundred. Current quantum algorithm research focusses on NISQ circuits, which work without error correction, because they may offer a quantum advantage on near-term devices.

The methodology helps researchers determine whether NISQ quantum computers can tackle real-world computational problems by focussing on short-term challenges. It provides abstractions for NISQ computers, where hardware details are crucial to cutting-edge results.

It lets users organise gates on the device, plan time within quantum hardware constraints, and specify gate behaviour using native gates to precisely manage quantum circuits. Cirq data structures are optimised for building NISQ quantum circuits to help users maximise their use. Cirq's architecture targets NISQ circuits, so researchers and developers can experiment with them and find noise-reducing ways.

Key traits and talents

Cirq has many quantum circuit capabilities:

Circuit Manufacturing/Manipulation This provides a flexible and easy interface for designing quantum circuits. User-defined measurements, qubits, and quantum gates can match their mathematical description. Custom and flexible gate definitions are supported by the framework. Users can learn about moments, insertion strategies, and qubit gates to build quantum circuits. Symbolic variable parameterised circuits work too. Circuits can be chopped, sliced, and diced to improve them.

Hardware modelling Hardware restrictions drastically affect a circuit's feasibility on modern hardware. Cirq devices can manage these constraints. Noise and hardware device modelling are supported.

Modelling Cirq includes density matrix and wave function integrated quantum circuit simulators. These simulators can handle noisy quantum channels with full density matrix or Monte Carlo simulations. Cirq connects with cutting-edge wave function simulators like qsim for high-performance simulation. The Quantum Virtual Machine (QVM) can emulate quantum hardware with these simulators. Quantum circuit simulation is vital for algorithm development and testing before hardware implementation.

Optimising and Transforming Circuits Optimisation, compilation, and circuit transformation are framework functions. Many quantum circuit optimisers for hardware testing are included.

Implementing Hardware Cirq is cloud-integrable with larger simulators or future quantum hardware. It simplifies quantum circuit operation for quantum processors. Cirq lets users run quantum circuits on Google's quantum hardware via its Quantum Computing Service. The Google AI Quantum team designs circuits for Google's Bristlecone processor using Cirq as a programming interface and plans to make it cloud-available. It can also submit quantum circuits to cloud platforms like Azure Quantum for execution on QPUs, IonQ, and Quantinuum simulators.

Interoperability It supports SciPy and NumPy. Cross-platform, it supports Linux, MacOS, Windows, and Google Colab.

Applications and use cases

Cirq is crucial to Quantum Machine Learning (QML), which combines machine learning and quantum computing. QML uses quantum computing to speed up machine learning. Cirq implements quantum machine learning algorithms on NISQ devices. Quantum neural networks mimic neuronal behaviour to find patterns and predict.

Quantum Support Vector Machine (QSVM) algorithms can be built on Cirq using quantum circuits for linear algebra operations and quantum feature maps to encode data into quantum states. Quantum SVM algorithms exist. Cirq Quantum implementations of popular machine learning methods have been made.

Cirq can be used to test quantum algorithms like the Quantum Approximate Optimisation Algorithm (QAOA) and Variational Quantum Eigensolver (VQE) for machine learning applications. QAOA, a hybrid quantum-classical technique, handled combinatorial optimisation problems.

Quantum computers, which can be duplicated using Cirq, are perfect for optimisation problems because they can investigate numerous answers. This reduces training time and finds optimal machine learning model parameters.

Cirq is also used in machine learning to create quantum versions of classical algorithms like decision trees, apply quantum error correction to improve model robustness, simulate chemical reactions for drug discovery, and encode classical data into quantum states. Many quantum gate functions are needed to build complex machine learning circuits with Cirq.

This is used for QML and Google quantum processor end-to-end tests. Early adopters of Cirq simulated quantum autoencoders, implemented QAOA, integrated it into hardware assessment software, simulated physical models like the Anderson Model, and integrated it with quantum compilers.

Close-term algorithms in quantum chemistry challenges can be facilitated by OpenFermion-Cirq.

Support and Community

Over 200 people contributed. Researchers, software engineers, technical writers, and students are encouraged to contribute to its open and inclusive community. Communities organise weekly virtual open source meetings including Quantum Circuit Simulation Weekly Sync, TensorFlow Quantum Weekly Sync, OpenFermion Weekly Sync, and Cirq Weekly Sync.

On Quantum Computing Stack Exchange, utilise the cirq tag for Cirq questions. GitHub provides good initial issues and contribution criteria for programming contributors. Larger features use an RFC (Request for Comment). The Quantum AI website's Cirq home page offers examples, reference documentation, and text-based, Jupyter notebook, and video tutorials. Releases occur every three months.

Combinations

Google Quantum AI's open-source software stack includes Cirq. It includes the open-source hybrid quantum-classical machine learning library TensorFlow Quantum. It also interacts with OpenFermion family libraries for chemistry and material science. More integrated Google stack products include Qualtran for fault-tolerant quantum computing, Stim for huge Clifford circuits and quantum error correction, ReCirq for Cirq experiments, and Qsim for high-performance simulation. Use Cirq to submit quantum circuits to third-party cloud services like Microsoft Azure Quantum to access IonQ and Quantinuum hardware.

Conclusion

Finally, Google's Quantum AI team developed Cirq, an open-source Python framework for NISQ quantum computer creation and experimentation. Its full circuit design control, robust simulation capabilities, and interfaces for executing circuits on real quantum hardware and integrated simulators make it crucial in quantum machine learning research.

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Quantum Support Vector Machines In Prostate Cancer Detection

Quantum SVMs

Recent studies show that  Quantum Machine Learning (QML) techniques, particularly Quantum Support Vector Machines (QSVMs), can improve disease detection, especially in complex and unbalanced healthcare datasets. In datasets for diabetes, heart failure, and prostate cancer, quantum models outperform conventional machine learning methods in key areas.

Modern medicine struggles to accurately and earlyly diagnose diseases. Unbalanced datasets in medicine, where there are often many more positive examples than negative cases, are a key impediment. This imbalance makes standard machine learning algorithms perform worse. Scientists are investigating whether quantum computing, which uses entanglement and superposition, can improve pattern recognition in these tough scenarios.

A comparative analysis by Tudisco et al. and published by Quantum Zeitgeist compared QNNs and QSVMs to classical algorithms like Logistic Regression, Decision Trees, Random Forests, and classical SVMs. Quantum methods were tested on prostate cancer, heart failure, and diabetic healthcare datasets to overcome unbalanced data.

QSVMs outperform QNNs and classical models on all datasets. This suggests quantum models excel at difficult categorisation problems. This superiority was notably evident in datasets with significant imbalance, a common healthcare issue. The Heart Failure dataset is severely imbalanced, and standard methods often fail to achieve high recall. Quantum models did better. Quantum models, particularly QSVMs, performed better at detecting positive examples (high recall) in these situations, implying improved diagnosis accuracy in complex clinical scenarios. Quantum models look more beneficial with class difference.

QNNs had good precision scores but overfitted training data, limiting their usefulness. Overfitting occurs when a model learns the training data too well and catches noise and features instead of essential patterns, reducing generalisation performance on unseen data. However, QSVMs were more resilient and reliable. QSVM's high recall across all datasets shows its ability to dependably identify positive cases in various clinical scenarios. Avoiding overfitting in QNNs may require studying alternate circuit design and hyperparameter tuning.

A study called “Quantum Support Vector Machine for Prostate Cancer Detection: A Performance Analysis” examined how QSVM could improve prostate cancer detection over regular SVM. Early identification improves prostate cancer treatment and results. Classical SVMs increase biomedical data interpretation, but large, high-dimensional datasets limit them. QSVMs, which use quantum notions like superposition and entanglement, can manage multidimensional data and speed up operations.

The prostate cancer technique used the Kaggle Prostate Cancer Dataset, which initially comprised 100 observations with 9 variables, including clinical and diagnostic data. The dataset's initial class imbalance was corrected using RandomOverSampler during preparation. The data was normalised and normalised using MinMaxScaler and StandardScaler to increase feature comparability and prepare for quantum encoding. Oversampled to 124 samples, processed data was divided into training (80%) and testing (20%) subsets.

The QSVM approach relied on a quantum feature map architecture, the ZZFeatureMap with full entanglement, carefully selected and tested to match the dataset. This feature map encodes conventional data into quantum states, allowing the quantum system to express complex data correlations in high-dimensional regions using entanglement. QSVM estimates the inner product (overlap) of quantum states that represent data points to generate the kernel function for SVM classification. This estimator measures the likelihood of witnessing the starting state using a quantum circuit.

Prostate cancer experiments provide compelling evidence:

Kernel matrix analysis revealed different patterns. The RBF kernel of the classical SVM showed high similarity values across data points, suggesting a strongly connected feature space. However, QSVM's ZZFeatureMap produced a more dispersed feature space with fewer high off-diagonal values. This implies that the quantum feature space's unique properties boosted class distinguishability.

QSVM outperformed classical SVM (87.89% accuracy, 85.42% sensitivity) on the training dataset with 100% accuracy and sensitivity. As shown, the quantum feature map distinguishes classes without overlap during training.

On the test dataset, both models were 92% accurate. QSVM surpassed SVM in essential medical diagnostic measures, with 100% sensitivity and 93.33% F1-Score on test data, compared to 92.86% and 92.86% for SVM.

Importantly, the QSVM model had no False Negatives (missing malignant cases) in the test data. Only one False Negative occurred in the SVM model. QSVM's great sensitivity is vital in medical circumstances when a false negative could lead to an ailment going undiagnosed and untreated. Quantum feature mapping increases class separation and allows more complex representations.

Cross-validation studies demonstrated that the SVM model was more stable across data subsets than the QSVM, suggesting that the QSVM model overfitted to the training data despite its great performance on the test set. We discuss how QSVM's improved sensitivity and F1-Score aid medical diagnosis. Quantum feature mapping's ability to create a unique, dispersed feature space, especially when separating complex data points, improves performance. QSVM was used to categorise prostate cancer datasets for the first time.