Quantum Statistics in Modern Computing Applications

Exponential quantum advantage in processing massive classical data by John Preskill https://lnkd.in/eUTvGHaX Abstract Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We validate these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP = BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

I’m excited to share this new work from our IBM Quantum team in collaboration with Oak Ridge National Laboratory. This is a major demonstration of what we mean by realizing useful Quantum-centric supercomputing. Building on the chemistry work developed with RIKEN (https://lnkd.in/eK8jW-Wp) last year, and the previous Krylov demonstration with University of Tokyo (https://lnkd.in/eae_8zGc), the IBM Quantum and ORNL teams developed a quantum algorithm for ground states with convergence guarantees similar to phase estimation, while retaining the error mitigation aspect of sample-based methods. Putting together sample-based approaches and Krylov methods, we call this sample-based Krylov quantum diagonalization (SKQD). The algorithm can be used to compute ground state energies of quantum systems for many lattice models relevant in materials science and high-energy physics. SKQD is demonstrated experimentally on 85 qubits and 6,000 two-qubit gates on IBM quantum processors, against the ground state of the Anderson impurity model, obtaining high accuracies for problem sizes beyond the reach of exact diagonalization. This marks one of the largest implementations of quantum diagonalization to date, and points at how quantum computing, combined with classical computation in quantum-centric supercomputing environments, will enable us to push beyond classical methods for interesting applications. These new results also show again how algorithmic discovery is essential, especially for quantum-centric supercomputing architectures. Classical algorithms for materials science have made an impressive progress in the last decades. However, by thinking of quantum-classical workflows where quantum can deliver a value that cannot be matched by classical, we will move closer to demonstrating quantum advantage. Congratulations again to the team on this achievement. Check out the paper here: https://lnkd.in/epwCrG5R.

Google’s 69-Qubit Quantum Simulator Outperforms Supercomputers in Key Calculations Researchers from Google and the PSI Center for Scientific Computing have developed a 69-qubit quantum simulator that can outperform the fastest classical supercomputers in studying complex quantum systems. This breakthrough brings unprecedented accuracy in modeling quantum processes, unlocking new possibilities in materials science, magnetism, and thermodynamics. Key Features of Google’s Quantum Simulator • Combines Digital & Analog Quantum Computing: The simulator supports both universal quantum gates (digital mode) and high-fidelity analog evolution, providing superior performance in cross-entropy benchmarking experiments. • Beyond Classical Computational Limits: This hybrid approach enables calculations that classical supercomputers cannot efficiently simulate, especially in quantum material and energy research. • Specialized for Quantum Simulations: Unlike general-purpose quantum computers, this simulator is optimized for modeling quantum interactions, making it a powerful tool for scientific discovery. Digital vs. Analog Quantum Computing • Digital Quantum Computing: • Uses quantum gates to manipulate qubits, similar to logic gates in classical computing. • Best suited for algorithms, machine learning, and cryptography applications. • Analog Quantum Computing: • Models physical quantum systems directly, simulating real-world interactions with fewer computational steps. • Ideal for studying material science, condensed matter physics, and quantum thermodynamics. Why This Matters • Accelerating Scientific Research: The simulator could help discover new materials, improve energy storage, and refine magnetism-based technologies. • Advancing Quantum Supremacy: By achieving results beyond classical computation, this simulator cements Google’s lead in quantum research. • Potential for Quantum AI Integration: Combining digital and analog approaches may enhance machine learning models and optimize large-scale computations. What’s Next? • Expanding Qubit Count: Google may scale up its hybrid quantum simulations, pushing closer to full-scale quantum supremacy. • Exploring More Applications: Future research could apply these simulations to biophysics, drug discovery, and nuclear physics. • Potential Industry Collaborations: Google’s breakthrough may lead to partnerships in materials engineering and quantum-enhanced AI systems. This 69-qubit quantum simulator represents a major leap in computational power, proving that quantum systems can now surpass supercomputers in specialized scientific tasks, bringing us closer to practical quantum applications.

Interesting approach alert! QUBO-based SVM tested on QPU (Neutral Atoms). A recent study, "QUBO-based SVM for credit card fraud detection on a real QPU," explores the application of a novel quantum approach to a critical cybersecurity challenge: credit card fraud detection. Here are some of the key findings: * QUBO-based SVM model: The study successfully implemented a Support Vector Machine (SVM) model whose training is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem. This approach could leverage the capabilities of quantum processors. * Performance: The results demonstrate that a version of the QUBO SVM model, particularly when used in a stacked ensemble configuration, achieves high performance with low error rates. The stacked configuration uses the QUBO SVM as a meta-model, trained on the outputs of other models. * Noise robustness: Surprisingly, the study observed that a certain amount of noise can lead to enhanced results. This is a new phenomenon in quantum machine learning, but it has been seen in other contexts. The models were robust to noise both in simulations and on the real QPU. * Scalability: Experiments were extended up to 24 atoms on the real QPU, and the study showed that performance increases as the size of the training set increases. This suggests that even better results are possible with larger QPUs. Practical implications: This research highlights the potential of quantum machine learning for real-world applications, using a hybrid approach where the training is performed on a QPU and the testing on classical hardware. This approach makes the model applicable on current NISQ devices. The model is also advantageous because it uses the QPU only for training, reducing costs and allowing the trained model to be reused. * Ideal for cybersecurity and regulatory issues: The study also observed that the model preserves data privacy because only the atomic coordinates and laser parameters reach the QPU, and the model test is done locally. Here the article: https://lnkd.in/d5Vfhq2G #quantumcomputing #machinelearning #cybersecurity #frauddetection #neutralatoms #QPU #NISQ #quantumml #fintech #datascience

> Sharing resource < Big paper this morning: "Quantum advantage for learning shallow neural networks with natural data distributions" by Laura Lewis, Dar Gilboa, and Jarrod R. McClean Abstract: The application of quantum computers to machine learning tasks is an exciting potential direction to explore in search of quantum advantage. In the absence of large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum probably approximately correct (PAC) and quantum statistical query (QSQ) models have been proposed to study quantum algorithms for learning classical functions. Despite numerous works investigating quantum advantage in these models, we nevertheless only understand it at two extremes: either exponential quantum advantages for uniform input distributions or no advantage for potentially adversarial distributions. In this work, we study the gap between these two regimes by designing an efficient quantum algorithm for learning periodic neurons in the QSQ model over a broad range of nonuniform distributions, which includes Gaussian, generalized Gaussian, and logistic distributions. To our knowledge, our work is also the first result in quantum learning theory for classical functions that explicitly considers real-valued functions. Recent advances in classical learning theory prove that learning periodic neurons is hard for any classical gradient-based algorithm, giving us an exponential quantum advantage over such algorithms, which are the standard workhorses of machine learning. Moreover, in some parameter regimes, the problem remains hard for classical statistical query algorithms and even general classical algorithms learning under small amounts of noise. Link: https://lnkd.in/e65uhbKS #quantumadvantage #quantummachinelearning #quantumalgorithm #research #paper