Variational algorithms are a class of algorithms used in quantum computing and machine learning to approximate complex probability distributions by optimizing a parameterized family of simpler distributions. They are particularly useful in scenarios where exact solutions are intractable, leveraging techniques like variational inference to efficiently find approximate solutions.

Variational Algorithms

Variational algorithms

Quantum computing leverages the principles of quantum mechanics to process information in ways that classical computers cannot, using qubits that can exist in multiple states simultaneously. This allows for potentially exponential increases in computing power, enabling solutions to complex problems in fields like cryptography, optimization, and materials science.

quantum computing

Machine learning is a subset of artificial intelligence that involves the use of algorithms and statistical models to enable computers to improve their performance on a task through experience. It leverages data to train models that can make predictions or decisions without being explicitly programmed for specific tasks.

machine learning

complex probability distributions

Parameterized family of distributions

simpler distributions

Exact solutions refer to precise and analytical solutions to mathematical problems or equations, without approximations or numerical methods. They are crucial in understanding the underlying mechanics of complex systems, providing insights that are often not evident through numerical simulations alone.

exact solutions

Intractable solutions

Variational inference is a technique in Bayesian statistics that approximates complex posterior distributions through optimization, offering a scalable alternative to traditional sampling methods like Markov Chain Monte Carlo. It transforms the inference problem into an optimization problem by introducing a family of simpler distributions and finding the closest match to the true posterior using the Kullback-Leibler divergence.

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