Quantum Bayesian Network Approximation via Markov Moralization
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Solution Overview
Problem
Current quantum computing systems struggle to represent and compute directed graphical models, particularly Bayesian networks, using topologies corresponding to undirected graphs, which are more complex and less compact, making them challenging to train and infer.
Innovation Solution
The system transforms a Bayesian network into a Markov network, utilizing a quantum processor with symmetric qubit coupling, allowing the quantum processor to execute the Markov network representation, and generates samples to determine parameters for approximating predictions, leveraging moralization and Boltzmann machine structures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a quantum processor with symmetric coupling is used to represent a Bayesian network, then the problem can be mapped to the quantum processor topology, but the representation becomes less compact and more complex
Solution Approach 1:
The patent introduces a Markov network as an intermediary representation that bridges the gap between Bayesian networks and quantum processor topologies. The Markov network serves as a mediator that can be represented on undirected graph quantum processors while preserving the essential probabilistic relationships needed for inference
Solution Approach 2:
The patent transforms the graphical model representation by changing parameters - specifically converting from directed edges in Bayesian networks to undirected edges in Markov networks. This parameter change allows the model to be compatible with symmetric coupling quantum processors while maintaining computational functionality
2Productivity
If a Markov network is used instead of a Bayesian network, then the quantum processor can execute the model, but training and inference become more challenging and computationally intensive
Solution Approach 1:
The patent performs preliminary action by pre-processing the Bayesian network into a Markov network representation before quantum processing. This includes moralization of the graph and parameter transformation, which prepares the model in advance for quantum execution while reducing the computational burden during actual quantum inference
3Device complexity
If directed edges are used to represent causal relationships, then the representation is compact and inference is straightforward, but the quantum processor topology cannot be directly utilized
Solution Approach 1:
The patent addresses the asymmetry between directed edges in Bayesian networks and symmetric coupling in quantum processors by transforming the directed graph into an undirected Markov network. This removes the directional asymmetry while preserving the essential probabilistic dependencies through the moralization process
Data Source
AI summary
Techniques are provided for computing problems represented as directed graphical models via quantum processors with topologies and coupling physics which correspond to undirected graphs. These include techniques for generating approximations of Bayesian networks via a quantum processor capable of computing problems based on a Markov network-based representation of such problems. Approximations may be generated by moralization of Bayesian networks to Markov networks, learning of Bayesian networks' probability distributions by Markov networks' probability distributions, or otherwise, and are trained by executing the resulting Markov network on the quantum processor.