Quantum Boltzmann Machine Equilibrium Sampling via Hybrid Architecture
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Solution Overview
Problem
Current machine learning methods using Boltzmann machines require complex post-processing and are inefficient in generating equilibrium samples from eigenstates of quantum Hamiltonians, limiting their application in quantum computing and quantum machine learning.
Innovation Solution
A quantum Boltzmann machine implemented on a quantum computer, utilizing qubits and couplers, generates equilibrium samples from eigenstates of a quantum Hamiltonian, such as a transverse Ising Hamiltonian, and uses a hybrid computer system with a digital computer for training and validation, simplifying the process and reducing the need for post-processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If classical Boltzmann machines are used for machine learning, then they can follow simple learning procedures with visible and hidden units, but they require complex post-processing and are inefficient in generating equilibrium samples
Solution Approach 1:
The patent replaces the classical mechanical system of Boltzmann machines with a quantum mechanical system. Quantum Boltzmann machines use qubits and quantum Hamiltonians instead of classical units and energy functions, enabling the system to naturally generate equilibrium samples through quantum evolution without requiring complex classical post-processing algorithms.
Solution Approach 2:
The patent changes the fundamental parameters of the system from classical to quantum domain. By using quantum states, quantum Hamiltonians, and quantum thermal evolution, the system achieves efficient sample generation. The parameter transformation includes using quantum density matrices instead of classical probability distributions and quantum thermal states instead of classical Boltzmann distributions.
2Productivity
If quantum effects are introduced to improve sample generation, then equilibrium samples from quantum Hamiltonians can be obtained, but the device complexity increases with quantum devices and qubits
Solution Approach 1:
The patent creates a universal quantum Boltzmann machine framework that can handle multiple machine learning tasks using the same quantum hardware architecture. The quantum system serves multiple functions: generating equilibrium samples, performing quantum machine learning inference, and optimizing parameters, thereby justifying the quantum device complexity through multi-functional capability.
Solution Approach 2:
The patent introduces a hybrid quantum-classical system where a quantum computer acts as an intermediary between the classical control system and the quantum Boltzmann machine. The quantum computer prepares quantum states and performs measurements, while classical computers handle optimization and analysis, distributing the complexity across different computational paradigms.
3Measurement precision
If quantum annealing is used to find low-energy states, then quantum tunneling can reach energy minimum more accurately and quickly, but the system requires precise control of quantum effects
Solution Approach 1:
The patent applies preliminary thermalization steps before quantum annealing to ensure the system starts from a known quantum thermal state. This preliminary action prepares the quantum system in a controlled manner, making the subsequent quantum tunneling and annealing process more predictable and easier to control, thereby reducing the operational complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables efficient training of quantum Boltzmann machines, providing high-quality samples for machine learning tasks and eliminating the need for extensive post-processing, thereby enhancing the speed and accuracy of quantum machine learning applications.
Implementation Method 1
quantum effects, such as quantum tunneling, as a source of delocalization to reach an energy minimum more accurately and/or more quickly than classical annealing
Data Source
AI summary
A hybrid computer generates samples for machine learning. The hybrid computer includes a processor that implements a Boltzmann machine, e.g., a quantum Boltzmann machine, which returns equilibrium samples from eigenstates of a quantum Hamiltonian. Subsets of samples are provided to training and validations modules. Operation can include: receiving a training set; preparing a model described by an Ising Hamiltonian; initializing model parameters; segmenting the training set into subsets; creating a sample set by repeatedly drawing samples until the determined number of samples has been drawn; and updating the model. Operation can include partitioning the training set into input and output data sets, and determining a conditional probability distribution that describes a probability of observing an output vector given a selected input vector, e.g., determining a conditional probability by performing a number of operations to minimize an upper bound for a log-likelihood of the conditional probability distribution.