Adiabatic Quantum Hilbert Space Mapping
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Solution Overview
Problem
Current methods for mapping datasets from a Hilbert space of a given dimension to a different dimension, such as using kernel functions, become computationally intensive for large datasets, leading to bottlenecks in machine learning applications.
Innovation Solution
A computer-implemented method utilizing an adiabatic quantum device to map datasets by generating encoded samples through a q-body Ising Hamiltonian, with classical external fields driving the evolution from an initial to a final state, and performing projective measurements to determine qubit values, resulting in binary vectors representing transformed data samples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If kernel functions are used to map datasets from one Hilbert space to another, then the ability to separate data samples using linear separators is improved, but the computational complexity increases significantly for large datasets
Solution Approach 1:
The patent replaces the classical mechanical computation system with a quantum system. Specifically, it uses quantum circuits to implement feature mapping that would classically require kernel functions. The quantum system uses qubits and quantum gates to transform input features into a higher-dimensional Hilbert space, achieving the same data separation capability as kernel methods but with exponential speedup for certain computations.
Solution Approach 2:
The patent employs quantum dimensionality by mapping classical input features into a quantum Hilbert space using quantum circuits. Each classical feature becomes a quantum state, and the quantum circuit transformations effectively perform the feature mapping into higher dimensions. This allows the system to achieve complex nonlinear separations through linear operations in the quantum domain, resolving the contradiction between separation capability and computational complexity.
2Adaptability or versatility
If explicit feature maps are used to transform each data sample, then the dimensionality of the feature space can be increased, but the computational cost becomes prohibitive for large datasets
Solution Approach 1:
The patent substitutes quantum mechanics for classical computation in the feature transformation process. Instead of explicitly computing transformed features using classical algorithms, the system uses quantum circuits to naturally perform the transformation during the quantum state evolution. This allows the system to achieve high-dimensional feature space adaptability while maintaining computational efficiency through quantum parallelism.
Solution Approach 2:
The patent performs feature space transformation preliminarily by encoding input features into quantum states before the main computation. The quantum circuit is designed to pre-establish the appropriate feature space representation, so that subsequent quantum operations work directly with the transformed features. This preliminary quantum encoding avoids the need for expensive explicit feature map computations that would be required in a classical system.
3Productivity
If quantum circuits are used to map datasets, then the training and execution speed of machine learning models is improved, but the device complexity increases due to quantum hardware requirements
Solution Approach 1:
The patent introduces a hybrid classical-quantum system where a classical computer serves as an intermediary between the user and the quantum device. The classical system handles data preprocessing, quantum circuit design, and result interpretation, while the quantum device performs only the core feature mapping and computation. This intermediary architecture allows the system to leverage quantum speedup for training and execution while managing quantum hardware complexity through a familiar classical interface.
Solution Approach 2:
The patent segments the machine learning system into distinct classical and quantum components. The classical portion handles data input, circuit compilation, and output processing, while the quantum portion is dedicated to feature mapping and computation. This segmentation allows each component to be optimized independently, enabling fast quantum computation while managing overall system complexity through clear separation of concerns and specialized hardware usage.
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 reduces the complexity of machine learning models, enabling faster training and execution, reduces overfitting, and allows for the use of linear models, while leveraging quantum correlations for enhanced learning performance.
Implementation Method 1
causing the adiabatic quantum device to evolve from an initial state at ti=0 to a final state at tf=t wherein t≤T
Implementation Method 2
configuring the adiabatic quantum device by embedding each encoded sample into a q-body Ising Hamiltonian H representative of the adiabatic quantum device
Implementation Method 3
performing a projective measurement along a z axis at the final state to determine a value of each qubit of the adiabatic quantum device
Implementation Method 4
configuring the adiabatic quantum device by embedding each encoded sample into a q-body Ising Hamiltonian H representative of the adiabatic quantum device and defined by
Data Source
AI summary
A computer-implemented method is disclosed for mapping a dataset from a Hilbert space of a given dimension to a Hilbert space of a different dimension, the method comprising obtaining a dataset, for each data sample of the dataset, for a plurality of episodes, generating an encoded sample; configuring an adiabatic quantum device by embedding each encoded sample into a q-body Hamiltonian H representative of an adiabatic quantum device, causing the adiabatic quantum device to evolve from an initial state to a final state; and performing a projective measurement along z axis at the final state to determine the value of each qubit; generating a corresponding binary vector representative of the given data sample in a transformed Hilbert space using the determined value of each qubit at each episode and providing a mapped dataset comprising each of the generated corresponding binary vectors.