PINN-Based Counter-Diabatic Term Determination for Quantum Optimization
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Solution Overview
Problem
Existing methods for determining counter-diabatic (CD) terms in quantum systems are complex and inefficient, especially for many-body systems, as they require intricate computations and are not scalable for large numbers of qubits.
Innovation Solution
The use of Physics-Informed Neural Networks (PINNs) to optimize the configuration of CD terms by defining a loss function that minimizes the CD terms, allowing for the determination of optimal counter-diabatic terms and scheduling functions for quantum computing applications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods are used to determine counter-diabatic terms, then accuracy can be maintained, but computational complexity and time increase significantly
Solution Approach 1:
The patent replaces traditional mechanical/computational methods of determining counter-diabatic terms with a quantum computing approach. The quantum computer executes algorithms that efficiently calculate CD terms by leveraging quantum parallelism and interference, substituting classical computational mechanics with quantum mechanical processes that naturally model the quantum system's behavior.
Solution Approach 2:
The patent changes the parameter representation by expressing the counter-diabatic Hamiltonian in terms of Pauli matrices and their time derivatives. This parameter transformation allows the problem to be solved more efficiently on quantum computers, as the Pauli basis naturally aligns with quantum computational operations and enables compact representation of the Hamiltonian evolution.
2Measurement precision
If traditional methods are used to determine counter-diabatic terms, then accuracy can be maintained, but the method is not scalable to large numbers of qubits
Solution Approach 1:
The patent replaces scalable-limiting classical computational methods with quantum computing algorithms that inherently scale better. The quantum algorithm's complexity grows polynomially rather than exponentially with the number of qubits, enabling scalability to large quantum systems while maintaining accuracy through the quantum mechanical framework.
Solution Approach 2:
The patent segments the determination of counter-diabatic terms into independent calculations for each Pauli matrix component. This segmentation allows parallel computation of individual terms, improving scalability as each component can be processed separately and combined, reducing the computational burden for large numbers of qubits.
3Productivity
If the evolution time is reduced to improve productivity, then non-adiabatic excitations increase but PINNs can optimize to maintain accuracy
Solution Approach 1:
The patent implements feedback through Physics-Informed Neural Networks that continuously monitor and adjust the evolution schedule. The PINN uses the adiabatic condition as a feedback criterion, optimizing the time-dependent parameter λ(t) to maintain adiabaticity even during faster evolution. The network learns from physical constraints and adjusts the evolution trajectory to prevent non-adiabatic transitions.
Solution Approach 2:
The patent transforms the static adiabatic condition into a dynamic optimization problem. Instead of fixing the evolution schedule, the system dynamically adjusts the evolution parameter λ(t) based on real-time constraints and objectives. The PINN optimizes the time-dependent evolution path, allowing the system to adaptively maintain adiabaticity while achieving faster evolution times through intelligent scheduling.
Data Source
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AI summary
The invention pertains to a computer-implemented method for solving an optimization problem using an analog quantum computer. The method comprises the steps of: (a) training a Physics-informed Neural Network (PINN) using a plurality of training samples to address a Counter-Diabatic driving problem in a quantum system, wherein training the PINN comprises: - defining a temporal domain as the input of the PINN, - constructing the PINN on the basis of the temporal domain, - obtaining outputs from the PINN and derivating them, - updating the temporal domain with derivated outputs; and (b) obtaining a set of counterdiabatic terms as the solution for the counter-diabatic driving problem from the PINN; (c) differentiating at least one partial differential equation characterizing a time-dependent behavior of the system; (d) minimizing a loss function; and (e) solving, using the set of counterdiabatic terms, the optimization problem.