Quantum Chemical VQE With State Reuse for Penalty-Term Convergence
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Solution Overview
Problem
The inefficiency of variational quantum eigensolver (VQE) computations due to iterative updates of the penalty term coefficient, leading to increased computation time in obtaining ground state energy values.
Innovation Solution
A method that alternately iterates the process of updating a coefficient in a penalty term equation and searching for a ground state by changing the quantum state of a many-electron system, utilizing the final state of previous iterations as the initial state in subsequent iterations to enhance convergence and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the VQE computation is performed iteratively while updating the penalty term coefficient, then the accuracy of the ground state energy value is improved, but the computation time increases
Solution Approach 1:
The patent applies preliminary action by using the final state from the previous iteration as the initial state for the next iteration. This prepares the quantum state in advance for the subsequent computation, allowing the system to converge faster to the ground state energy value without requiring a complete restart from an initial guess in each iteration.
Solution Approach 2:
The patent implements continuity of useful action by maintaining the quantum state information across iterations. Instead of discarding the final state after each iteration, the system continuously builds upon it, ensuring that the useful computational work is preserved and extended in the next iteration, thereby reducing redundant computations.
2Manufacturing precision
If the penalty term coefficient is updated frequently, then the convergence to the correct number of electrons is achieved, but the number of iterations increases
Solution Approach 1:
By setting the final state as the initial state for the next iteration, the system performs preliminary preparation that carries forward the accumulated computational progress. This reduces the number of iterations needed to achieve the correct electron number accuracy, as each iteration builds upon the previous results rather than starting from scratch.
Solution Approach 2:
The patent employs parameter changes by dynamically adjusting the penalty term coefficient across iterations while maintaining continuity of the quantum state. This allows the system to adapt the coefficient value based on convergence progress, achieving accurate electron number control without requiring an excessive number of iterations.
3Reliability
If a penalty term is added to the Hamiltonian to enforce electron number constraints, then the physical correctness of the state is improved, but the complexity of the computation increases
Solution Approach 1:
The penalty term is incorporated into the Hamiltonian in advance, before the VQE computation begins. This preliminary inclusion of the constraint ensures that the physical correctness requirement is built into the computational framework from the start, avoiding the need for complex post-processing or iterative corrections that would increase computational complexity.
Solution Approach 2:
The patent manages computation complexity by treating the penalty term coefficient as a可调 parameter that can be optimized across iterations. By adjusting this parameter systematically, the system maintains physical correctness through the electron number constraint while managing the overall computational complexity through controlled parameter evolution rather than structural complexity increases.
Data Source
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AI summary
An information processing apparatus iterates a process of updating a value of a coefficient in a third equation and a process of searching for a ground state of a many-electron system. The third equation is obtained by adding a term, which is a product of a second equation relating to the number of electrons in the many-electron system and the coefficient, to a first equation for computing a physical quantity of the many-electron system. The search process employs a variational quantum eigensolver method and searches for the ground state of the many-electron system by setting, in the (k + 1)th search process, a final state of the many-electron system obtained in one of the first to k-th search processes as an initial state, and then changing the quantum state of the many-electron system from the initial state such that the expected value of the third equation is reduced.