Hybrid Quantum Circuit Optimization via Jacobi Sweeps and Anderson Acceleration
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Solution Overview
Problem
Variational quantum algorithms face challenges in optimizing the parameters of quantum circuits due to the presence of local minima, large indefinite regions, and 'barren plateaus' with small gradients, making conventional optimization techniques ineffective for achieving the global minimum of the observable expectation value.
Innovation Solution
A hybrid method combining Jacobi diagonalization and Anderson acceleration, which involves sampling grid points for quantum circuit parameters, determining a tomography function, and iteratively optimizing parameters through Jacobi sweeps and Anderson/Pulay DIIS sequence acceleration to improve the observable expectation value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional optimization techniques are used to optimize quantum circuit parameters, then the optimization process is simple to implement, but the convergence to global minimum is poor due to local minima and barren plateaus
Solution Approach 1:
The patent segments the quantum circuit parameters into N nonoverlapping groups, where each group contains G one-qubit rotation gates. This segmentation allows the optimization problem to be divided into smaller subproblems, where each subset of M groups is optimized independently through grid point sampling and tomography function determination, making the complex optimization more tractable while improving convergence reliability
Solution Approach 2:
The patent performs preliminary sampling of (2G+1)M grid points for parameter subsets before determining the tomography function. This preliminary action of evaluating the observable expectation value at multiple grid points provides sufficient information to construct an accurate tomography function, which then guides the optimization toward the global minimum more reliably
2Measurement precision
If the number of grid points for parameter sampling is increased, then the accuracy of tomography function determination is improved, but the computational cost increases
Solution Approach 1:
The patent applies partial action by sampling only (2G+1)M grid points for each subset of M parameter groups rather than exhaustively sampling all possible parameter combinations. This partial sampling provides sufficient accuracy for determining the tomography function while significantly reducing computational cost compared to full parameter space exploration
Solution Approach 2:
By segmenting parameters into groups and optimizing subsets independently, the patent reduces the number of grid points needed per optimization step from exponential in the total number of parameters to polynomial in the subset size, achieving a balance between accuracy and computational feasibility
3Productivity
If more parameter groups are optimized simultaneously, then the convergence speed improves, but the computational complexity and resource requirements increase
Solution Approach 1:
The patent implements a dynamic optimization process where the subset size M can be adjusted based on available computational resources and convergence requirements. This allows the system to adaptively balance convergence speed against computational complexity, optimizing parameter groups in flexible batches rather than fixed increments
Data Source
AI summary
The optimization of circuit parameters of variational quantum algorithms is a challenge for the practical deployment of near-term quantum computing algorithms. Embodiments relate to a hybrid quantum-classical optimization methods. In a first stage, analytical tomography fittings are performed for a local cluster of circuit parameters via sampling of the observable objective function at quadrature points in the circuit parameters. Optimization may be used to determine the optimal circuit parameters within the cluster, with the other circuit parameters frozen. In a second stage, different clusters of circuit parameters are then optimized in “Jacobi sweeps,” leading to a monotonically convergent fixed-point procedure. In a third stage, the iterative history of the fixed-point Jacobi procedure may be used to accelerate the convergence by applying Anderson acceleration/Pulay's direct inversion of the iterative subspace (DIIS).