Pauli String Selection for Variational Quantum Eigensolver
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Solution Overview
Problem
Variational Quantum Eigensolver (VQE) consumes many resources due to statistical processing of quantum computations, particularly in handling a large number of Pauli strings, which leads to inefficient computation and increased resource consumption.
Innovation Solution
A method is introduced to select Pauli strings with less influence on the eigenvalue of the qubit Hamiltonian, group unselected Pauli strings based on joint measurability, and add selected Pauli strings to these groups, reducing the number of quantum computations required while maintaining accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all Pauli strings are processed in VQE, then measurement precision is improved, but productivity deteriorates due to increased quantum computations
Solution Approach 1:
The patent extracts and removes Pauli strings with coefficients below a threshold value from the Hamiltonian expansion. By identifying and eliminating these low-contribution terms, the method reduces the total number of Pauli strings that require quantum measurement, thereby decreasing computational overhead while maintaining eigenvalue calculation accuracy within acceptable bounds
Solution Approach 2:
The patent applies different treatment strategies to different Pauli strings based on their individual coefficient magnitudes. High-coefficient Pauli strings are measured with full precision, while low-coefficient strings are either measured coarsely or excluded entirely. This localized quality adjustment optimizes the balance between overall accuracy and computational efficiency
2Productivity
If Pauli strings are grouped by joint measurability, then productivity is improved by reducing quantum computations, but device complexity increases due to grouping operations
Solution Approach 1:
The patent segments the set of Pauli strings into multiple groups based on their joint measurability properties. Each group contains Pauli strings that can be measured simultaneously without requiring separate quantum circuit executions. This segmentation enables batch processing of measurements, reducing the total number of quantum computation rounds needed
Solution Approach 2:
The patent performs preliminary classification and grouping of Pauli strings before the actual VQE computation begins. By pre-organizing Pauli strings into jointly measurable groups and identifying those below threshold, the method prepares an optimized measurement schedule in advance, avoiding complex real-time decision-making during quantum execution
Data Source
AI summary
VQE is accelerated by performing receiving a qubit Hamiltonian representing a linear combination of a plurality of Pauli strings. Selecting, among the plurality of Pauli strings, one or more Pauli strings that have less influence than a threshold on an eigenvalue of the qubit Hamiltonian. Grouping, based on joint measurability, the unselected Pauli strings among the plurality of Pauli strings into a plurality of groups of jointly measurable Pauli strings Determining that one or more of the selected one or more Pauli strings is jointly measurable with Pauli strings in one of the plurality of groups And adding one or more of the selected one or more Pauli strings to the one of the plurality of groups.