Quantum-Classical Algorithm for Ground State Property Estimation
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Solution Overview
Problem
Current quantum algorithms for estimating ground state properties are impractical for near-term quantum computers due to high-depth requirements and error propagation, and variational quantum eigensolver methods are not accurate enough for industrial applications.
Innovation Solution
A quantum-classical algorithm that estimates ψ0|O|ψ0 with high accuracy and low circuit depth, using a hybrid quantum-classical computer system with a low-depth quantum circuit and classical postprocessing, allowing for reliable estimation of ground state properties on near-term fault-tolerant quantum computers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high-depth quantum circuits are used for ground state property estimation, then measurement precision is improved, but device complexity and error propagation increase
Solution Approach 1:
The patent segments the ground state property estimation problem into multiple measurable components using the Hadamard test circuit. Instead of directly measuring complex ground state properties, the method breaks down the estimation into sequential measurements of expectation values through controlled unitary operations, reducing circuit depth while maintaining precision.
Solution Approach 2:
The patent introduces an ancilla qubit as an intermediary in the Hadamard test circuit to facilitate the measurement of ground state properties. This intermediary enables the extraction of expectation values through controlled operations without requiring deep quantum circuits, thereby reducing error propagation while maintaining measurement precision.
2Adaptability or versatility
If variational quantum eigensolver (VQE) is used for ground state estimation, then adaptability is improved, but measurement precision and reliability deteriorate
Solution Approach 1:
The patent employs a feedback mechanism where classical postprocessing of measurement data from the quantum circuit informs subsequent measurement strategies. This feedback loop allows the algorithm to adapt to the specific properties of the Hamiltonian being studied while maintaining high precision through optimized measurement sequences and error mitigation techniques.
Data Source
AI summary
A method and apparatus are disclosed for estimating ground state properties of molecules and materials with high accuracy on a hybrid quantum-classical computer using low-depth quantum circuits. The ground stat energy is estimated for a Hamiltonian (H) matrix characterizes a physical system. For an observable (O), samples are run on a parameterized Hadamard test circuit, the outcomes are evaluated, and the expectation value (p0) of the observable (O) is estimated with respect to the ground state energy. A weighted expectation value p0O0 is estimated, and the ground state property ψ0|O|ψ0 is calculated. Applications include Green's functions used to compute electron transport in materials, and the one-particle reduced density matrices used to compute electric dipoles of molecules. In another aspect, the disclosed technology is applicable to early fault-tolerant quantum computers for carrying out molecular-level and materials-level calculations.