Quantum Imaginary-Time Control for Faster Ground State Convergence
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Solution Overview
Problem
Existing methods for obtaining the ground state of a quantum system, such as quantum imaginary-time evolution, require stringent overlapping relationships and high control capabilities, affecting convergence rates and computational efficiency.
Innovation Solution
A quantum computing method combining quantum imaginary-time evolution and real-time control, reducing requirements for initial states and control capabilities by utilizing a set of control methods that accelerate convergence through partial controllability and dynamic adjustments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum imaginary-time evolution is used to obtain the ground state, then the ground state can be obtained through eigenvalue evolution, but the convergence rate is greatly affected by the overlapping relationship between initial state and lowest eigenstate
Solution Approach 1:
The patent transforms the imaginary-time evolution parameter τ into a controllable variable that can be dynamically adjusted during the evolution process. By changing the parameter representation and allowing dynamic modification of the evolution parameter, the system can accelerate convergence without sacrificing the accuracy of ground state preparation.
Solution Approach 2:
The patent introduces dynamic control capabilities into the previously static imaginary-time evolution process. The evolution parameter can be dynamically adjusted based on the current state of the quantum system, transforming a fixed-parameter process into an adaptive dynamic process that optimizes convergence rate while maintaining accuracy.
2Measurement precision
If stringent overlapping relationships are required between initial state and lowest eigenstate, then ground state preparation is possible, but the control capability requirements increase significantly
Solution Approach 1:
The patent implements a feedback mechanism where the evolution parameter is continuously adjusted based on the current quantum state and the desired ground state properties. This feedback loop allows the system to automatically adapt the evolution process, reducing the need for precise initial state preparation and lowering control capability requirements.
Solution Approach 2:
The quantum system performs self-adjustment through the dynamic evolution parameter mechanism. The system automatically optimizes its own evolution process without requiring external intervention to precisely prepare the initial state, effectively making the ground state preparation process self-correcting and easier to control.
3Measurement precision
If the difference between other eigenstates and the lowest eigenstate is small, then the quantum system can be accurately described, but the convergence speed decreases exponentially
Solution Approach 1:
By making the evolution parameter dynamic and adjustable, the system can adapt its convergence behavior based on the eigenvalue spectrum. When eigenvalue differences are small, the dynamic parameter adjustment accelerates the evolution through the flat region, reducing the exponential time loss while maintaining the ability to resolve closely spaced eigenstates.
Solution Approach 2:
The patent applies preliminary adjustments to the evolution parameter before the system encounters the slow convergence region caused by small eigenvalue differences. By pre-adjusting the parameter to anticipate and counteract the expected slowdown, the system maintains faster convergence even when eigenvalue gaps are minimal.
Data Source
AI summary
A quantum computing method includes determining an initial quantum state of a quantum system, and inputting the initial quantum state to a quantum circuit corresponding to the quantum system and obtaining a quantum state outputted by the quantum circuit, wherein the outputted quantum state is a quantum circuit generation state corresponding to the quantum system. The method further includes updating a quantum system parameter based on the outputted quantum circuit generation state. The quantum system parameter includes a quantum imaginary-time parameter. The method further includes updating a quantum circuit parameter of the quantum circuit according to the updated quantum system parameter to obtain an updated quantum system, and determining a final quantum state of the quantum system as a minimum eigenstate of the quantum system.