Quantum Eigenvalue Estimation Time Evolution Optimization
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Solution Overview
Problem
Conventional time evolution procedures for quantum computer-based eigenvalue estimation face issues with information loss when t is over-estimated and sub-optimal precision when t is underestimated, leading to inaccurate eigenvalue estimation.
Innovation Solution
A method that involves calculating an upper bound for the maximum eigenvalue of a Hermitian matrix, initializing a time evolution value t, and iteratively updating it based on the results from quantum computer executions to optimize the time evolution process, ensuring accurate eigenvalue estimation by adjusting the number of bits used for representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the time evolution value t is over-estimated, then the eigenvalue estimation can be obtained, but information is lost and the result becomes false
Solution Approach 1:
The patent dynamically adjusts the time evolution value t based on the actual eigenvalue magnitude. Instead of using a fixed t, the system calculates t = 1/a where a is an upper bound on the maximum eigenvalue, and iteratively refines this value. This dynamic adaptation ensures that t is never over-estimated, preventing information loss while maintaining estimation accuracy.
Solution Approach 2:
The patent implements a feedback mechanism where the estimated eigenvalues are used to refine the time evolution value t in subsequent iterations. The system calculates the maximum absolute value of integers from quantum measurements and uses this to update t, creating a self-correcting loop that prevents both over-estimation and under-estimation.
2Loss of information
If the time evolution value t is under-estimated, then information is preserved, but the precision is sub-optimal as fewer bits are used to represent eigenvalues
Solution Approach 1:
The system dynamically determines the appropriate number of bits n based on the actual eigenvalue distribution. By calculating the maximum absolute value x of the integers and using this to adjust t, the system automatically optimizes the bit precision without manual intervention, ensuring both information preservation and optimal precision.
Solution Approach 2:
The patent changes the parameter n (number of bits) dynamically based on the measured data. The system determines n from the maximum absolute value x obtained from quantum measurements, allowing the bit precision to adapt to the actual requirements of the eigenvalue estimation problem.
3Ease of operation
If a fixed time evolution value t is used, then the quantum computer program is simple to execute, but the eigenvalue estimation accuracy varies with different input data
Solution Approach 1:
The patent performs preliminary calculations on the classical computer to determine an upper bound a for the maximum eigenvalue before executing the quantum program. This preliminary action allows the system to pre-calculate an initial time evolution value t = 1/a, which simplifies the quantum program execution while ensuring accuracy for the specific input data.
Solution Approach 2:
The system maintains flexibility by allowing dynamic adjustment of t based on the specific input data and measured eigenvalues. This dynamic capability enables the system to adapt to different problems without requiring complex quantum circuits, maintaining ease of execution while improving accuracy.
Data Source
AI summary
A method may include: a computer program populating a Hermitian matrix A with input data; calculating an upper bound a for a maximum eigenvalue for the Hermitian matrix A; initializing a time evolution value t=1/a; generating a first quantum computer program using the time evolution value t; communicating the first quantum computer program to a quantum computer; receiving a result including a binary value for each n-bit string and a probability for each binary value; converting each binary value into an integer; identifying a maximum absolute value of the integers; determining a value x for the maximum absolute value of all of the integers; updating the time evolution value t based on the value of x; generating a second quantum computer program using the updated time evolution value t; and communicating, by the classical computer program, the second quantum computer program to the quantum computer.