Quantum Circuit Fabrication via Diagonal Matrix Basis and Cyclic Alternation
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Solution Overview
Problem
The quantum imaginary time evolution unitary approximation method requires a good unitary basis for precision and involves solving linear equations, leading to increased measured data and circuit depth as systems grow, making it less feasible for large systems.
Innovation Solution
A method using a diagonal matrix basis composed of identity and Pauli Z matrices to reduce measured quantities and accelerate quantum imaginary time evolution by employing a cyclic alternating circuit structure of variational and diagonal control circuits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum imaginary time evolution unitary approximation method is used, then evolution precision can be maintained, but measured quantity increases sharply and circuit depth increases with system size
Solution Approach 1:
The patent segments the quantum imaginary time evolution process into multiple discrete time steps, where each step applies a unitary approximation circuit. This segmentation allows the evolution to be broken down into manageable segments that can be executed sequentially, reducing the measured quantity required at each step while maintaining overall precision through the cumulative effect of multiple precise small-step evolutions.
Solution Approach 2:
The patent changes the parameter representation by using a diagonal matrix basis composed of identity matrices and Pauli Z matrices. This parameter transformation simplifies the representation of the evolution operator, reducing the number of parameters that need to be measured and optimized, thereby decreasing the measured quantity while preserving evolution precision.
2Measurement precision
If quantum imaginary time evolution unitary approximation method is used, then evolution precision can be maintained, but circuit depth increases with evolution duration
Solution Approach 1:
The patent segments the evolution duration into multiple small time steps, with each step implemented by a shallow unitary approximation circuit. By dividing the total evolution into many small segments, each individual circuit layer remains shallow, but the cumulative effect achieves the desired long-time evolution precision through sequential application of these shallow circuits.
Solution Approach 2:
The patent employs periodic application of unitary approximation circuits at discrete time steps throughout the evolution process. This periodic action allows the system to maintain precision through repeated controlled transformations while keeping each individual transformation shallow, thereby managing overall circuit depth through rhythmic, structured evolution steps.
3Quantity of substance
If diagonal matrix basis with identity and Pauli Z matrices is used, then measured quantity is reduced, but requires specific basis selection
Solution Approach 1:
The patent transforms the parameter space by selecting a specific diagonal matrix basis composed of identity matrices and Pauli Z matrices. This parameter change reduces the measured quantity by restricting the evolution to a simplified basis set, making the optimization problem more tractable while still capturing the essential physics of the quantum evolution.
Solution Approach 2:
The patent applies local quality by using different matrix types (identity and Pauli Z) in specific positions within the diagonal matrix basis. This localized assignment of matrix properties optimizes the representation for specific measurement scenarios, reducing the overall measured quantity while maintaining the necessary expressive power for accurate evolution.
4Measurement precision
If unitary approximation is performed with second-order or higher, then precision is improved, but quantity of observations increases sharply
Solution Approach 1:
The patent applies partial action by using second-order unitary approximation, which provides sufficient precision for many practical applications without requiring the full complexity of higher-order approximations. This partial approximation strikes an optimal balance between precision and observed quantity, achieving adequate accuracy while avoiding the exponential increase in measurements that would result from higher-order terms.
Data Source
AI summary
Disclosed are a method for obtaining a quantum circuit performed by a computer device, relating to the field of quantum technologies. The method includes: obtaining a combination of identity matrices and Pauli Z matrices as a diagonal matrix basis; determining a dynamical evolution relationship of imaginary time diagonal control based on the diagonal matrix basis and a dynamical evolution relationship of quantum imaginary time control; determining a first quantum circuit of imaginary time diagonal control based on the dynamical evolution relationship of imaginary time diagonal control; determining a second quantum circuit based on a variational quantum approximation algorithm; and cyclically alternating the first quantum circuit and the second quantum circuit to obtain a quantum circuit.