Quantum Circuit Parameter Initialization via Domain Decomposition
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Solution Overview
Problem
Optimizing quantum circuits is challenging due to barren plateaus, multiple local minima, and the presence of non-minima stationary points, which hinder convergence and accuracy in calculating physical properties of molecules and chemical compounds.
Innovation Solution
A hybrid quantum-classical computer system initializes and optimizes variational quantum circuits by decomposing physical systems into smaller subsystems, using a variational quantum eigensolver (VQE) and introducing entangling gates, with parameter initialization through domain decomposition and truncating circuit depth to minimize properties of subsystems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the quantum circuit is optimized as a whole system, then the global accuracy is improved, but the optimization process becomes trapped in barren plateaus and local minima
Solution Approach 1:
The patent divides the quantum circuit into multiple independent subsystems, each corresponding to a subsystem of the physical system. Each subsystem is optimized independently using local optimization algorithms, avoiding the barren plateaus that plague global optimization. The subsystems are then combined using entangling gates to form the complete circuit, achieving both local optimizability and global accuracy.
2Measurement precision
If the circuit depth is increased to improve calculation accuracy, then the precision of physical properties is improved, but the circuit becomes more complex and harder to optimize
Solution Approach 1:
The patent decomposes the deep circuit into multiple shallow subsystem circuits that can be optimized independently. Each subsystem circuit has reduced depth compared to the full circuit, making them more manageable. The subsystems are then combined through entangling gates to achieve the computational power of the original deep circuit without the optimization difficulties.
3Ease of operation
If domain decomposition is used to simplify optimization, then the optimization convergence is improved, but the circuit structure becomes more complex
Solution Approach 1:
The patent merges multiple independently optimized subsystem circuits using entangling gates to form the complete quantum circuit. This combining step integrates the benefits of domain decomposition (improved convergence) while maintaining a structured circuit architecture that reflects the underlying physical system's subsystems, making the increased complexity manageable and interpretable.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables efficient calculation of ground state energies and absorption spectra of molecules, overcoming convergence issues and improving accuracy by optimizing each subsystem independently and introducing entangling gates to enhance circuit performance.
Implementation Method 1
A quantum computer can be used to calculate physical properties of molecules and chemical compounds
Implementation Method 2
At least one entangling gate is introduced between at least two circuit subcomponents in the set of circuit subcomponents
Data Source
AI summary
A system and method for initializing and optimizing a variational quantum circuit on a hybrid quantum-classical computer, comprising a set of gates and a set of initial parameters representing a model of a physical system. A quantum circuit is generated comprising a set of smaller contiguous subcomponents which can be independently optimized to minimize a property of the physical system, such as ground state energy or the absorption spectrum of a molecule. At least one entangling gate is introduced between at least two circuit subcomponents. The initial parameters of the circuit components may be set according to values obtained from a parameter library. Once the initial parameters are set, the circuit components of the quantum computer proceed to optimization, which is independent for each subcomponent of the system. The optimization method may also include the use of a variational quantum eigensolver (VQE).