Annealing Training of Quantum Circuits on Hybrid Systems
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Solution Overview
Problem
Current hybrid quantum-classical computing systems face challenges in solving optimization problems due to imperfect control of qubits and limitations in the number of quantum gates, often resulting in issues like bad local minima and vanishing gradients.
Innovation Solution
The method involves using a classical computer to select variational parameters for a parametrized quantum circuit applied to a quantum processor with trapped ions, iteratively transforming the quantum state and measuring amplitudes to converge on a target joint distribution, employing an annealing training process that gradually lowers the annealing temperature to avoid local minima and vanishing gradients.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a NISQ device with shallow circuits is used in a hybrid quantum-classical computing system, then the system can solve optimization problems with limited noise, but the classical optimizer encounters bad local minima and vanishing gradients
Solution Approach 1:
The patent transforms the discrete optimization problem into a continuous parameter optimization problem by representing the quantum circuit parameters (rotation angles, evolution times) as continuous variables. This allows the use of gradient-based optimization methods that can navigate the solution space more effectively, avoiding bad local minima and vanishing gradients while maintaining solution reliability on NISQ devices
Solution Approach 2:
The patent introduces dynamic elements by making the quantum circuit depth and structure adaptive during optimization. The circuit parameters are continuously adjusted based on gradient information from the cost function, creating a dynamic optimization process that evolves the quantum circuit to better approximate the target distribution, thereby resolving the contradiction between reliability and optimization complexity
2Measurement precision
If the number of quantum gates is increased to improve solution accuracy, then the error rate increases due to noise in NISQ devices
Solution Approach 1:
The patent applies partial action by using only the necessary number of quantum gates required to achieve sufficient accuracy, rather than maximizing circuit depth. The variational quantum circuit is designed with just enough parameters to capture the essential features of the target distribution, avoiding the accumulation of noise from excessive gate operations while maintaining acceptable solution accuracy
Solution Approach 2:
The patent implements a feedback mechanism where the classical optimizer evaluates the output distribution from the quantum circuit, compares it to the target distribution using a cost function, and uses this feedback to adjust the quantum circuit parameters. This closed-loop approach allows the system to achieve high accuracy through iterative refinement rather than through deep circuits that would accumulate noise errors
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 provides reliable solutions to optimization problems by effectively navigating through the solution space without the pitfalls of bad local minima and vanishing gradients, enhancing the performance of hybrid quantum-classical computing systems.
Implementation Method 1
applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters, to transform the quantum processor from the initial state to a trial state
Implementation Method 2
measuring, by the system controller, an amplitude of the trial state, to generate a trial joint distribution of the set of variables
Implementation Method 3
The adaptive target joint distribution is a mixture of a uniform joint distribution of the set of variables with the target joint distribution, and the mixing coefficient is decreased in each iteration
Data Source
AI summary
A method of performing computation includes selecting samples of a set of variables and a target joint distribution, selecting a set of variational parameters to construct a parametrized quantum circuit, executing iterations, each iteration including applying the parametrized quantum circuit to the quantum processor based on the set of the variational parameters, to transform the quantum processor from an initial state to a trial state, measuring an amplitude of the trial state, to generate a trial joint distribution, and replacing the set of the variational parameters with another set of variational parameters, if a difference between the generated trial joint distribution and an adaptive target joint distribution is more than a predetermined value, and outputting the set of the variational parameters. The adaptive target joint distribution is a mixture of a uniform joint distribution with the target joint distribution, and a mixing coefficient is decreased in each iteration.