Quantum Optimization Circuits Using F-VQE State Filtering
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Solution Overview
Problem
Quantum computers, particularly NISQ computers, face challenges in efficiently solving combinatorial optimization problems due to noise and complexity, often converging to sub-optimal solutions and requiring extensive quantum resources, which are difficult to implement with contemporary hardware.
Innovation Solution
The implementation of a Filtering Variational Quantum Eigensolver (F-VQE) algorithm that uses a filtering operator to exclude high-energy states and retain low-energy states, reducing the number of qubits and circuit depth, and employing causal cones to optimize quantum circuits, combined with stochastic gradient descent for faster convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If VQE algorithm is used to solve combinatorial optimization problems, then quantum computers can address optimization tasks, but the algorithm requires extensive quantum resources and is prone to computational errors
Solution Approach 1:
The patent extracts and removes high-energy states from the quantum superposition using a filtering operator, retaining only the low-energy states that correspond to optimal or near-optimal solutions. This extraction of unwanted states reduces the computational burden and resource requirements while maintaining the optimization capability.
Solution Approach 2:
The patent modifies the energy threshold parameter of the filtering operator to control which states are retained. By adjusting this parameter, the system can optimize the balance between solution quality and computational resources required, adapting the algorithm to different problem sizes and complexity levels.
2Adaptability or versatility
If VQE algorithm is used to solve combinatorial optimization problems, then quantum computers can address optimization tasks, but the algorithm converges to sub-optimal solutions due to noise and complexity
Solution Approach 1:
The patent converts the harmful effect of noise and computational errors into a beneficial filtering mechanism. The filtering operator uses the energy measurements (which are affected by noise) to identify and retain only the lowest energy states, thereby converting noisy measurements into a selective retention process that improves solution reliability.
Solution Approach 2:
The patent implements a feedback mechanism where the energy measurements from quantum circuits are used to adjust the filtering operator's threshold and parameters. This feedback loop continuously refines which states are retained, improving the convergence to optimal solutions and reducing the impact of noise and computational errors.
3Productivity
If traditional VQE is used, then quantum circuits can be executed, but the circuit depth and number of qubits required are excessive for contemporary hardware
Solution Approach 1:
The filtering operator extracts and removes high-energy states from the quantum superposition, effectively reducing the search space. This extraction allows the quantum circuit to focus computational resources on a smaller subset of states, reducing the required circuit depth and qubit count while maintaining productivity.
Solution Approach 2:
Instead of exploring the entire Hilbert space as required by traditional VQE, the patent applies partial action by using the filtering operator to selectively retain only the lowest energy states. This partial exploration of the state space is sufficient for finding optimal solutions, thereby reducing the computational resources and circuit complexity required.
Data Source
AI summary
A computing system including one or more classical binary computers coupled to one or more quantum computers. The computing system is configured to process the one or more computing tasks including at least one combinatorial optimization task using a Filtering Variational Quantum Eigensolver (F-VQE) algorithm implemented by using one or more Ansätze circuits and a cost function arrangement to generate one or more quantum circuits in the quantum computer. The computing system iteratively applies a filtering operator to a cost function arrangement to generate a corresponding filtered cost function arrangement that excludes energy states that exceed an energy threshold and uses the filtered cost function arrangement in the one or more quantum circuits to generate output results.