Quantum Extremal Learning for NISQ Optimization
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Solution Overview
Problem
Current quantum computers, particularly Noisy, Intermediate-Scale Quantum (NISQ) devices, face limitations in the number of qubits and lack of error correction, making it difficult to implement quantum algorithms for optimization problems effectively, especially for mixed-type optimisation problems involving both discrete and continuous variables, and existing methods require classical intermediates or explicit problem Hamiltonians.
Innovation Solution
A hybrid quantum-classical algorithm, Quantum Extremal Learning (QEL), which uses a quantum feature map and a quantum neural network to model data, allowing both discrete and continuous variables, and optimizes input values without classical intermediates, leveraging quantum superposition for speedup.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If variational methods are used to solve optimisation problems on NISQ devices, then quantum computations can be performed with limited qubits and no error correction, but the depth of quantum circuits is limited due to noise scaling
Solution Approach 1:
The algorithm segments the optimisation problem into two parts: a quantum computer executes the quantum circuit to evaluate the cost function, while a classical computer performs the optimisation process. This segmentation allows the quantum computer to operate at limited depth without requiring error correction, as the classical optimiser handles the iterative process of finding optimal parameters.
Solution Approach 2:
A classical optimiser acts as an intermediary between the quantum circuit and the final solution. The classical optimiser receives cost function values from the quantum computer and iteratively adjusts parameters to minimize the cost function, thereby bridging the capability gap between NISQ device limitations and the requirements for deep circuits.
2Productivity
If hybrid quantum-classical algorithms are used, then classical computations can be offloaded to quantum computers, but additional classical computational overhead is introduced
Solution Approach 1:
The algorithm extracts the core quantum computational task (evaluating the cost function) from the overall optimisation process and delegates it to the quantum computer. The classical computer handles only the optimisation coordination, thereby minimizing classical overhead while maximizing quantum utilization.
3Adaptability or versatility
If quantum computers are used for machine learning applications, then access to exponentially large feature space is enabled, but practical implementation is limited by current device capabilities
Solution Approach 1:
The algorithm applies partial action by using a limited number of qubits available on NISQ devices to represent a subset of the exponentially large feature space. The quantum circuit processes only the necessary features for the given problem, achieving useful machine learning functionality without requiring full access to the complete feature space that would be needed for theoretical maximum performance.
Data Source
AI summary
Methods and systems determine a solution for an optimization problem using a quantum computer and a classical computer. The method comprises: receiving or determining, by the classical computer, a description of the problem; receiving or determining, by the classical computer, one or more quantum circuits defining gate operations to be executed by the quantum computer; determining, by the classical computer, an optimized first parametric quantum circuit comprising execution, by the quantum computer, of the gate operations; determining, using the quantum computer, an optimized input value in the input space; and determining, by the classical computer, the solution to the optimization problem based on the optimized input value and/or an output value corresponding to that optimized input value.