Improved QAOA With Eigenvalue Preprocessing for NISQ Circuits
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Solution Overview
Problem
The Quantum Approximate Optimization Algorithm (QAOA) faces inefficiencies due to the need for increased iteration times to achieve high performance, which is exacerbated by the limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, where noise is not fully mitigated and the number of qubits is limited.
Innovation Solution
An improved quantum approximate optimization algorithm that modifies the problem and mixing Hamiltonian operations during iteration steps, reducing the number of operations and circuit depth, suitable for NISQ devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the QAOA increases the number of iteration times to acquire high performance results, then the performance accuracy is improved, but the efficiency deteriorates and the computation time increases
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing the eigenvectors and eigenvalues of the problem Hamiltonian before the main optimization process. This preprocessing step allows the algorithm to work with pre-computed data during iterations, reducing the computational burden per iteration and enabling faster convergence without sacrificing accuracy
Solution Approach 2:
The patent uses copying by creating a classical representation (eigenvectors and eigenvalues) of the quantum problem Hamiltonian. This classical copy allows the optimization algorithm to operate on simplified data structures rather than full quantum states, significantly reducing computational complexity while preserving the essential problem characteristics
2Device complexity
If the QAOA uses a small depth quantum circuit, then the device complexity is reduced and it is more suitable for NISQ devices, but the number of operations must be increased to maintain performance
Solution Approach 1:
The patent segments the quantum optimization process into distinct phases: problem Hamiltonian construction, eigenvector computation, and optimization iteration. By separating these functions, the circuit depth in each phase can be optimized independently, allowing shallow circuits in the optimization phase while maintaining overall performance through efficient segmentation of computational tasks
Solution Approach 2:
The patent changes parameters by transforming the problem into an eigenvalue decomposition framework, where the optimization variables become parameters in a classical-quantum hybrid algorithm. This parameter transformation allows the use of shallow quantum circuits for state preparation while achieving high performance through efficient parameter optimization in the classical component
3Adaptability or versatility
If the QAOA is implemented on NISQ devices with limited qubits and noise, then the hardware requirements are met, but the noise cannot be completely mitigated and performance is limited
Solution Approach 1:
The patent introduces an intermediary classical computation step that computes eigenvectors and eigenvalues of the problem Hamiltonian. This classical intermediary processes the quantum problem data in a noise-free environment, then passes the processed information back to the quantum device for final optimization, effectively shielding the quantum computation from noise while maintaining hardware compatibility
Solution Approach 2:
The patent applies preliminary action by pre-computing the spectral decomposition of the problem Hamiltonian before quantum optimization. This preprocessing eliminates the need for the quantum device to handle complex Hamiltonian evolution directly, reducing exposure to noise while maintaining adaptability to NISQ hardware constraints
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 achieves performance comparable to QAOA with fewer operations and a smaller circuit depth, making it more suitable for NISQ devices.
Implementation Method 1
an initialization step of changing a plurality of qubits initialized into a superposition state by using a Hadamard gate
Implementation Method 2
The quantum entanglement may mean a state in which two or more states are quantumly connected to each other, so that they cannot be handled separately in each state
Implementation Method 3
The QAOA can find the approximate optimization solution through quantum characteristics of a quantum state and an optimization algorithm in classical computing
Implementation Method 4
The qubit may be determined as one state while the quantum superposition state is released when being observed
Data Source
AI summary
The present disclosure relates to quantum approximate optimization technology, and more particularly, to an apparatus and method for an improved quantum approximate optimization algorithm. In one embodiment, the disclosure describes a method for implementing a quantum approximate optimization algorithm, which is performed by a processor of a quantum computing device.