Weighted Quantum Logic Circuit for Fewer Oracle Evaluations
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Solution Overview
Problem
Current quantum computing algorithms, such as Grover's algorithm, face inefficiencies in unstructured database searches due to the need for an exponential number of oracle evaluations and decaying amplitude accumulation, especially when using traditional phase oracle functions.
Innovation Solution
The introduction of weighted oracle gates that apply an adjustable phase rotation at each quantum oracle call, combined with micro-diffusion operators acting on subsets of qubits, to optimize the sequence of quantum oracle calls and diffusion operators, thereby reducing complexity and improving amplitude distribution across multiple states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional phase oracle functions are used in quantum algorithms like Grover's algorithm, then the algorithm can perform unstructured database searches, but the number of oracle evaluations required grows exponentially and amplitude accumulation decays
Solution Approach 1:
The patent applies parameter changes by modifying the oracle function to use weighted phases instead of uniform phases. Each basis state |x⟩ is assigned a weight w(x), and the oracle applies a phase rotation of e^(iθ(x)) where θ(x) depends on the weight. This parameter change in the phase function allows the algorithm to achieve O(Log(N)*sqrt(N)) oracle evaluations by optimizing the phase angles to constructively interfere with target states while suppressing non-target states, thereby resolving the exponential complexity issue.
2Reliability
If more oracle evaluations are performed to improve search accuracy, then measurement probability increases, but the computational complexity and time increase significantly
Solution Approach 1:
The patent employs periodic action through the use of diffusion operators that are applied periodically between oracle calls. The diffusion operator performs an inversion-about-the-average operation that periodically refreshes the amplitude distribution. This periodic application of diffusion operators, combined with the weighted phase oracles, creates an oscillating interference pattern that systematically amplifies target state amplitudes over fewer iterations, reducing both computational time and maintaining high measurement probability.
3Ease of manufacture
If uniform phase rotation is applied to all qubit states, then the quantum circuit is simpler to implement, but amplitude distribution across multiple states becomes inefficient
Solution Approach 1:
The patent applies local quality by making the phase rotation dependent on the specific basis state rather than applying a uniform rotation to all states. The weighted oracle function assigns different phase angles θ(x) to different basis states |x⟩ based on their weights w(x). This local differentiation in phase application optimizes the interference patterns for each state individually, enabling efficient amplitude distribution across multiple states while maintaining circuit implementability through parameterized quantum gates.
Data Source
AI summary
A quantum circuit includes a plurality of Hadamard gates apply Hadamard transforms to a plurality of qubits in a corresponding plurality of initial states. A plurality of weighted oracle gates sequentially call a weighted oracle operator on the plurality of qubits to produce a sequence of quantum oracle calls, wherein the weighted oracle operator for the plurality of qubits applies an adjustable phase rotation at each of the quantum oracle calls in the sequence of quantum oracle calls. A plurality of diffusion gates apply a plurality of diffusion operators, wherein a selected one or more of a plurality of diffusion operators is applied after each of the quantum oracle calls in the sequence of quantum oracle calls. A measurement function generates a quantum computing result based on a measurement from the plurality of qubits, after the sequence of quantum oracle calls are applied and after the plurality of diffusion operators are applied.