Quantum Phase Estimation via Majority Sampling Grid
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Solution Overview
Problem
Current quantum phase estimation methods, such as Kitaev's algorithm, require numerous measurements and calculations, increasing the depth of quantum circuits and inefficiency in determining quantum phases.
Innovation Solution
A method involving a series of quantum circuits with a majority sampling approach, where measurements for cosine and sine components are counted to determine the quantum phase based on the majority of 0 and 1 measurements, reducing the number of required measurements and circuit depth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Kitaev's algorithm is used for quantum phase estimation, then the quantum phase can be determined through sine and cosine calculations, but the number of measurements and circuit depth increase significantly
Solution Approach 1:
The quantum phase estimation problem is segmented into multiple independent quantum circuits, each responsible for estimating a specific bit of the phase. Instead of using a single complex circuit as in traditional approaches, the method divides the estimation task across several simpler circuits that can be executed independently and whose results are combined to form the complete phase estimate.
Solution Approach 2:
The method transitions from a time-sequential measurement approach to a spatial-parallel architecture by organizing multiple quantum circuits in a two-dimensional grid structure. This allows simultaneous execution of multiple measurements across different circuits, effectively trading temporal depth for spatial parallelism and reducing the overall circuit depth required.
2Measurement precision
If repeated measurements are performed to extract quantum phase using arctangent, then the phase can be determined, but the process becomes lengthy and inefficient
Solution Approach 1:
The method performs preliminary actions by pre-organizing multiple quantum circuits in a structured grid before execution. Each circuit is pre-configured with specific phase shift operations and measurement settings, allowing the system to quickly extract phase information without requiring iterative adjustments or repeated full-cycle measurements during the actual estimation process.
Solution Approach 2:
The method changes the measurement parameters by using different phase shift values (e.g., 0, π/2, π, 3π/2) across different circuits in the grid. This parameter variation allows simultaneous extraction of multiple phase components in parallel, dramatically improving estimation efficiency compared to sequential measurement approaches that use fixed parameters.
3Reliability
If more quantum circuits are added to perform multiple measurements, then measurement completeness improves, but the quantum device depth increases
Solution Approach 1:
The measurement task is segmented across multiple independent quantum circuits arranged in a grid, where each circuit performs a specific measurement with particular phase settings. This segmentation allows the system to achieve comprehensive measurement coverage through parallel execution of simpler circuits rather than sequential execution of a single deep circuit.
Solution Approach 2:
The method merges the results from multiple parallel quantum circuit measurements into a unified phase estimation. By combining the output data from circuits executed simultaneously across the grid, the system achieves complete measurement information while maintaining short individual circuit durations, effectively merging spatial parallelism with temporal efficiency.
Data Source
AI summary
A method of determining a quantum phase of quantum device including performing a plurality of measurements for cosine and sine components of the quantum phase; counting a number of measurements in a vertical axis for the sine component and counting a number of measurements in a horizontal axis for the cosine component; and determining the quantum phase based on a majority of a number of 0 measurements and a number of 1 measurements of the sine component and the cosine component.