Quantum State Comparison Using Local Randomized Measurements
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Solution Overview
Problem
The challenge of comparing a priori unknown quantum states generated on different devices and/or at different times remains unsolved, particularly for mixed quantum states.
Innovation Solution
A method and system for comparing quantum states by transforming them with local unitary operations and measuring the transformed states using local measurements, determining a similarity measure based on the trace product of the quantum states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If full quantum state tomography is used to compare quantum states, then measurement precision is improved, but device complexity and measurement resources increase exponentially
Solution Approach 1:
The patent extracts only the essential information needed for quantum state comparison by using randomized measurements and classical shadows. Instead of performing full quantum state tomography which requires exponential measurement resources, the method extracts relevant statistical properties (classical shadows) that suffice for comparing quantum states, thereby dramatically reducing measurement complexity while maintaining comparison accuracy.
Solution Approach 2:
The patent changes the measurement parameters from fixed basis measurements required by traditional tomography to randomized measurements across different bases. By varying the measurement parameters (choice of measurement basis) randomly and collecting statistical data, the method achieves efficient quantum state comparison without the exponential overhead of complete tomography.
2Adaptability or versatility
If quantum states from different devices and locations are compared, then versatility is improved, but reliability of comparison decreases due to device variations
Solution Approach 1:
The patent implements a universal comparison protocol that works across different quantum devices and platforms. The method uses device-independent randomized measurements and classical shadow techniques that can be applied to any quantum state regardless of the physical platform (superconducting qubits, trapped ions, photonic systems, etc.), thereby achieving versatile cross-platform comparison while maintaining reliability through standardized measurement procedures.
Data Source
AI summary
A method includes providing a first quantum state at a first node, transforming the first quantum state to obtain a first plurality of transformed quantum states, and measuring the first plurality of transformed quantum states to obtain a first set of measurement results. The method further includes providing a second quantum state at a second node, transforming the second quantum state to obtain a second plurality of transformed quantum states, the second plurality of unitary operations corresponding to the first plurality of unitary operations, and measuring the second plurality of transformed quantum states to obtain a second set of measurement results. A similarity measure between the first quantum state and the second quantum state is determined in terms of the first set of measurement results and the second set of measurement results, the similarity measure including a trace product of the first quantum state and the second quantum state.