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Límite inferior analítico sobre la complejidad de consulta para transformaciones de operaciones unitarias
Tatsuki Odake1, Satoshi Yoshida1, Mio Murao1,2
1The University of Tokyo, Department of Physics, Graduate School of Science, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan.
Physical review letters
|December 19, 2025
Resumen
Este estudio establece límites inferiores analíticos para la complejidad de consulta de operaciones unitarias como la inversión y la conjugación. Los hallazgos demuestran la optimalidad de los protocolos existentes y revelan limitaciones para ciertos métodos.
Área de la Ciencia:
- Computación cuántica
- Álgebra lineal
- Teoría de la información
Sus antecedentes:
- Las operaciones unitarias son fundamentales en la computación cuántica.
- Los protocolos eficientes para manipular operaciones unitarias desconocidas son cruciales.
- El trabajo previo estableció protocolos deterministas para la conjugación compleja, la inversión y la transposición.
Objetivo del estudio:
- Establecer límites inferiores analíticos para la complejidad de consulta de la inversión, transposición y conjugación compleja unitaria.
- Evaluar la optimalidad de los protocolos deterministas exactos existentes.
- Explorar la posibilidad de protocolos catalíticos para la conjugación compleja unitaria.
Principales métodos:
- Derivación de límites inferiores analíticos utilizando un nuevo marco de diferenciación.
- Análisis de la complejidad de consulta para funciones diferenciables generales f: SU(d) → SU(d).
- Extensión del marco a entornos parcialmente conocidos y probabilísticos.
Principales resultados:
- Se estableció un límite inferior de d^2 para la inversión unitaria, demostrando la optimalidad asintótica de los protocolos de inversión O(d^2).
- Se demostró la imposibilidad de protocolos catalíticos para la conjugación compleja unitaria.
- Se extendió el análisis a escenarios con conocimiento parcial y resultados probabilísticos.
Conclusiones:
- Los límites inferiores establecidos proporcionan límites fundamentales en la eficiencia de la manipulación de operaciones unitarias desconocidas.
- Los protocolos de inversión deterministas exactos son asintóticamente óptimos.
- Los protocolos catalíticos no son viables para la conjugación compleja unitaria, lo que resalta los desafíos únicos de esta operación.
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