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Programmed Electrical Stimulation in Mice

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Resource Quantification for the No-Programing Theorem.

Aleksander M Kubicki¹, Carlos Palazuelos^2,3, David Pérez-García^2,3

¹Departamento de Análisis Matemático, Universitat de València, 46100 Burjassot, Spain.

Physical Review Letters

|April 2, 2019

Summary

This summary is machine-generated.

The no-programming theorem shows universal quantum processors are impossible. This study quantifies approximate versions, significantly reducing required resources using geometric Banach space theory.

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Area of Science:

Quantum Information Science
Quantum Computation Theory

Background:

The no-programming theorem fundamentally limits universal programmable quantum processors.
Approximate models exist, but minimal resource requirements remain unclear.

Purpose of the Study:

To investigate quantitative statements of the no-programming theorem.
To establish improved bounds on resources for approximate universal quantum processors.

Main Methods:

Exploiting a novel connection between quantum channels and Banach space embeddings.
Applying classical geometric Banach space theory tools.

Main Results:

Exponentially improved bounds on the resources needed for approximate quantum processors.
Demonstrated a new link between quantum information and geometric analysis.

Conclusions:

The study provides a clearer understanding of the resource costs for approximate quantum computation.
New mathematical tools offer a powerful approach to quantum information processing problems.