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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Path Integral Optimization as Circuit Complexity.

Hugo A Camargo^1,2, Michal P Heller¹, Ro Jefferson¹

¹Max Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Mühlenberg 1, 14476 Potsdam-Golm, Germany.

Physical Review Letters

|August 7, 2019

Summary

This summary is machine-generated.

This study connects geometric circuit complexity in quantum information theory to path integral deformations in 2D conformal field theories. We demonstrate how path integral optimization can be realized within gate counting, linking these complexity measures.

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Area of Science:

Quantum Information Theory
Quantum Field Theory
Conformal Field Theory

Background:

Early research on field theory complexity used geometric approaches from quantum information theory.
Alternative complexity definitions based on path integral deformations lack clear connections to standard measures.

Purpose of the Study:

To bridge the gap between geometric circuit complexity and path integral deformations in 2D conformal field theories.
To show how path integral optimization can be concretely realized within the gate counting framework.

Main Methods:

Investigated two-dimensional conformal field theories.
Employed path integral optimization techniques.
Utilized gate counting within a standard framework.

Main Results:

Explicitly demonstrated the connection between path integral optimization and gate counting.
Showed that Weyl rescaling of background geometry leads to the Liouville action via gate counting.
Identified the Liouville action as a specific instance within a broader class of cost functions.

Conclusions:

Established a concrete link between two distinct approaches to quantum field theory complexity.
Provided a framework for understanding path integral deformations through the lens of circuit complexity.
Highlighted the role of geometric deformations and cost functions in defining complexity.