Evolution of Quantum Systems by Diagrams of States

TL;DR

This paper introduces Diagrams of States, a graphical method to represent and analyze quantum system evolution, aiding understanding and design of quantum computations.

Contribution

It presents a novel diagrammatic approach for representing quantum states, transformations, and errors, enhancing analysis and conception of quantum circuits.

Findings

Diagrams of States effectively visualize quantum information processing.

The method applies to density matrices, partial traces, and Kraus operators.

It facilitates the design of quantum algorithms and error analysis.

Abstract

We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for representations of quantum states by density matrices, partial trace operations, density matrix purification and time-evolution by Kraus operators. Following these representations, we describe by diagrams of states the most general transformations related to singlequbit decoherence and errors. Diagrams of states prove to be a useful approach to analyze quantum computations, by offering an intuitive graphic representation of the processing of quantum information. They also help in conceiving novel quantum computations, from describing the desired information processing to deriving the final implementation by quantum gate arrays.