Digital Simulation of Single Qubit Markovian Open Quantum Systems: A Tutorial

TL;DR

This tutorial reviews methods for simulating single qubit Markovian open quantum systems, introduces a modified quantum algorithm that avoids classical sampling, and employs quantum forking to reduce circuit complexity.

Contribution

It consolidates existing simulation methods into a unified framework and presents a novel quantum algorithm that simplifies implementation by eliminating classical randomness.

Findings

The modified algorithm removes the need for classical random sampling.

Quantum forking enables efficient simulation of open quantum channels.

The approach reduces the number of C-NOT gates required in the circuit.

Abstract

One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more complex open quantum systems. In this tutorial, we introduce the methods used in the simulation of single qubit Markovian open quantum systems. It combines various existing notations into a common framework that can be extended to more complex open system simulation problems. The only currently available algorithm for the digital simulation of single qubit open quantum systems is discussed in detail. A modification to the implementation of the simpler channels is made that removes the need for classical random sampling, thus making the modified algorithm a strictly quantum algorithm. The modified algorithm makes use of quantum forking to implement the simpler channels that approximate the total channel. This circumvents the need for quantum circuits with a large number of C-NOT gates.