# Quantum teleportation do it yourself with Q#

Quantum computing nowadays is the one of the hottest topics in the computer science world.
Recently IBM unveiled the IBM Q System One: a 20-qubit quantum computer which is touting as “the world’s first fully integrated universal quantum computing system designed for scientific and commercial use”.

In this article I’d like how to show the quantum teleportation phenomenon. I will use the Q# language designed by Microsoft to simplify creating quantum algorithms.

In this example I have used the quantum simulator which I have wrapped with the REST api and put into the docker image.

Quantum teleportation allows moving a quantum state from one location to another. Shared quantum entanglement between two particles in the sending and receiving locations is used to do this without having to move physical particles along with it.

# 1. Theory

Let’s assume that we want to send the message, specific quantum state described using Dirac notation:

$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$

Additionally we have two entangled qubits, first in Laboratory 1 and second in Laboratory 2:

$$|\phi^+\rangle=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$$

thus we starting with the input state:

$$|\psi\rangle|\phi^+\rangle=(\alpha|0\rangle+\beta|1\rangle)(\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle))$$ $$|\psi\rangle|\phi^+\rangle=\frac{\alpha}{\sqrt{2}}|000\rangle + \frac{\alpha}{\sqrt{2}}|011\rangle + \frac{\beta}{\sqrt{2}}|100\rangle + \frac{\beta}{\sqrt{2}}|111\rangle$$

To send the message we need to start with two operations applying CNOT and then Hadamard gate.

CNOT gate flips the second qubit only if the first qubit is 1.

Applying CNOT gate will modify the first qubit of the input state and will result in:

$$\frac{\alpha}{\sqrt{2}}|000\rangle + \frac{\alpha}{\sqrt{2}}|011\rangle + \frac{\beta}{\sqrt{2}}|110\rangle + \frac{\beta}{\sqrt{2}}|101\rangle$$

Hadamard gate changes states as follows:

$$|0\rangle \rightarrow \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle))$$

and

$$|1\rangle \rightarrow \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle))$$

$$\frac{\alpha}{\sqrt{2}}(\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle))|00\rangle + \frac{\alpha}{\sqrt{2}}(\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle))|11\rangle + \frac{\beta}{\sqrt{2}}(\frac{1}{\sqrt{2}}(|0\rangle-|1\rangle))|10\rangle + \frac{\beta}{\sqrt{2}}(\frac{1}{\sqrt{2}}(|0\rangle-|1\rangle))|01\rangle$$

and:

$$\frac{1}{2}(\alpha|000\rangle+\alpha|100\rangle+\alpha|011\rangle+\alpha|111\rangle+\beta|010\rangle-\beta|110\rangle+\beta|001\rangle-\beta|101\rangle)$$

which we can write as:

$$\frac{1}{2}(|00\rangle(\alpha|0\rangle+\beta|1\rangle)+|01\rangle(\alpha|1\rangle+\beta|0\rangle)+|10\rangle(\alpha|0\rangle-\beta|1\rangle)+|11\rangle(\alpha|1\rangle-\beta|0\rangle))$$

Then we measure the states of the first two qubits (message qubit and Laboratory 1 qubit) where we can have four results:

• $|00\rangle$ which simplifies equation to: $|00\rangle(\alpha|0\rangle+\beta|1\rangle)$ and indicates that the qubit in the Laboratory 2 is $\alpha|0\rangle+\beta|1\rangle$

• $|01\rangle$ which simplifies equation to: $|01\rangle(\alpha|1\rangle+\beta|0\rangle)$ and indicates that the qubit in the Laboratory 2 is $\alpha|1\rangle+\beta|0\rangle$

• $|10\rangle$ which simplifies equation to: $|10\rangle(\alpha|0\rangle-\beta|1\rangle)$ and indicates that the qubit in the Laboratory 2 is $\alpha|0\rangle-\beta|1\rangle$

• $|11\rangle$ which simplifies equation to: $|11\rangle(\alpha|1\rangle-\beta|0\rangle)$ and indicates that the qubit in the Laboratory 2 is $\alpha|1\rangle-\beta|0\rangle$

Now we have to send the result classical way from Laboratory 1 to Laboratory 2.

Finally we know what transformation we need to apply to qubit in the Laboratory 2
to make its state equal to message qubit:

$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$

if Laboratory 2 qubit is in state:

• $\alpha|0\rangle+\beta|1\rangle$ we don’t need to do anything.

• $\alpha|1\rangle+\beta|0\rangle$ we need to apply NOT gate.

• $\alpha|0\rangle-\beta|1\rangle$ we need to apply Z gate.

• $\alpha|1\rangle-\beta|0\rangle$ we need to apply NOT gate followed by Z gate

This operations will transform Laboratory 2 qubit state to initial message qubit state thus we moved the particle state from Laboratory 1 to Laboratory 2 without moving particle.

# 2. Code

Now it’s time to show the quantum teleportation using Q# language. I have used Microsoft Quantum Development Kit to run the Q# code inside the .NET Core application. Additionally I have added the nginx proxy with the angular gui which will help to show the results.
Everything was put inside the docker to simplify the setup.

Before you will start you will need git, docker and docker-compose installed on your machine (https://docs.docker.com/get-started/)

To run the project we have to clone the repository and run it using docker compose:

git clone https://github.com/qooba/quantum-teleportation-qsharp.git
cd quantum-teleportation-qsharp
docker-compose -f app/docker-compose.yml up


Now we can run the http://localhost:8020/ in the browser:

Then we can put the message in the Laboratory 1, click the Teleport button, trigger for the teleportation process which sends the message to the Laboratory 2.

The text is converted into array of bits and each bit is sent to the Laboratory 2 using quantum teleportation.

In the first step we encode the incoming message using X gate.

if (message) {
X(msg);
}


Then we prepare the entanglement between the qubits in the Laboratory 1 and Laboratory 2.

H(here);
CNOT(here, there);


In the second step we apply CNOT and Hadamard gate to send the message:

CNOT(msg, here);
H(msg);


Finally we measure the message qubit and the Laboratory 1 qubit:

if (M(msg) == One) {
Z(there);
}

if (M(here) == One) {
X(there);
}


If the message qubit has state $|1\rangle$ then we need to apply the Z gate to the Laboratory 2 qubit.
If the Laboratory 1 qubit has state $|1\rangle$ then we need to apply the X gate to the Laboratory 2 qubit. This information must be sent classical way to the Laboratory 2.

Now the Laboratory 2 qubit state is equal to the initial message qubit state and we can check it:

if (M(there) == One) {
set measurement = true;
}


This kind of communication is secure because even if someone will take over the information sent classical way it is still impossible to decode the message.

# Boosting Elasticsearch with machine learning – Elasticsearch, RankLib, Docker

Elastic search is powerful search engine. Its distributed architecture give ability to build scalable full-text search solution. Additionally it provides comprehensive query language.

Despite this sometimes the engine and search results is not enough to meet the expectations of users. In such situations it is possible to boost search quality using machine learning algorithms.

In this article I will show how to do this using RankLib library and LambdaMart algorithm . Moreover I have created ready to use platform which:

1. Index the data
2. Helps to label the search results in the user friendly way
3. Trains the model
4. Deploys the model to elastic search
5. Helps to test the model

The whole project is setup on the docker using docker compose thus you can setup it very easy.
The platform is based on the elasticsearch learning to rank plugin. I have also used the python example described in this project.

Before you will start you will need docker and docker-compose installed on your machine (https://docs.docker.com/get-started/)

To run the project you have to clone it:

git clone https://github.com/qooba/elasticsearch-learning-to-rank.git


Then to make elasticsearch working you need to create data folder with appropriate access:

cd elasticsearch-learning-to-rank/
mkdir docker/elasticsearch/esdata1
chmod g+rwx docker/elasticsearch/esdata1
chgrp 1000 docker/elasticsearch/esdata1


Finally you can run the project:

docker-compose -f app/docker-compose.yml up


Now you can open the http://localhost:8020/.

# 1. Architecture

There are three main components:

A. The ngnix reverse proxy with angular app
B. The flask python app which orchestrates the whole ML solution
C. The elastic search with rank lib plugin installed

### A. Ngnix

I have used the Ngnix reverse proxy to expose the flask api and the angular gui which helps with going through the whole proces.

ngnix.config

server {
listen 80;
server_name localhost;
root /www/data;

location / {
autoindex on;
}

location /images/ {
autoindex on;
}

location /js/ {
autoindex on;
}

location /css/ {
autoindex on;
}

location /training/ {
proxy_set_header   Host                 $host; proxy_set_header X-Real-IP$remote_addr;
proxy_set_header   X-Forwarded-For      $proxy_add_x_forwarded_for; proxy_set_header X-Forwarded-Proto$scheme;

proxy_pass http://training-app:5090;
}
}


This is the core of the project. It exposes api for:

• Indexing
• Labeling
• Training
• Testing

It calls directly the elastic search to get the data and do the modifications.
Because training with RankLib require the java thus Docker file for this part contains default-jre installation. Additionally it downloads the RankLib-2.8.jar and tmdb.json (which is used as a default data source) from: http://es-learn-to-rank.labs.o19s.com/.

Dockerfile

FROM python:3

RUN \
apt update && \
apt-get -yq install default-jre
RUN pip install -r requirements.txt
EXPOSE 5090
CMD ["python", "-u", "app.py"]


### C. Elastic search

As mentioned before it is the instance of elastic search with the rank lib plugin installed

Dockerfile

FROM docker.elastic.co/elasticsearch/elasticsearch:6.2.4
RUN /usr/share/elasticsearch/bin/elasticsearch-plugin install \
-b http://es-learn-to-rank.labs.o19s.com/ltr-1.1.0-es6.2.4.zip


All layers are composed with docker-compose.yml:

version: '2.2'
services:
elasticsearch:
build: ../docker/elasticsearch
container_name: elasticsearch
environment:
- discovery.type=single-node
- bootstrap.memory_lock=true
- xpack.security.enabled=false
- "ES_JAVA_OPTS=-Xms512m -Xmx512m"
ulimits:
memlock:
soft: -1
hard: -1
volumes:
- ../docker/elasticsearch/esdata1:/usr/share/elasticsearch/data
networks:
- esnet

training-app:
build: ../docker/training-app
networks:
- esnet
depends_on:
- elasticsearch
environment:
- ES_HOST=http://elasticsearch:9200
- ES_INDEX=tmdb
- ES_TYPE=movie
volumes:

nginx:
image: "nginx:1.13.5"
ports:
- "8020:80"
volumes:
- ../docker/frontend-reverse-proxy/conf:/etc/nginx/conf.d
- ../docker/frontend-reverse-proxy/www/data:/www/data
depends_on:
- elasticsearch
- training-app
networks:
- esnet

volumes:
esdata1:
driver: local

networks:
esnet:


# 2. Platform

The platform helps to run and understand the whole process thought four steps:

A. Indexing the data
B. Labeling the search results
C. Training the model
D. Testing trained model

### A. Indexing

The first step is obvious thus I will summarize it shortly. As mentioned before the default data source is taken from tmdb.json file but it can be simply changed using ES_DATA environment variable in the docker-compose.yml :

training-app:
environment:
- ES_HOST=http://elasticsearch:9200
- ES_INDEX=tmdb
- ES_TYPE=movie
- ES_FEATURE_SET_NAME=movie_features
- ES_MODEL_NAME=test_6
- ES_MODEL_TYPE=6
- ES_METRIC_TYPE=ERR@10


Clicking Prepare Index the data is taken from ES_DATA file and indexed in the elastic search.

ES_HOST – the elastic search url
ES_USER/ES_PASSWORD – elastic search credentials, by default authentication is turned off
ES_INDEX/ES_TYPE – index/type name for data from ES_DATA file
ES_FEATURE_SET_NAME – name of container for defined features (described later)
ES_MODEL_NAME – name of trained model kept in elastic search (described later)
ES_MODEL_TYPE – algorithm used to train the model (described later).
ES_METRIC_TYPE – metric type (described later)

We can train and keep multiple models in elastic search which can be used for A/B testing.

### B. Labeling

The supervised learning algorithms like learn to rank needs labeled data thus in this step I will focus on this area.
First of all I have to prepare the file label_list.json which contains the list of queries to label e.g.:

[
"rambo",
"terminator",
"babe",
"die hard",
"goonies"
]


When the file is ready I can go to the second tab (Step 2 Label).

For each query item the platform prepare the result candidates which have to be ranked from 0 to 4.

You have to go through the whole list and at the last step
the labeled movies are saved in the file :

# grade (0-4)   queryid docId   title
#
# Use them to populate your query templates
#
# qid:1: rambo
# qid:2: terminator
# qid:3: babe
# qid:4: die hard
#
# https://sourceforge.net/p/lemur/wiki/RankLib%20File%20Format/
#
#
4 qid:1 # 7555 Rambo
4 qid:1 # 1370 Rambo III
4 qid:1 # 1368 First Blood
4 qid:1 # 1369 Rambo: First Blood Part II
0 qid:1 # 31362 In the Line of Duty: The F.B.I. Murders
0 qid:1 # 13258 Son of Rambow
0 qid:1 # 61410 Spud
4 qid:2 # 218 The Terminator
4 qid:2 # 534 Terminator Salvation
4 qid:2 # 87101 Terminator Genisys
4 qid:2 # 61904 Lady Terminator
...


Each labeling cycle is saved to the separate file: timestamp_judgments.txt

### C. Training

Now it is time to use labeled data to make elastic search much more smarter. To do this we have to indicate the candidates features.
The features list is defined in the files: 1-4.json in the training-app directory.
Each feature file is elastic search query eg. the {{keyword}}
(which is searched text) match the title property:

{
"query": {
"match": {
"title": "{{keywords}}"
}
}
}


In this example I have used 4 features:
– title match keyword
– overview match keyword
– keyword is prefix of title
– keyword is prefix of overview

I can add more features without code modification, the list of features is defined and read using naming pattern (1-n.json).

Now I can go to the Step 3 Train tab and simply click the train button.

At the first stage the training app takes all feature files and build the features set which is save in the elastic search (the ES_FEATURE_SET_NAME environment variable defines the name of this set).

In the next step the latest labeling file (ordered by the timestamp) is processed (for each labeled item the feature values are loaded) eg.

4 qid:1 # 7555 Rambo


The app takes the document with id=7555 and gets the elastic search score for fetch defined feature.
The Rambo example is translated into:

4   qid:1   1:12.318446 2:10.573845 3:1.0   4:1.0 # 7555    rambo


Which means that score of feature one is 12.318446 (and respectively 10.573845, 1.0, 1.0 for features 2,3,4 ).
This format is readable for the RankLib library. And the training can be perfomed.
The full list of parameters is available on: [https://sourceforge.net/p/lemur/wiki/RankLib/][https://sourceforge.net/p/lemur/wiki/RankLib/].

The ranker type is chosen using ES_MODEL_TYPE parameter:
– 0: MART (gradient boosted regression tree)
– 1: RankNet
– 2: RankBoost
– 4: Coordinate Ascent
– 6: LambdaMART
– 7: ListNet
– 8: Random Forests

The default used value is LambdaMART.

Additionally setting ES_METRIC_TYPE we can use the optimization metric.
Possible values:
– MAP
– NDCG@k
– DCG@k
– P@k
– RR@k
– ERR@k

The default value is ERR@10

Finally we obtain the trained model which is deployed to the elastic search.
The project can deploy multiple trained models and the deployed model name is defined by ES_MODEL_NAME.

### D. Testing

In the last step we can test trained and deployed model.

We can choose the model using the ES_MODEL_NAME parameter.

It is used in the search query and can be different in each request which is useful when we need to perform A/B testing.

Happy searching 🙂