Quantum Chemistry Simulation on Quantum Computers

Quantum computation was proposed initially partly to simulate the physical universe because of the likeness of the nature and quantum systems. Some experimental simulations of Hawking radiation or Kibble-Zurek mechanisms were carried out in condensed matter systems, but they are simply too expensive to carry out. However, some scientists performed simulations on molecular systems using a quantum computer with an array of superconducting qubits. They performed the electronic structure calculation, as reported in “Scalable Quantum Simulation of Molecular Energies,” published in Physical Review X. Later, Google’s Quantum AI Team, Microsoft’s QuArC Team, and Caltech reports their work on simulating electronic structure using a quantum computer, that reduces running time but increases accuracies. Their work was reported in “Low-Depth Quantum Simulation of Materials,” also published in Physical Review X. The same team, adding a Harvard’s group, further studied the application of these molecular systems lined up as a linear array to design algorithms in quantum computers. It is reported in “Quantum Simulation of Electronic Structure with Linear Depth and Connectivity,” published in Physical Review Letters.

These people published an open-source software package, a Python library, called OpenFermion. It facilitates simulation of quantum algorithms in fermionic systems.

For a completeness, a few years ago, another group of scientists published a Python package, QuTiP, that helps simulating the open quantum systems.

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Toying with Word2Vec

One fascinating application of deep learning is the training of a model that outputs vectors representing words. A project written in Google, named Word2Vec, is one of the best tools regarding this. The vector representation captures the word contexts and relationships among words. This tool has been changing the landscape of natural language processing (NLP).

Let’s have some demonstration. To use Word2Vec in Python, you need to have the package gensim installed. (Installation instruction: here) And you have to download a trained model (GoogleNews-vectors-negative300.bin.gz), which is 3.6 GB big!! When you get into a Python shell (e.g., IPython), type

from gensim.models.word2vec import Word2Vec
model = Word2Vec.load_word2vec_format('GoogleNews-vectors-negative300.bin', binary=True)

This model enables the user to extract vector representation of length 300 of an English word. So what is so special about this vector representation from the traditional bag-of-words representation? First, the representation is standard. Once trained, we can use it in future training or testing dataset. Second, it captures the context of the word in a way that the algebraic operation of these vectors has meanings.

Here I give 5 examples.

A Juvenile Cat

What is a juvenile cat? We know that a juvenile dog is a puppy. Then we can get it by carry out the algebraic calculation \text{puppy} - \text{dog} + \text{cat} by running

model.most_similar(positive=['puppy', 'cat'], negative=['dog'], topn=5)

This outputs:

[(u'kitten', 0.7634989619255066),
(u'puppies', 0.7110899686813354),
(u'pup', 0.6929495334625244),
(u'kittens', 0.6888389587402344),
(u'cats', 0.6796488761901855)]

which indicates that “kitten” is the answer (correctly!) The numbers are similarities of these words with the vector representation  \text{puppy} - \text{dog} + \text{cat} in descending order. You can verify it by calculating the cosine distance:

from scipy.spatial import distance
print (1-distance.cosine(model['kitten'], model['puppy']+model['cat']-model['dog']))

which outputs 0.763498957413.

Mogu, my cat, three years ago when she was still a kitten
Mogu, my cat, three years ago when she was still a kitten

This demonstration shows that in the model, \text{puppy}-\text{dog} and \text{kitten}-\text{cat} are of similar semantic relations.

Capital of Taiwan

Where is the capital of Taiwan? We can find it if we know the capital of another country. For example, we know that Beijing is the capital of China. Then we can run the following:

model.most_similar(positive=['Beijing', 'Taiwan'], negative=['China'], topn=5)

which outputs

[(u'Taipei', 0.7866502404212952),
(u'Taiwanese', 0.6805002093315125),
(u'Kaohsiung', 0.6034111976623535),
(u'Chen', 0.5905819535255432),
(u'Seoul', 0.5865181684494019)]

Obviously, the answer is “Taipei.” And interestingly, the model sees Taiwan in the same footing of China!

Taipei (taken from Airasia: http://www.airasia.com/mo/en/destinations/taipei.page)

Past Participle of “eat”

We can extract grammatical information too. We know that the past participle of “go” is “gone”. With this, we can find that of “eat” by running:

model.most_similar(positive=[‘gone’, ‘eat’], negative=[‘go’], topn=5)

which outputs:

[(u'eaten', 0.7462186217308044),
(u'eating', 0.6516293287277222),
(u'ate', 0.6457351446151733),
(u'overeaten', 0.5853317975997925),
(u'eats', 0.5830586552619934)]

Capital of the State of Maryland

However, this model does not always work. If it can find the capital of Taiwan, can it find those for any states in the United States? We know that the capital of California is Sacramento. How about Maryland? Let’s run:

model.most_similar(positive=['Sacramento', 'Maryland'], negative=['California'], topn=5)

which sadly outputs:

[(u'Towson', 0.7032245397567749),
(u'Baltimore', 0.6951349973678589),
(u'Hagerstown', 0.6367553472518921),
(u'Anne_Arundel', 0.5931429266929626),
(u'Oxon_Hill', 0.5879474878311157)]

But the correct answer should be Annapolis!

Downtown Annapolis (taken from Wikipedia)

Blue crabs (lunch in Cantler's Riverside Inn, Annapolis, MD)
Blue crabs (lunch in Cantler’s Riverside Inn, Annapolis, MD)

More About Word2Vec

Word2Vec was developed by Tomáš Mikolov. He previously worked for Microsoft Research. However, he switched to Google, and published a few influential works on Word2Vec. [Mikolov, Yih, Zweig 2013] [Mikolov, Sutskever, Chen, Corrado, Dean 2013] [Mikolov, Chen, Corrado, Dean 2013] Their conference paper in 2013 can be found on arXiv. He later published a follow-up work on a package called Doc2Vec that considers phrases. [Le, Mikolov 2014]

Earlier this year, I listened to a talk in DCNLP meetup spoken by Michael Czerny on his award-winning blog entry titled “Modern Methods for Sentiment Analysis.” He applied the vector representations of words by Word2Vec to perform sentiment analysis, assuming that similar sentiments cluster together in the vector space. (He took averages of the vectors in tweets to extract emotions.) [Czerny 2015] I highly recommend you to read his blog entry. On the other hand, Xin Rong wrote an explanation about how Word2Vec works too. [Rong 2014]

There seems to be no progress on the project Word2Vec anymore as Tomáš Mikolov no longer works in Google. However, the Stanford NLP Group recognized that Word2Vec captures the relations between words in their vector representation. They worked on a similar project, called GloVe (Global Vectors), which tackles the problem with matrix factorization. [Pennington, Socher, Manning 2014] Radim Řehůřek did some analysis comparing Word2Vec and GloVe. [Řehůřek 2014] GloVe can be implemented in Python too.

Continue reading “Toying with Word2Vec”

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