This document provides an overview of quantum computing and common algorithms used on different types of quantum computers. It discusses how quantum computers work using qubits or qumodes and the existing gate-based and quantum annealing-based architectures. Some examples of algorithms that could run on these quantum computers are presented, including for supervised and unsupervised machine learning tasks as well as graph and network analysis problems. Researchers can access existing quantum computers through the cloud or simulate circuits classically.

1. Colleen M. Farrelly

2. A short introduction

3.  Quantum computing is a relatively new
field of computing with chips based on
quantum mechanics.
 Some quantum computers exist already.
 However, most extant quantum computers
are still too small of circuits to be practical.
 Several different types of quantum
computers exist/are possible.
 Each has its own strengths and
weaknesses on certain problems.

4.  One approach replaces binary (0/1)
bits with a quantum version, the
qubit.
 Qubits can take many different
values, depending on the operations
performed on them.
 Superposition (quantum mechanics
property) allows a qubit to be in all
possible states at once.
 This is helpful when computing
combinatorial solutions
(simultaneous search rather than
iterative).
 Limited by number of qubits in the
circuit, though.

5.  Practically, two types of qubit chips
exist:
 Gate-based (IBM, Rigetti…)
 Quantum-annealing-based (D-Wave)
 Gate-based tends to be more accurate
in benchmarking.
 Researchers can:
 Gain access to the actual quantum
computers through the cloud
 Simulate the circuits using a classical
computer and special Python
package.

6.  A different type of quantum
circuit is possible using
continuous versions of qubits,
called qumodes.
 These are photonic circuits, upon
which continuous transformations
can be made on the photon through
the circuit.
 Information is stored in qubits.
 Qumodes retrieve the information
and operate on it.
 A functioning qumodes computer
doesn’t exist yet, but simulation
software is available in Python.

7. A short overview of common target algorithms on different types of
quantum computers

8.  Supervised learning
 Given a set of predictors, how can we
predict an outcome?
 Which predictors are most important?
 Unsupervised learning
 Given a set of data, what relationships
can we find?
 What clusters exist?
 Network analysis
 How are people connected to each other?
 How is information passed among people
in the same social group?

9.  Many machine learning algorithms focus on
supervised learning.
 Algorithms learn the relationship between a set of
possible predictors and an outcome of interest.
 Some examples include deep learning, random forest,
and logistic regression.
 Most of these algorithms are rooted in generalized
linear models.
 Qumodes applications (Xanadu) abound these
days, including quantum generalized linear
modeling, quantum deep learning, and quantum
boosted regression.

10.  Unsupervised learning aims to either:
 Learn groupings of data (by combining
individuals)
 Learn reductions of the data (by combining
predictors)
 Clustering algorithms are quite important
in unsupervised learning, including k-
means clustering.
 Many qubit clustering-type algorithms
exist, including Rigetti’s quantum
clustering algorithm, qubit-based
persistent homology, and D-Wave’s semi-
supervised classification algorithm.

11.  Graphs and network data are ubiquitous
today:
 Social networks connecting people
 Gene networks connecting genes/proteins
 Epidemic networks
 Ranking of individuals and ties between
individuals in the network is a key problem
in the study of graphs.
 Stopping of epidemic spread in disease
networks
 Disintegration of links between terror cells
 Many quantum graph-based/network
analysis algorithms exist, particularly on
qubit systems:
 Quantum max flow/min cut algorithms
 Quantum coloring problems
 Quantum clique-finding

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Quantum machine learning. Nature, 549(7671), 195.
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Welt, 3(2), 38-41.
 Izaac, J., Quesada, N., Bergholm, V., Amy, M., &Weedbrook, C. (2018). Strawberry
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 Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S.
(2018). Continuous-variable quantum neural networks. arXiv preprint
arXiv:1806.06871.
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geometric analysis of data. Nature communications, 7, 10138.
 Pakin, S., & Reinhardt, S. P. (2018, June). A Survey of Programming Tools for D-Wave
Quantum-Annealing Processors. In International Conference on High Performance
Computing (pp. 103-122). Springer, Cham.
 Zhang, D. B., Xue, Z. Y., Zhu, S. L., & Wang, Z. D. (2019). Realizing quantum linear
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