1. Quantum Computing: An Overview
Dave Clader, Ph.D.
Member of the Principal Professional Staff at Johns Hopkins University Applied Physics Laboratory

2. Why build a quantum computer?
Shor’s killer app (1994) - Polynomial time integer factorization
Code breaking is nice but…
We are also interested in applications of broader interest
Next: Overview of quantum computing
“The race is on to construct the first quantum code breaker, as the winner will hold the key to the entire Internet. From international, multibillion-dollar financial transactions to top-secret government communications, all would be vulnerable to the secret-code-breaking ability of the quantum computer.”
- From book review of J.P. Dowling, Schrodinger’s Killer App: Race to Build the World’s First Quantum Computer (2013).

3. Young’s Double Slit Experiment
Thought experiment: Shine a laser at an object with two narrow slits. Place a photo-detector on a wall behind the object and measure the incoming photons. Where do they land?
Photon/Particle picture
Wave picture

4. Young’s Double Slit Experiment
Thought experiment: Shine a laser at an object with two narrow slits. Place a photo-detector on a wall behind the object and measure the incoming photons. Where do they land?
Photon/Particle picture
Wave picture
In both pictures, the intensity pattern on the detector is the same. Single photons interfere with themselves! It’s as if a single photon went through both paths simultaneously! This is known as superposition in quantum mechanics.

5. Quantum computing
Quantum mechanical superposition can be used for computing
A classical bit is either 0 or 1, while a quantum bit can be both 0 and 1 simultaneously or any arbitrary superposition
The classical registers only make use of the north and south poles of the Bloch sphere. A quantum computer utilizes the entire sphere.
Non-intuitive gates can be created with the concept of a qubit. In classical logic a NOT is a well defined gate. With a quantum computer, we can create a square-root of NOT gate. This has no classical analogue.

6. Quantum logic gate equivalents
In classical computing, one requires a complete set of logic gates for Boolean functions
e.g. AND, OR, NOT
In quantum computing, we require a complete set of unitary operators that can form an arbitrary unitary operator on n qubits
e.g., Clifford + T, where Clifford is the Clifford group (Pauli, Identity, Phase Gate, CNOT, Hadamard) and T is the p/8 gate
A quantum computer is universal in that we can map our complete set of logical gates to a quantum equivalent
Toffoli
CNOT

7. Exponential size memory
The amount of information stored in a quantum register grows exponentially with the number of qubits
For a single qubit, a generic state is
c0 and c1 are complex numbers
For two qubits
In general
An n qubit system requires 2n complex numbers to fully specify
Led Feynman to conjecture in 1982 that the only way one could efficiently simulate quantum physics was with a quantum system itself [R. P. Feynman, Int. J. of Theoretical Phys. 21, 467 (1982)].

8. Quantum parallelism Suppose we wish to evaluate the function
On a classical computer we require N evaluations for N inputs
On a quantum computer we can place all inputs into superposition and, with only a single evaluation of the function f, calculate all possible outputs

9. Measuring the superposition
With superposition and a single function evaluation we have calculated f(x) for every possible value of x
Does this do any good?
What happens when we try and read the values?
Current state:
Probability to measure y:
We could do equally well by choosing a single x at random and calculating f(x) classically

10. Solving the read-out problem
Not all is lost – rather than measuring getting random values of x and f(x) we could instead learn something about the function f(x) as a whole
Is it a constant or balanced Boolean function?
Is it periodic and if so, what is it’s period?
This leads to the general features that all quantum algorithms exhibiting speedup have
Small number of inputs
Massive combinatorial blowup during computation
Single or few numbers of outputs
E.g., given the graph on right and the entrance, find the exit node
Fig. 2 from A.M. Childs, et al., In Proc. Of the 35th ACM Symposium on Theory of Computing, page 59 (2003). arXiv:quant-ph/

11. Shor’s Algorithm Breaks RSA encryption
The backbone of internet security
Finding prime factors p and q when given N is computationally expensive on a classical computer. It is exponentially faster on a quantum computer. This function is an example of a one way function. When given p and q, determining if it equals N is trivial.
The quantum algorithm, does not actually solve the above problem. Rather it solves a related problem, order finding where one seeks to find a value r that satisfies
You can convince yourself that the order is related to the period of a function since
Thus Shor’s algorithm reduces to period finding, which a quantum computer is very good at!

12. Quantum Chemistry
Computational chemists seek to model complicated electronic structures and molecules to gain insight into the simulation of chemical dynamics, protein folding, photosynthetic systems, etc.
Unfortunately, simulating large quantum systems (e.g. molecules) is intractable on classical computers
Feynmen’s original motivation
Quantum chemists are looking to use a simplified quantum computer to simulate molecular orbitals
Big Plus: Does not requires a full-scale universal quantum computer.
This will likely be the first application of a quantum computer
See e.g. B. P. Lanyon, et al., “Towards Quantum Chemistry on a Quantum Computer,” Nature Chemistry 2, 106 (2010).

13. Quantum Machine Learning
Fig. 1 from Biamonte, et al., arXiv: (2016).

14. Quantum Optimization
Figure from Wikipedia “Quantum Annealing”
Quantum mechanics allows particles to “tunnel” through barriers. Quantum algorithms have been proposed that exploit this to speed up certain optimization problems.

15. Experimental realizations
Superconductors
Ions
Optical
Neutral Atoms
Spin qubits

16. How close are we?
ENIAC circa 1950
Moore’s Law

17. Quantum Moore’s Law Quantum “Moore’s Law” Quantum “ENIAC”
M. Mariantoni, et al., “Photon shell game in three-resonator circuit quantum electrodynamics”, Nature Phys. 7, 287 (2011).
Fig. 3 from Devoret and Schoelkopf, Science 339, 1169 (2013).
Superconducting qubits have seen a 7 order of magnitude performance increase in the last decade. With a similar improvement in the number of qubits, a quantum computer would be capable of breaking modern encryption schemes.

18. Seven stages in the development of QC

19. Commercial Interests
IBM Announced “IBM Q” quantum systems and services delivered via the IBM cloud on March 6, 2017
Google has announced plans to commercialize quantum technology in five years. See Nature comment in vol 543, page 171 dated March 9, 2017.
Microsoft has been focused on machine learning and simulation algorihtms, and is taking a long shot bet on topological qubits. Most recently the have hired leading experts from ETH Zurich and TU Delft.

20. Prominent Startups
Based in Berkeley, CA. Has raised over $70M in venture capital funding. Focused on superconducting qubits.
Based in College Park, MD. Started by a UMD and Duke professor.
Founded by three Yale professors, focused on superconducting qubits.
Many others besides this – too many to list!

21. Conclusions
Quantum computing is an exciting research area with a variety of possible applications
Recently the race to develop these machines has started taking shape with prominent tech firms making big bets in the space and startups joining the race

22. Thank You!