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

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).

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

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.

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.

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

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)].

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

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

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/0209131

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!

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).

Quantum Machine Learning Fig. 1 from Biamonte, et al., arXiv:1611.09347 (2016).

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.

Experimental realizations Superconductors Ions Optical Neutral Atoms Spin qubits

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

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.

Seven stages in the development of QC

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.

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!

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

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