Applied quantum physics today Quantum control and simulation

Applied quantum physics (today) Quantum control and simulation 2012 Quantum sensing 2016 Quantum phases of matter Quantum communication https: //www. youtube. com/watch? v=T 2 DXrs 0 Op. HU; https: //www. nobelprize. org/nobel_prizes/physics/laureates

• We are often taught in school that physics consists of the never-ending interplay between theorist and experimentalist. Theorists propose models for experimentalists to verify, while unexpected experimental results cause theorists to adjust their models. Theory Expt. However, we should all realize that we live in a time when quantum mechanics has already been shown to describe “small & cold” physical processes. • Quantum physics is not questioned, but is studied for understanding and applications.

1. To notice interesting quantum mechanical effects, • Stimulated emission 2. To demonstrate (or realize) these effects using available (quantum) technologies, • First laser: "a solution looking for a problem" 3. To develop new technologies based on these effects which have potential applications to the “real world”. http: //www. press. uchicago. edu/Misc/Chicago/284158_townes. html

Quantum control and simulation 2012 Quantum sensing 2016 Quantum phases of matter Quantum communication https: //www. youtube. com/watch? v=T 2 DXrs 0 Op. HU; https: //www. nobelprize. org/nobel_prizes/physics/laureates

Slide courtesy of John Preskill; https: //arxiv. org/abs/1801. 00862

• We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers. Factoring is the best known example. No efficient classical algorithm for factoring is known, and not for lack of trying. Factoring numbers which are thousands of bits long is out of reach classically, yet eventually will be feasible quantumly. • Consider the probability distribution of measurement outcomes for n-qubits in a quantum computer. Complexity theory arguments, based on plausible assumptions, indicate that no efficient classical algorithm can efficiently sample from this distribution. • We don’t know how to simulate a quantum computer efficiently using a digital (“classical”) computer. It is not for lack of trying. The cost of the best simulation algorithm rises exponentially with the number of qubits. • The power of quantum computing is limited. For example, we don’t believe that quantum computers can efficiently solve worst-case instances of NPhard optimization problems (e. g. , the traveling salesman problem). Slide courtesy of John Preskill; https: //www. q 2 b. us/s/Keynote-John-Preskill. pdf; https: //arxiv. org/abs/1801. 00862

“It's possible that to understand complex biological processes, we will need such tools as quantum automata. … One of the reasons for this is because the quantum phase space is much bigger than classical: where classical space has N discrete levels, a quantum system allowing their superposition will have c^N. … These heuristic calculations point to a much larger potential complexity of the behavior of a quantum system when compared to its classical imitator. ” “Nature isn’t classical, dammit, and if you want to make a simulation of Nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem because it doesn’t look so easy. ” Yu. I. Manin, 1980 R. P. Feynman, 1981

• To be able to perform gates on a quantum computer, we a candidate system and a high degree of control over it. And before we can scale the computer up, we need to focus on the smallest component – a two-level system. To get there, various technological achievements were performed, such as advancements in cooling and techniques to probe the system non-destructively. 2012 photon Nobel prize information 2012

• A phase is a region in some parameter space in which thermal equilibrium states possess some properties in common that can be distinguished from those in other phases. • The traditional telling that symmetry characteristics are universal is now understood to be incorrect—phases may differ only in their topological properties. Liquid and gas are the same phase! Nobel prize information 2016 A modern phase diagram 2016

• Certain phase called topological phases can allow you to store quantum information non-locally in order to hide it from the environment and protect it from errors. • We do not need this technology for classical computing because it is digital! • We can store quantum information non-locally in topologically distinct configurations of loops such that no local probe can disturb the information. John Martinis, Google

Quantum control and simulation 2012 Quantum sensing 2016 Quantum phases of matter https: //www. youtube. com/watch? v=T 2 DXrs 0 Op. HU; https: //www. nobelprize. org/nobel_prizes/physics/laureates

• Quantum devices (based for example on defects in diamond) can achieve higher sensitivity and spatial resolution than other sensors, with potential applications to biology, medicine, magnetometry, accelerometry, gravimetry, etc. Single-cell magnetic imaging using a quantum diamond microscope Diagram of an MNP-labeled target cell above the diamond surface, surrounded by unlabeled normal blood cells. MNP labels are magnetized by the externally applied magnetic bias field B 0, which is aligned as shown with the diamond [111] axis. The magnetic field produced by the MNPs is imaged using the shallow NV layer near the diamond surface to produce the characteristic dipole-like pattern shown (distorted here for perspective).

• The uncertainty principle can be used to generate a secure key. During such a protocol, Alice and Bob generate a private key (i. e. , string of bits) to be shared among them. During key generation, they can test to see if there is an eavesdropper. This protocol relies only on the world being quantum.

Slide courtesy of John Preskill; https: //www. q 2 b. us/s/Keynote-John-Preskill. pdf; https: //arxiv. org/abs/1801. 00862

• While the applications are clear, it is currently unclear which technology will actually build the first practical quantum computer. • This lack of a precise focus on one technology has stimulated a broad and thrilling theoretical investigation into all areas of quantum mechanics which are even remotely useful in building quantum devices. • The area that characterizes this thesis is open quantum systems — the study of quantum systems which are in contact with a larger environment or reservoir. http: //www. sciencemag. org/news/2016/12/scientists-are-close-building-quantum-computer-can-beat-conventional-one

Closed quantum system Closed classical system atom Open classical system Open quantum system HOT BATH atom COLD BATH Leakage of photon out of cavity http: //abstrusegoose. com/406 Quantum “heat engine”

Unitary Non. Unitary System + Environment System 1. Correlations (of system) with environment develop slowly Born approximation 2. Excitations (caused by system) of environment decay quickly Markov approximation 3. Neglect fast-oscillating terms (compared to system timescale of interest) Rotating wave approximation H. -P. Breuer and F. Petruccione, Theory of Open Quantum Systems; C. Gardiner and P. Zoller, Quantum Noise

Thank you for this opportunity to speak! 18