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FROM NIELS BOHR to QUANTUM COMPUTING* Klaus Mølmer, Department of Physics and Astronomy, University of Aarhus, Denmark†

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FROM NIELS BOHR to QUANTUM COMPUTING* Klaus Mølmer, Department of Physics and Astronomy, University of Aarhus, Denmark† FRYBA1 Proceedings of IPAC2017, Copenhagen, Denmark FROM NIELS BOHR TO QUANTUM COMPUTING* Klaus Mølmer, Department of Physics and Astronomy, University of Aarhus, Denmark† Abstract quickly appreciated that cooling of atoms, squeezing of Quantum mechanics replaces determinism with proba- light, control of molecular wave packets … would enable bilistic predictions for measurement outcomes and de- new precise studies and applications, but also truly revo- scribes microscopic particles by wave functions as if they lutionary possibilities emerged. are simultaneously at different locations. The paradoxical Among them were ideas to employ quantum mecha- properties of quantum mechanics caused painstaking nisms for applications outside of physics: quantum money discussions between Schrödinger, Einstein and Bohr who that cannot be counterfeited, unbreakable quantum cryp- disagreed fundamentally about the meaning of the theory. tograhy, and quantum computing. Richard Feynman’s Today, scientists and engineers try to harness the hotly 1982 proposal for quantum computing also included the debated issues of those discussions for technological idea to simulate quantum many-body physics and chemis- applications in quantum encrypted data transmission and try by use of a suitably controllable quantum system. in quantum computing that uses quantum states to do Research in quantum computing has received much at- many calculations in parallel. tention since the theoretical proposal of promising algo- rithms in the mid 1990’s. Following generous funding INTRODUCTION for more than a decade, the European Union has just released its plan to sponsor a 1 Bn € Flagship in Quantum In 1913, Niels Bohr introduced his model of the atom Technologies, engaging both Industry and Academia. with an electron orbiting the atomic nucleus as a satellite Similar activities are operated at national level, and big in orbit around a planet. In 1926 this description was companies like Google, IBM, Microsoft, Alibaba are very replaced by Schrödinger’s wave function which abandons active in the area. A Canadian company, D-Wave, already the classical position and momentum of the electron and offers a quantum computer/simulator on the market. introduces a wave function which provides probabilistic information about where the electron will be found in an experiment. In 1927, Albert Einstein questioned whether Table 1: Classical and Quantum Computer the path that a particle takes through a double-slit appa- Classical Quantum ratus could be determined by measurement in an experi- ment and, hence, reveal a “hidden” reality beneath the Laptop Computer wave formalism. In 1935, with Podolsky and Rosen, he Processor Intel i7 Not known proposed that wave functions of two particles could be Clock 3.3 GHz 1 kHz prepared such that probing of one particle would turn the RAM 6 Gb 1000 bits probabilistic description of the other one into a state of Price 1000 $ 1 Billion $ definite position – “spooky action at a distance”. Niels Bohr offered replies to both challenges which refined the Table 1 presents a brief comparison of some properties interpretation of the theory, but both Einstein and Schrö- of conventional classical computers (left) and our opti- dinger remained skeptical, and physicists still have no mistic expectations to the performance of a quantum single, common interpretation of the quantum theory. computer (right). The reader may note that existing clas- For decades, a “shut up and calculate“ attitude reigned sical computers are about a million times faster, a million and quantum mechanics was successfully employed in all times larger and a million times cheaper (!) than their areas of physics and chemistry, while only a small group anticipated quantum counterpart. How can that be? This of scientists kept pursuing the paradoxical aspects of the article will answer that question and review aspects of theory and the interpretation debate. This, however, quantum computing from their basic principles, over the changed after test experiments by John Clauser and Alain algorithms that they may employ to the physical architec- Aspect in the 1970’s and 1980’s showed that we may tures pursued in current research. actually prepare quantum systems in the laboratories and demonstrate the features proposed as Gedanken experi- FROM BITS TO QUBITS ments by Einstein. Not only, did this lead to a revived interest in the discussions of foundations, it also inspired In modern computers data is encoded in physical prop- a whole new approach to experimental quantum research, erties such as voltages, currents, magnetizations, light with an aim to design, prepare, and control, rather than intensities, etc., restricted to explore a pair of values des- merely observe quantum states and their evolution. It was ignated to represent the logical bit values 0 and 1. Com- ___________________________________________ puting takes place as a physical process, involving suita- * Work supported by the European Union’s Horizon 2020 research and innovation program under grant agreement No 712721; and the ARL- ble interactions among different physical components, CDQI through cooperative agreement W911NF-15-2-0061; and by the and rules of digital logic show that basic one-bit and two- 2017 CC-BY-3.0 andVillum by the respective authors Foundation. bit operations suffice to carry out any computation. In the © † email address : [email protected] electronics computer, the transistor accommodates the ISBN 978-3-95450-182-3 10 Opening, Closing and Special Presentations Copyright 4852 03 Special Presentation Proceedings of IPAC2017, Copenhagen, Denmark FRYBA1 interactions between pairs of data bits, represented as problem of prime factoring. We have no efficient method electric voltages and the miniaturization of transistors and to find the factors of a large number, N=x·y, and merely integration of circuit elements on chips have led to the trying candidate values takes a number of trials roughly incredible performance of modern computers. proportional to the smallest factor which may be of order The idea behind quantum computers is the simple ob- √N and thus scales exponentially with the data size of the servation that if a data bit can be encoded in discrete input number (number of digits). states |Ψ> = |0> or |1> such as the spin states of an elec- Note that while finding a factor may require tests of tron or a nucleus or the electronic ground and excited many candidate values, we only request the read-out of states in an atom, then we can also prepare and manipu- one output value in the end, and Shor’s algorithm exactly late superposition states of the form: proposes how quantum parallel evolution may yield a final state with an almost certain measurement outcome |> =|0>+|1>. that reveals the factors of N. Widely used encryption schemes employ a mathemati- Such a state, in a sense, represents data values 0 and 1 cal operation on the secret message which takes a large at the same time, and we call it a quantum bit or qubit. number N as a parameter; N can be safely announced Two qubits may simultaneously populate all four product publicly by the recipient of the message, as long as she is states |00>, |01>, |10> and |11>, and N bits may simulta- the only one who knows its factors. She is therefore the neously populate states representing all 2N possible num- only one who can subsequently decrypt the received mes- bers that can be written by N bits. sage, as this operation requires use of the factors x and y Logical one- and two-bit operations such as NOT and and another mathematical function. In the war on terror XOR have quantum equivalents, and any classical com- (and out of curiosity concerning even their best allies’ putation can be implemented on a register of qubits, by a smart phone conversations) several countries operate sequence of unitary processes, i.e., as the time evolution systematic eavesdropping activities, but without the abil- imposed by a suitable sequence of one-body and two- ity to decrypt messages such activities make no sense. body interactions. The Schrödinger equation is linear, and Shor’s algorithm thus spurred great interest and funding an initial superposition state therefore must evolve into a for research and development of quantum technologies to superposition of the output states resulting from each enable construction of physical platforms capable to input - the same way as a wavefunction, representing a evolve and maintain quantum superposition states of particle at several locations, evolves during a scattering many individual systems. In particular, military and intel- process into a final state wavefunction with several final ligence authorities became interested, but with the pro- locations or scattering directions. When applied to our posal of other applications and algorithms and a growing multibit quantum register, we thus obtain the tantalizing number of connected applications for communication, possibility that a single run of a sequence of (gate) opera- sensing, synchronization, navigation, … , broader inter- tions that constitutes our algorithm performs a simultane- ests are now directed to quantum information technolo- ous calculation on all possible input register states. gies. Just one quantum operation per second on 100 qubits, is equivalent to 2100 ~ 1030 classical bit operations per BUILDING A QUANTUM COMPUTER second and such a modest device, thus, vastly outper- The potential of quantum computing can only be re- forms all existing computer resources since the
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