A Conceive Overview and Outlook on Quantum Computing

A conceive overview and outlook on Quantum Computing

White Paper (March 2020, v1.0)

Abstract: The idea is not new but fascinating achievements in recent years have shown that quantum computers will become reality. They are not just ‘faster computers’ but follow a different approach that opens up a wide range of new and novel applications. Promising developments have been made in recent years, but it is still unclear which technology will boost the quantum computer like it has been the case for classical computers with the development of the transistor. Many more years of research and engineering are needed before fully working quantum computers will exist. However, there are promising drivers that will sustain the continuous development, even when the current hype in the media will cease.

Introduction: What is a quantum (20-qubit) quantum computer, IBM Q computer? System One, designed for scientific and For decades, quantum computers where commercial use. This did not only attract the interest of specialists but also the merely a theoretical construct. The idea of a quantum computer dates back to 1960, attention of a broader public because of a hype in the media. when Richard Feynman1 suggested, that instead of the classical approach with Qubits are the quantum version of the binary data units (bits), a different classical bits. These qubits can be made of approach could be thought of. At atomic photons (light particles), atoms, electrons, scales, nature behaves rather differently molecules or perhaps something else. A than at macroscopic level. These qubit is a two-state system that can be in phenomena are described by quantum multiple states at the same time. Just think physics. Instead of using binary data units of Schrödinger’s cat that is death and alive that only can take a value of 1 or 0, it at the same time. This is called would be highly interesting to use data superposition. There is another quite units with quantum properties, i.e. that can intriguing phenomena in quantum physics: take a value of 1 and 0 at the same time entanglement. Entanglement is an with a given probability. Hence, a different extremely strong correlation between two type of computers on the basis of quantum or more particles that links them in perfect data units, so-called qubits, could be more unison (even over macroscopic distances!). appropriate to deal with quantum A computing device that uses quantum phenomena rather than classical computers systems (qubits) – which have the ability that use bits that are binary data units. to be found in superposition states and In the late 1990ies, the first demonstrators entangled states – and hence can capitalize showed that quantum computers are on quantum phenomena, is called feasible. In 2019, IBM unveiled its first quantum computer.

1 / 5 Why the hype? of Shor’s algorithm was demonstrated by Because quantum computers work in a IBM in 2001.3 This implies that the public rather different way than regular key using RSA encryption can be easily broken, given a sufficiently large quantum computers. A regular computer tries to solve a problem the same way you might computer. Longer keys are a possible try to find out an unknown phone number counter measure.4 – by trying one number after the next until Different type of applications: The you got the correct number. A quantum simulation of quantum systems has often computer, however, makes use of been said to be the ‘holy grail’ of quantum superposition and tries all possible applications. A classical computer can numbers at the same time and represent only a limited number of instantaneously finds the correct one. interacting particles. While even the most How is this possible? Two bits can have powerful classical computers today will four possible states: [00,01,10,11], but fail to represent a system of 40 interacting only one at the time. Two qubits can particles, a (fully performing) quantum represent exactly the same states: computer with 40 qubits can do the job. [00,01,10,11], but all four at the same time This opens up new ways to simulate and because of superposition. This is a bit like study interactions at atomic level. having four classical computers running at Organic simulations and materials science the same time. If you add more bits to a could be among the first useful classical computer, you still can represent applications for quantum computing. It could help to design new drugs and new only one state at a time. But if you add more qubits to a quantum computer, the materials, such as superconductors that power increases exponentially: with n work at room temperature. But also, applications in machine learning, qubits you can simultaneously represent 2n states. This exponential growth with communication, high-frequency trading, increasing number of qubits is what makes forecasts, etc. are likely to be revolutionized by quantum computers. quantum computers so interesting. But quantum computers are not only potentially extremely fast, they are also Still a long way to go more suitable for certain difficult task (e.g. It is not that simple to build a quantum their reversibility helps solving non- computer and there are still a lot of polynomial problems, which are easy in challenges. To perform quantum one direction but hard in the opposite computation, qubits must all be in states of sense) and new applications. For example: superposition and entanglement. This Factorizing large numbers: Encryption is coherent state must be long enough to run a given calculation before interactions with used in many cases to secure websites, the surrounding environment leads to emails, network services, credit cards, SIM cards, the Bitcoin network and many more. decoherence that scrambles the qubits. The so-called RSA encryption is the most Hence, the coherence-time should be as important technique used today and relies long as possible. Larger systems tend to on a public key which is the product of two lose quantum properties quicker, i.e. have very large (several hundredths of digits) shorter coherence-times what makes prime numbers. Factoring such large scaling more difficult. numbers within reasonable time is Another reason why quantum computing is impossible for conventional computers. so difficult are quantum errors. Like just But in 1994, Peter Shor proposed a about every other process in nature at quantum algorithm2 (Shor algorithm) that atomic levels: quantum computers have to significantly reduces the runtime of deal with noise. Random fluctuations will number factorization. The implementation occasionally flip the state of a qubit and 2 / 5 interaction with the environment alter the Today, the development of quantum- coherence. computational hardware has a strong focus It possible that quantum computation can on increasing the Quantum Volume. be made fault-tolerant, i.e. robust against errors and inaccuracies when the physical Which technology will prevail? error rate is below a given threshold.5 To make a qubit, a system is needed that Hence, fully operational and performing can attain a state of quantum superposition quantum computers will need more than between two states. For the physical just a lot of qubits. The machines will have realization, many different approaches to to have longer coherence-times, lower find the best suitable system are currently error rates and fault-tolerant algorithms. being investigated. A few examples: Adding more qubits without any of these Superconducting quantum computer: improvements does not make a quantum Qubits are implemented by the state of computer more powerful. small superconducting circuits. LC- circuits7 are quantum harmonic oscillators How to measure the performance of a and know superposition of wavefunctions quantum computer? (eigenstates) like this is the case for There is often a strong focus on the classical harmonic oscillators. number of qubits. However, the number of Superconducting LC-circuits are suitable qubits is not necessary the first and for sure as building blocks for qubits and the fabrication techniques are well known not the sole performance indicator. from conventional integrated circuits. In IBM introduced in 2017 a metric called order to isolate the ground state (0) and the Quantum Volume6 that indicates the first exited energy level (1) from higher relative complexity of a problem that can energy levels, nonlinear Josephson be solved by quantum computers. junctions are used as inductors. The number of qubits and the number of Nuclear magnetic resonance (NMR) operations that can be performed are called quantum computer: Qubits are made from the width and depth of a quantum circuit. spin states of nuclei within molecules. The The deeper the circuit, the more complex quantum states are probed through NMR. of an algorithm the computer can run. NMR quantum computers differ from Circuit depth is influenced by such things other approaches because they use an as the number of qubits, how qubits are ensemble of systems (molecules), rather interconnected, gate and measurement than a single pure state. A lot of recent and errors, device cross talk, circuit compiler impressive practical accomplishments in efficiency, and more factors. Quantum quantum computing have been made using Volume analyzes the collective NMR quantum computers. Solid-state performance and efficiency of these factors NMR Kane quantum computer use as well and then produces a single, easy-to- radio pulses to interact with the qubits. But understand Quantum Volume number. The the qubits are made of deposited larger the number, the more powerful the phosphorus on a silicon lattice. quantum computer. Spin-qubit quantum computer: Qubits are IBM tested the following three quantum made of the spin state of trapped electrons computers (Quantum Volume result in (spin-based) or by the electron position in a brackets): 5-qubit Tenerife/IBM 2017 (4), double quantum dot of trapped ions 20-qubit Tokyo 2018 (8), and 20-qubit (special-based). Quantum dots are IBM Q System One 2019 (16). nanoparticles made of any semiconductor material. The material of choice is silicon. Spin-qubit computers (or quantum dot

3 / 5 computers) are promising for future years away. The theoretical foundation is scalable computers. However, quantum well established, but theoretical dots are very sensitive to the developments alone will be no good electromagnetic environment and it is still without a matching technology. Many a challenge how long-range coupling aspects still require further exploration and (needed for a qubit lattice) could be are subject to scientific and engineering realized. studies. That covers quantum algorithms, Trapped ion quantum computer: Qubits are understanding dynamics and control of made from trapped ions. Unlike quantum decoherence, atomic scale technology and worthwhile applications. dots that are electronically controlled, they are optically controlled. This allows, next Different qubit technologies have different to sensing abilities, the integration over advantages and drawbacks. For example, longer distances. the cycle time (clock rate) for Cavity quantum electrodynamics: Cavity superconducting qubits is with a few quantum electrodynamics (cavity QED) is nanoseconds far faster than in the case of the study of the interaction between light trapped ions that need microseconds. Fast confined in a reflective cavity and atoms or cycle times are of interest to applications other particles. Qubits can be represented like high-frequency trading. On the other by photon states or by atom states. Photons hand, the coherence time of a are being used to communicate between superconducting qubits is with a few the different states. The approach allows a milliseconds rather short and they lose their memory very fast. The trapped ion true quantum computer because it can create, manipulate and preserve qubits have, on the other hand, coherence superposition and entanglements. times typically on the order of several seconds. Thus, one can imagine hybrid Linear optical quantum computer (LOQC): quantum computers that use make use of Qubits are represented by photon states. different assets from different Superpositions of quantum states of technologies. In this sense, also hybrid photons can be easily represented, detected classical-quantum computers hold a and transmitted what makes LOQC promising potential. Despite the rapid promising candidates for quantum progress being made, the large number of communication. potential candidates for qubits show that Topological quantum computer: This is a the search for the most appropriate theoretical quantum computer that employs technology is still ongoing. quasiparticles (particle-like objects that Next to drivers like security or science, emerges from interactions inside matter) as applications that can yield economical qubits. It is unclear if such a quantum value will surely influence and shape the computer will ever exist, but their future of quantum computers. For example, topological properties, which make the pharmaceutical companies have a high quantum states extremely robust, are very interest to simulate at biological molecules interesting. at quantum level to figure out what they will do. However, such and other promising applications are still too far Future of Quantum Computing away to capture substantial venture capital. A large-scale quantum computer that outperforms classical computers is still

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1 Feynman, R., There’s plenty of room at the bottom. California Institute of Technology, Engineering and Science magazine, 1960.

2 Shor, P., Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings 35th annual symposium on foundations of computer science, pages 124–134. Ieee, 1994.

3 Vandersypen, L., Steffen, M., Breyta, G., et al., Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance, Nature, 414 (6866): 883–887, 2001

4 The National Institute of Standards and Technology (NIST) recommends 2048-bit keys for RSA (NIST Publication 800-57, 2015). RSA-2048 has 617 decimal digits (2,048 bits). A key length of 3072 bits should be used if security is required beyond 2030.

5 Aharonov, D. & Ben-Or, M., Fault-Tolerant Quantum Computation With Constant Error Rate, arXiv:quant- ph/9906129, 1999

6 Bishop, L., Bravyi, S, Cross, A., Gambetta, J., and Smolin, J., Validating quantum computers using randomized model circuits, Quantum Volume. Technical Report, 2017.

7 The LC-circuit is an electric circuit consisting of an inductor L, and a capacitor C. It is a simple harmonic oscillator with a harmonic potential, i.e. an equal energy spacing between all the energy levels. The ground level (0) and the first exited energy level (1) of superconducting LC-circuits can be used as building blocks for qubits.

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