What is Quantum Computing?

QUANTUM COMPUTING

What is Quantum Computing? • Why we need Quantum Computing? • Quantum Computing Principle

What can Quantum Computers do? • Addressing molecular problem • Elucidating reaction mechanism

How do Quantum Computers work? • Quantum Algorithms • Quantum Gates

How do I get started with Quantum Computing • Cloud Quantum Computing

History

• [Digital image]. (n.d.). Retrieved January, 2018, from https://www.cnet.com/news/ibm-quantum-computers-business-mooreslaw-qubit/

Simulating Physics with Computers Richard Feynman 1918 - 1988 Nobel Prize in Physics 1965

“If you want to simulate nature, we should build a Quantum Computer.”

In 1982, proposed an idea to create machine based on the laws of Quantum Mechanics rather than the laws of classical physics.

• [Digital image]. (n.d.). Retrieved December, 2017, from https://en.wikipedia.org/wiki/Richard_Feynman • Feynman, R. P. (1982). Simulating physics with computers. International journal of theoretical physics, 21(6-7), 467-488.

Quantum theory, the Church– Turing principle and the universal David Deutsch quantum In 1985, developed the Quantum Turing computer Machine, showing that quantum circuits 1953 - Present

are universal. • [Digital image]. (n.d.). Retrieved December, 2017, from https://medium.com/the-physics-arxiv-blog/deeper-than-quantum-mechanics-david-deutschs-newtheory-of-reality-9b8281bc793a • Deutsch, D. (1985, July). Quantum theory, the Church–Turing principle and the universal quantum computer. In Proc. R. Soc. Lond. A (Vol. 400, No. 1818, pp. 97-117). The Royal Society.

Shor’s Algorithm

Quantum computers are more powerful than conventional computers.

Peter Shor 1959 - Present

In 1994, Peter Shor came up with a quantum algorithm to factor very large numbers in polynomial time. • [Digital image]. (n.d.). Retrieved December, 2017, from http://www-math.mit.edu/~shor/ • Shor, P. W. (1999). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review, 41(2), 303-332.

Grover’s Algorithm 𝑂 (𝑁 ) 𝑂( 𝑁)

Lov Grover 1961 - Present

In 1996, using Quantum concepts, Lov Grover created an ultra-fast algorithm to search into non indexed databases. • [Digital image]. (n.d.). Retrieved December, 2017, from http://www.dcs.warwick.ac.uk/~tim/quantumcomputing/when/slide5.html • Grover, L. K. (1996, July). A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (pp. 212-219). ACM.

Quantum Computers 7 Qubit NMR Quantum Computer

1998

Google’s D-Wave With 28 Qubits

2006 2000

D-Wave 2000Q With 2000 Qubits

2015 2007

2 Qubit NMR First 12 Qubit Quantum Computer Quantum Computer

2017

D-Wave QC With 1000 Qubits

• https://en.wikipedia.org/wiki/Timeline_of_quantum_computing

More than 40 companies are involved in development of Quantum Computers including Microsoft, Google, IBM, Intel, Toshiba, etc.

• https://en.wikipedia.org/wiki/List_of_companies_involved_in_quantu m_computing_or_communication

In just 35 years of history, we have a QUANTUM COMPUTERS which can:

• Solve ground state energy of H2, BeH2 and LiH • Be used to elucidate the reaction mechanism for biological nitrogen fixation.

• Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671), 242. • Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017). Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 201619152.

What is Quantum Computing?

• [Digital image]. (n.d.). Retrieved January, 2018, from https://www.theverge.com/2016/5/4/11589656/ibm-quantum-computing-cloud

• Calculation based on the laws of quantum mechanics. • Use quantum mechanical phenomena to perform operations on data • Operation done at an atomic/subatomic level

Classical Computers have enabled amazing things.

• [Digital image]. (2018, January). Retrieved from http://btc.bsdvt.org/index.php/2016/12/08/programmingand-computer-science-coming-in-fall-2017/

But…. There are still many problems that can’t solve

10 people

3.6 millions

• [Digital image]. (n.d.). Retrieved December, 2017, from http://fiin.info/10dining-table

Factor a number into primes 1 /3 𝐿 𝑂 (𝑒 )

3 𝑂 (𝐿 )

•N = p * q • N has L digits • Given N, what are p and q?

For L = 400 digits

Bond Length

• Digital image]. (n.d.). Retrieved January, 2018, from https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Linear_molecular_geometry.html • [Data]. (n.d.). Retrieved December, 2017, from http://cccbdb.nist.gov/diatomicexpbondx.asp

Simulating very large molecules • Account every repulsion and attraction of the nuclei. • The number goes exponentially the bigger the molecules. • Every single e- exerts an electrostat force on every single other e . e -

e

• Hoffman, B. M., Lukoyanov, D., Yang, Z. Y., Dean, D. R., & Seefeldt, L. C. (2014). Mechanism of nitrogen fixation by nitrogenase: the next stage. Chemical reviews, 114(8), 4041-4062.

• [Digital image]. (n.d.). Retrieved December, 2017, from https://www.youtube.com/watch?v=S52rxZG-zi0

Superposition • Property to exist in multiple states • If a particle can be in states |0> and |1>, then it can also be in the state α|0> + β|1>. • α and β are complex numbers. 2 2 •|α| +|β| =1 • [Digital image]. (n.d.). Retrieved December, 2017, from https://www.youtube.com/watch?v=S52rxZG-zi0

• [Digital image]. (n.d.). Retrieved December, 2017, from https://www.youtube.com/watch?v=S52rxZG-zi0

Entanglement • The ability of quantum systems to exhibit correlations between states within a superposition. • Imagine two qubits, each is state |0>+|1> (a superposition of the 0 and 1.) • We can entangle the two qubits such that the measurement of one qubit is always correlated to the measurement of the other qubit. • [Digital image]. (n.d.). Retrieved December, 2017, from https://www.youtube.com/watch?v=S52rxZG-zi0

How do Quantum Computers Work?

• [Digital image]. (n.d.). Retrieved January, 2017, from https://www.quora.com/How-were-quantum-algorithms-developed

The machine is activated by creating equal superposition of all 2n states.

Problem is encoded in system by applying gates which puts information into phase and amplitude of all 2n states.

Computer gives a solution by magnifying the amplitude of correct answer and shrink incorrect answers.

• [Digital image]. (n.d.). Retrieved December, 2017, from https://www.youtube.com/watch?v=S52rxZG-zi0

Quantum Gate Wires depict qubits

…boxes and different symbols depict operations on qubits

• Similar to the logical binary gates of classical computer. • Usually represented as Unitary Matrices. • Circuit Representation • Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

Pauli-X Gate • Acts on a single qubit

• Acting on pure states becomes a classical NOT gate

• Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

Pauli-X Gate • Acts on a general qubit state

• It is its own inverse

• Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

Hadamard Gate • Acts on a single qubit

• One of the most important gates for quantum computing

• Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

Hadamard Gate • An interesting example 1 2 |𝛼| = 2

1 2 |𝛽| = 2

• Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

Hadamard Gate • Applying another Hadamard gate - to the first result

- to the second result

• Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

Hadamard Gate

• So the state of the system has to be specified with complex amplitudes and cannot be specified with probabilities only • Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

So many gates… 1 𝑍= 0

0 −1

• Williams, C. P. (2010). Explorations in quantum computing. Springer Science & Business Media.

What can Quantum Computers do?

• [Digital image]. (n.d.). Retrieved December, 2017, from https://cen.acs.org/articles/95/i43/Chemistry-quantum-computings-killer-app.html

Addressing Molecular Problems • Used to address electronic structure problems. • To solve for the ground-state energy of manybody interacting fermionic Hamiltonians. • Here Quantum Computer is used to find the ground state energy of H2 , BeH2 and LiH.

𝐻|𝜑𝐺 >= 𝐸𝐺 |𝜑𝐺 > • [Digital image]. (n.d.). Retrieved January, 2018, from http://chocolatecake.hplulu.com/theobromine-chocolate/ • Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671), 242.

Spin orbital parity mapping Parity mapping of spin orbitals into qubits. Reduced to six qubits owing to fermionic spin and parity symmetries.

Superconducting quantum processor These qubits are coupled via two coplanar waveguide resonators (violet) and have individual coplanar waveguide resonators for control and read-out. • Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671), 242.

Hardware-efficient quantum circuit for trial-state preparation and energy estimation.

𝑞,𝑖 𝑈

𝜃 =𝑍

𝑞

𝑞,𝑖 𝜃1

𝑋

𝑞

𝑞,𝑖 𝜃2

𝑍

𝑞

𝑞,𝑖 𝜃3

𝑈𝐸𝑁𝑇 =

−𝑖𝐻 𝜏 𝑜 𝑒

Pulse sequence An example of the pulse sequence for the preparation of a six-qubit trial state, in which UENT is implemented as a sequence of two-qubit cross-resonance gates. • Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671), 242.

Experimental implementation of six-qubit optimization. The minimum energy of six-Qubit Hamiltonian describing BeH2 with an interatomic distance of 1.7 Ǻ. • Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671), 242.

Solving the ground-state energy

Black filled circle: Experimental results Dotted lines: Exact energy surfaces Shading: Density plots (See color scales)

• Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671), 242.

Elucidating reaction mechanism • Requires the identification of al relevant stable intermediates and transition state. • By augmenting classical calculation of reaction mechanisms with reliable estimates for relative and activation energies.

• [Digital Image]. (n.d.). Glowacki, D. R., Harvey, J. N., & Mulholland, A. J. (2012). Taking Ockham's razor to enzyme dynamics and catalysis. Nature chemistry, 4(3), 169. • Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017). Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 201619152.

Nitrogenase MoFe protein C – Gray O – Red H – White S – Yellow N – Blue Fe – Brown Mo – Cyan

• Nishibayashi, Y. (2015). Molybdenum-catalyzed reduction of molecular dinitrogen into ammonia under ambient reaction conditions. Comptes Rendus Chimie, 18(7), 776-784. • Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017). Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 201619152.

• •

QFCI – Quantum Full Configuration Interaction CAS – Complete active orbital space

Generic flowchart of a computational reaction mechanism elucidation with a quantum computer • Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017). Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 201619152.

Simulation time estimates • Structure 1 is for spin state S = 0 and charge +3 elementary charges with 54 electrons in 54 spatial orbitals. • Structure 2 is for spin state S = 1/2 and charge 0 with 65 electrons in 57 spatial orbitals

• Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017). Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 201619152.

Photosystem II This large enzymatic complex carries out some of the critical first steps in photosynthesis, using the energy from absorbed light to oxidize water and harvest electrons. Water oxidation occurs at a site called the manganese center, which future quantum computers could someday model. A deeper understanding of photosystem II’s chemistry could enable chemists to design catalysts for artificial photosynthesis, a renewable process to produce hydrogen and hydrocarbon fuels.

High-temperature superconductors Powerful quantum computers could predict superconductors that work at room temperature. Such materials would enable advances in magnets, motors, the power grid, and more. • [Digital image]. (n.d.). Retrieved December, 2017, from https://cen.acs.org/articles/95/i43/Chemistry-quantum-computings-killer-app.html

Spectroscopy Early quantum computers might more accurately determine the absorption spectra of chemicals, information that could help astronomers learn more about distant galaxies.

Solar-cell Materials Quantum computers could better simulate how charges move through the active materials in solar cells. Such information could enable researchers to predict and design new solar-cell materials that have different combinations of properties, such as low cost, flexibility, and high performance. • [Digital image]. (n.d.). Retrieved December, 2017, from https://cen.acs.org/articles/95/i43/Chemistry-quantum-computings-killer-app.html

How do you get started with Quantum Computing?

• [Digital image]. (n.d.). Retrieved January, 2018, from https://motherboard.vice.com/en_us/article/a3jkya/quantum-game-physicscomputer-puzzle

IBM Universal Quantum Computer • Anyone can register and start using quantum computer at no cost to one of IBM’s quantum processors via the IBM cloud. • You can run algorithms and experiment and collaborately explore the possibility of quantum computing. • You can check user guides and interactive demos to learn more about quantum principles. • You can also create and run algorithms in real quantum hardware using Quantum Composer and QISKit software developer kit.

IBM Universal Quantum Computer

• Research, I. (n.d.). Retrieved January, 2018, from https://quantumexperience.ng.bluemix.net/qx

Quantum Composer

IBM Universal Quantum Computer

• Research, I. (n.d.). Retrieved January, 2018, from https://quantumexperience.ng.bluemix.net/qx

https://quantumexperience.ng.bluemix.net/qx

IBM Universal Quantum Computer

• Research, I. (n.d.). Retrieved January, 2018, from https://quantumexperience.ng.bluemix.net/qx

• Research, I. (n.d.). Retrieved January, 2018, from https://quantumexperience.ng.bluemix.net/qx

• Research, I. (n.d.). Retrieved January, 2018, from https://quantumexperience.ng.bluemix.net/qx

• [Digital image]. (n.d.). Retrieved December, 2017, from https://www.youtube.com/watch?v=S52rxZG-zi0

Deuteron Binding Energy with 5 Qubit Cloud Quantum Computing

• Dumitrescu, E. F., McCaskey, A. J., Hagen, G., Jansen, G. R., Morris, T. D., Papenbrock, T., ... & Lougovski, P. (2018). Cloud Quantum Computing of an Atomic Nucleus. arXiv preprint arXiv:1801.03897.

"My students don't understand Quantum Mechanics, because I don't understand it. Nobody understand Quantum Mechanics." ~ Richard Feynman

Acknowledgement

• Chemistry Faculty, University of South Dakota. • Professor Sykes and Dr. Kadal. • All my friends and relatives.

“Do not let your difficulties fill you with anxiety, after all it is only in the darkest nights that stars shine more brightly.” ~ Imam Ali (A.S.)