Quantum Computers and Quantum Chemistry

QUANTUM COMPUTERS AND QUANTUM CHEMISTRY

Jarrod McClean Aspuru-Guzik Group Harvard University PROMISES OF QUANTUM CHEMISTRY

Understanding

Control THE ELECTRONIC STRUCTURE PROBLEM

“The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.” -Paul Dirac

WHAT’S SO “COMPLICATED”?

Electrons: One mole Particles in universe TRADITIONAL SOLUTION TRADITIONAL CHALLENGES BEYOND THE MEAN FIELD

Virtual

Occupied ALTERNATIVES

DFT: Errors in transition states, Charge transfer excitations, anions,…

Full Configuration Interaction: Exact (within a basis)

M. Head-Gordon, M. Artacho, Physics Today 4 (2008) QUANTUM MARIONETTE

Engineer Let system naturally Measure interesting Hamiltonian explore quantum space parts of the system QUANTUM COMPUTING NOTATION QUANTUM PHASE ESTIMATION

Prep Evolution Measurement

Classical: Quantum:

Challenge: Coherence time

Aspuru-Guzik, Dutoi, Love, Head-Gordon, Science 309, 1704–1707 (2005). A New Co-design Perspective

Currently: Given a task, design quantum circuit (or computer) to perform it.

Problem: General or optimal solution can require millions of gates.

Alternative: Given a task and the current architecture, find the best solution possible.

42.02

Peruzzo†, McClean†, Shadbolt, Yung, Zhou, Love, Aspuru-Guzik, O’Brien. Nature Communications, 5 (4213):1– 7, 2014. † Equal Contribution by authors EASY TASK FOR A QUANTUM COMPUTER

•Efficient to perform on any prepared quantum state •In general, it may be very hard to calculate this expectation value for classically for some states Variational Basics

Variational Formulation:

Can write a Hermitian Hamiltonian as:

By Linearity:

Easy for a Quantum Computer: Easy for a Classical Computer: Computational Algorithm QUANTUM HARDWARE STATE ANSATZ

Any Quantum Device with “knobs”

Advantages: •Use the complexity of your device to your advantage •Always satisfies a variational principle •Coherence time requirements are set by the device, not algorithm Model System Physical Implementation Experimental Electronic Curve

He H R feature QUANTUM COMPUTATION IS APPROACHING

Timeline of key events: Quantum chemistry on quantum computers

Feynman proposes to Aspuru-Guzik and co-workers simulate quantum systems show that the calculation of In a series of papers 5-9, with quantum computers. molecular ground-state the groups of Aspuru-Guzik, energies will scale polynomially Microsoft Research and 1 on a quantum computer . Matthias Troyer clarify what kind of scaling we can expect A qubit that is stable enough for quantum chemical algorithms for a trillion operations without Lloyd confirms that Feynman ’s on quantum computers. too many errors? proposal is possible 10.

1981 1996 1997 2005 2010 2014/2015 2020–2025? 2030–2035?

Abrams and Lloyd devise a Aspuru-Guzik and White complete quantum algorithm experimentally calculate A small quantum computer with a few hundred qubits for for simulating a quantum system properties of H 2 with photonic based on time evolutio n11. quantum computer technolog y2. quantum chemical calculations of small molecules?

In order for the equations that underlie this multireference problems. T ey are a nuisance small but multireference-ridden reactive time evolution to be encoded into logical in conventional quantum chemistry but are metal centres could be calculated using a operations that can be carried out by the not too demanding for a small quantum quantum computer while advanced linear- qubits, they need to be broken down into machine with a few hundred to a thousand scaling methods from conventional quantum discret e time steps. T e bigger the steps, the qubits. In this realm, studying Fe2S2 — the chemistry would be well-suited to treat the fewer operations you need and that makes reactive centre in the electron transfer surrounding organic portion of the protein. for better scaling. But if you make the sMueckteps , eNaturenzyme fe rChemistryrodoxin — ha 7,s e s361tabli–sh363ed (2015) But much must happen before every too large, you introduce errors. “T e question itself as both Troyer’s and Aspuru-Guzik’s chemist has a quantum computer handy so people have been trying to get their heads favourite showcase problem. With the newly today’s quantum chemists should not throw in around recently is ‘What is the largest time optimized algorithms, an FCI calculation on the towel. Scuseria, at least, has by no means step that you can take without having large Fe2Se2 would indeed f nish within minutes or given up on conventional methods: “I believe errors in your answer?’” Aspuru-Guzik hours on a 150-qubit quantum computer; no that there is a polynomial-cost answer to the says. In early 2014, Matthias Troyer and the quantum chemist would even dare to dream strong correlation problem. We just haven’t Microsof team were looking to answer this that this calculation could be performed found it yet.” he says. And Troyer hopes that question and initial analysis revealed5 that, to on a classical computer. But, for the f rst the developments in quantum computing will give accurate answers, the time steps required generation of quantum computers, fulf lling give rise to “quantum-competition inspired” 9 lead to a ter rible scaling of N . But subsequent Scuseria’s wish to treat [Mn12] tetramers leaps in solving the big problems in quantum analysis and optimization by both teams has will be a stretch. T is is not only because chemistry with conventional methods. brought it down signif cantly6–9. T e latest it would need 2,000 qubits but depending Instead of worrying over their beers that results show that the scaling might be as good on the gate time and exact scaling, Scuseria quantum computers could put them out of as N4 or N3 in some cases, Svore says. would also probably have to wait years for work, quantum chemists should channel their What exactly this progress means in the calculation to f nish. And that’s nothing ef orts and design better algorithms to treat practice depends on how fast the computer compared with studying high-temperature small multireference cases. With the prospect could per form individual operations; superconductors with quantum computers: of beating a quantum computer to keep you computer scientists call this the gate time. optimistically assuming a gate time of about motivated, now seems to be the best time ever If trapped ions are used as qubits, the ten nanoseconds, Troyer estimates that this to devote a career to approximate methods in current gate time amounts to about 10 computation would last for as long as the age conventional quantum chemistry. ❐ microseconds; the big rival technology — of the universe. superconducting qubits — needs about 100 It does not look like the early generations Leonie Mueck is an Associate Editor at Nature nanoseconds. “If we can get a machine with of quantum computers will revolutionize the based in London, UK. about 200 qubits and the gate time is not way we do quantum chemistry. Instead of e-mail: [email protected] more than a microsecond then we have some transforming the maze of current quantum really interesting applications.” says Troyer. chemical methods into a highway, they References In other words, we could perform an FCI will most likely add just another quick side 1. Aspuru-Guzik, A., Dutoi, A., Love, P. J. & Head-Gordon, M. Sci ence 309, 1704–1707 (2005). calculation that is intractable on a classical road that one would use to solve a specif c 2. Lanyon, B. P. et al. Nature Chem. 2, 106–111 (2010). computer in minutes or maybe hours. range of chemical problems. “It will be 3. Per uzzo, A. et al. Nature Commun. 5, 4213 (2014). T is is wonderful news for computer like now, the only dif erence is that we 4. Kassal I. et al. Annu. Rev. Phys. Chem. 62, 185–207(2011). 5. Wecker D. et al. Phys. Rev. A 90, 022305 (2014). scientists. But what does it mean for could do FCI on slightly bigger systems,” 6. McClean, J. et al. J. Phys. Chem. Lett. 5, 4368–4380 (2014). chemists? Would this progress allow for Troyer comments. To get the best of both 7. Hastings, M. B. et al. Quantum Inf. Comput. 15, 1–21 (2015). treating problems of real chemical interest? worlds, Troyer envisions quantum–classical 8. Babbush, R. et al. Phys. Rev. A 91, 022311 (2015). 9. Poulin, D. et al. Quantum Inf. Comput. 15, 361–384 (2015). In general, it seems that a quantum computer hybrid methods: in metalloenzymes, like 10. Lloyd, S. Sci ence 273, 1073–1078 (1996). would have the biggest impact for small ferrodoxins, haemoglobins or cytochromes, 11. Abrams, D. & Lloyd, S. Phys. Rev. Lett. 79, 2586–2589 (1997).

NATURE CHEMISTRY | VOL 7 | MAY 2015 | www.nature.com/ naturechemistry 363

•Quantum computers offer a new route forwards to understanding and predicting the properties of chemical and material systems

•Considering both the problem and the available architecture offers a new way to utilize available quantum resources today

•A small scale implementation has been built and tested on quantum hardware

•Quantum software as well as quantum hardware is being pursued in industry, national labs, and academia and may be here sooner than we thought

Acknowledgements

Harvard University: Alan Aspuru-Guzik Man-Hong Yung Ryan Babbush Aspuru-Guzik Group

University of Bristol: Jeremy O’Brien Alberto Peruzzo Xiao-Qi Zhou Pete Shadbolt

Haverford College: Peter Love