Quantum Reform

feature Quantum reform

Leonie Mueck

Quantum computers potentially offer a faster way to calculate chemical properties, but the exact implications of this speed-up have only become clear over the last year. The first quantum computers are likely to enable calculations that cannot be performed classically, which might reform quantum chemistry — but we should not expect a revolution.

t had been an exhausting day at the 2012 International Congress of Quantum IChemistry with countless presentations reporting faster and more accurate methods for calculating chemical information using computers. In the dry July heat of Boulder, Colorado, a bunch of young researchers decided to end the day with a cool beer, but the scientific discussion didn’t fade away. Thoughts on the pros and cons of all the methods — the approximations they involved and the chemical problems that they could solve — bounced across the table, until somebody said “Anyway, in a few years we will have a quantum computer and our approximate methods will be obsolete”. An eerie silence followed. What a frustrating thought! They were devoting their

careers to quantum chemistry — working LIBRARY PHOTO RICHARD KAIL/SCIENCE tirelessly on applying the laws of quantum mechanics to treat complex chemical of them offering a different trade-off between cannot do on a ‘classical’ computer, it does problems with a computer. And in one fell accuracy and computational feasibility. not look like all the conventional quantum- swoop, would all of those efforts be wasted Enter the universal quantum computer. chemical methods will become obsolete or as chemists turn to quantum computers and This dream machine would basically work that quantum chemists will be out of their their enormous computing power? like a normal digital computer; it would jobs in the foreseeable future. Instead of a be programmable and could carry out quantum revolution, it looks like we will be Quantum-chemical cravings any imaginable algorithm. But instead of confronted with a quantum reform. Ever since its beginnings, quantum electronic circuits representing bits, it would chemistry has been on a starvation diet — contain quantum circuits representing The scale of the problem adapting to limited computational resources quantum bits — or qubits. These can be Although there are confusingly many like an organism adapts to a scarcity of constructed using all sorts of quantum approximations that are used in quantum nutrients. In the 1920s and 1930s, the great systems like nuclear spins or the electronic chemistry, it has been very successful. forefathers of the subject already knew the states of ions trapped in electromagnetic “Quantum chemistry has become a very exact mathematical laws to describe the fields. “Right now we are in the very early mature field,” explains Gus Scuseria, a quantum mechanical behaviour of electrons stages of quantum computing in terms of quantum chemist from Rice University in in molecules. But, as Paul Dirac put it, actual implementation,” explains Krysta Houston, Texas. Today, all chemists can get “the exact application of these laws leads Svore from Microsoft Research. But once their hands on user-friendly programs to to equations much too complicated to be this dream machine has become reality, the calculate ground-state energies, molecular soluble”. Dirac proved to be quite the prophet expected quantum leap in computing power geometries or spectral parameters, — even for today’s supercomputers, using promises an end to quantum chemistry’s using clever approximations to the exact the Schrödinger equation to exactly calculate starvation diet, providing the resources to solution. This exact solution is called full properties of even simple molecules is too calculate exact solutions to the previously configuration interaction (FCI) — and complicated. But just like with a starvation unsolvable equations and removing the need it takes full account of electron–electron diet, quantum chemists adapted to the for approximate methods. interactions, unlike the more simplistic restricted computational resources, building However, in the past year, researchers methods that just approximate those their vocation around the development of have started to clarify exactly what changes interactions by crude averaging. To carry out ever more sophisticated approximations to the first generation of quantum computers FCI calculations the necessary computational the exact solutions. This has resulted in a will bring. And although we will probably resources are enormous and they grow — or wealth of quantum chemical methods, each be able to perform computations that we scale — exponentially with the system size,

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© 2015 Macmillan Publishers Limited. All rights reserved feature which is measured by the number of spin Schrödinger equations at hand, which is concurs Troyer — at least for the first orbitals in the molecule. That means you can what a quantum computer promises, then we generation of small quantum computers with realistically perform such calculations only will be able to predict — always.” says Alan a few hundred qubits. And so Svore’s group on atoms and tiny molecules with a handful Aspuru-Guzik from Harvard University. In joined forces with Troyer and started to look of electrons in a few spin orbitals. other words, quantum chemists could stop at the prospects of quantum chemistry on The methods that quantum chemists worrying about approximations and just quantum computers. have developed to sensibly approximate the solve problems exactly. The main reason Their studies are carried out with a healthy FCI solution bring down the computational for the speed-up is simple: on a classical dose of pragmatism; having proof that FCI resources to something bearable — that is you computer, the electronic wave function — calculations scale polynomially is a good can comfortably calculate chemical properties which contains all the information about how start, but there are still some very practical of molecules with a few hundred atoms the electrons behave in a molecule — needs questions that need answering. It is crucial within hours or days on a supercomputer. a huge amount of memory to be stored. The to know what exactly the x in an Nx scaling The approximations have an effect on how number of required bits scales exponentially would be to get an idea about how long the required computational resources with the number of spin orbitals, hence the calculations would actually take on quantum scale with system size: rather than scaling exponential scaling of FCI calculations. But, computers. The question is whether they will exponentially, they scale polynomially, that is being quantum systems themselves, quantum finish in an amount of time that a quantum if N is the number of spin orbitals, the scaling computers represent electrons in molecules chemist is willing to wait — say a few is Nx. The value ofx depends on, the exact much more effortlessly — the number of months. “If the scaling is N10, it’s faster than approximations that you make: the smaller x, necessary qubits only grows linearly with the a classical computer but it might just take the cruder the approximation and the larger number of spin orbitals. Consequently, you forever.” Troyer says. And if that “forever” is the errors. But a smaller x also means that you also need fewer operations to manipulate too long for even the most patient quantum need less computational resources and can the qubits, explains Aspuru-Guzik. Back in chemists, quantum chemistry will never be treat larger molecules in less time. In other 2005 he showed, theoretically, that an FCI the killer application for quantum computers. words, the methods form a hierarchy in terms calculation indeed scales polynomially on a of computational resources and accuracy. quantum computer1. A quantum of solace As a rule of thumb, you can comfortably use And since then he has been developing In 2014, advances in determining the exact N7 methods to treat a few tens of atoms and algorithms for quantum chemistry on scaling and designing algorithms to get get a result that is accurate enough for most quantum computers — although there is it down to a practically manageable level chemical purposes. For very large molecules, no quantum computer yet to implement have come so thick and fast that they even there are even tricks to bring N6 methods anything of interest. Apart from a few proof- overwhelmed quantum-computing veteran down to linear scaling while keeping errors to of-principle calculations of the hydrogen Aspuru-Guzik. “It’s been an interesting a minimum. molecule and He–H+ the field has little year,” he says in reference to the progress But there is a caveat. “85 years after experimental work to show for itself 2,3. For that has been made in designing specific

Schrödinger’s equation we have solved half a calculation of one of Scuseria’s [Mn12] algorithms that use as few operations on the of the problems,” Scuseria demurs. For quite fragments you’d need at least 500 qubits qubits as possible. some time, he has been unsuccessfully racking — and we are far from having a quantum A quantum algorithm for quantum his brain about the notorious ‘multireference’ computer of that size. But Aspuru-Guzik is chemistry looks fundamentally different from or ‘strong correlation’ cases that make up the optimistic: “We will see this in our lifetime,” its classical counterpart. For example, when unsolved half. If two or more electronic states he says. Matthias Troyer, from ETH Zürich, searching for the ground-state energy of a of a molecule are very close in energy, all the is bold enough to be more specific. “First we molecule with a classical algorithm, you first elegant approximations used to bring the need one qubit that’s really stable long-term, encode a rough guess of a molecule’s wave scaling down no longer hold. Unfortunately, for a few hours or a few days, and that can be function in a huge array of numbers. Then this happens for some of the most interesting manipulated,” Troyer says. It needs to be stable you search for the optimal solution iteratively. chemical problems, such as understanding enough to perform in the order of a trillion The corresponding quantum algorithm, on transition-metal compounds, bond-breaking operations on it without making too many the other hand, proceeds in three steps. First, and single-molecule magnets to name just errors. Troyer thinks this could be achieved the wave function is encoded into qubits that a few. And some of the most enigmatic within 5–10 years. “And then another 10 years are prepared in a quantum superposition problems in physics belong to the class of and we have a small quantum computer — state. This superposition is the pinch of strong-correlation problems, too, for example but that’s optimistic,” he says. magic in quantum computers, the resource high-temperature superconductivity. Scuseria At least this is close enough for giant making them more powerful simulators for sighs. He would love to perform quantum- companies like Microsoft to get involved. quantum systems than classical computers. chemical calculations on big metal clusters Krysta Svore manages the Quantum While classical bits can only assume the — like tetramers of the well-known single- Architecture and Computation group at states 0 or 1, the laws of quantum mechanics molecular magnet fragment [Mn12] — but Microsoft Research. “We want to be ready allow qubits to be in a superposition between it’s a strong correlation problem. There are with killer applications should a quantum all the classical states and thus hold more methods giving you “some results”, Scuseria computer one day be built.” she says to information. The second step is for these explains, but at present there are none that explain the rationale behind their efforts qubits to search for the right answer while give you the right answer for every case of to design quantum computing algorithms undergoing an evolution in time, and the strong correlation. for quantum chemistry. The essential third step involves a measurement being A quantum computer would solve this requirement for a killer application is that the made to extract the desired information from problem using a completely different strategy, quantum computer must be better at solving the superposition state4. one that greatly reduces the scaling of FCI the problem than a classical computer. “So The heart of last year’s progress lies in calculations and makes them far quicker to far, the only thing that is feasible, that has the digging deeper into the second step — the compute. “If we have exact solutions to the application potential, is quantum chemistry” evolution of the quantum system in time.

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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 papers5-9, 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 possible10.

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 H2 with photonic based on time evolution11. quantum computer technology2. quantum chemical calculations of small molecules?

In order for the equations that underlie this multireference problems. They 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 discrete time steps. The 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 steps enzyme ferrodoxin — has established But much must happen before every too large, you introduce errors. “The 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 finish 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 Microsoft 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 first the developments in quantum computing will give accurate answers, the time steps required generation of quantum computers, fulfilling give rise to “quantum-competition inspired” 9 lead to a terrible 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. This is not only because chemistry with conventional methods. brought it down significantly6–9. The 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 finish. And that’s nothing efforts 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 perform 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 1. Aspuru-Guzik, A., Dutoi, A., Love, P. J. & Head-Gordon, M. In other words, we could perform an FCI will most likely add just another quick side Science 309, 1704–1707 (2005). calculation that is intractable on a classical road that one would use to solve a specific 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. Peruzzo, A. et al. Nature Commun. 5, 4213 (2014). This is wonderful news for computer like now, the only difference 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. Science 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).

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