## What do we do with a small quantum computer? - Abstracts

**Matthias Troyer**

ETH Zurich

Simulating classically-intractable quantum systems on (small) quantum computers

Some quantum many body systems, especially unfrustrated quantum magnets and bosonic systems can efficiently be simulated for up to millions of particles by quantum Monte Carlo simulations (QMC). Modern QMC methods allow the accurate exploration of properties in the strong coupling limit and deep in the quantum critical regime at quantum phase transitions. Other problems, such as frustrated magnets, fermions, and in general the dynamics of quantum many body systems in more than one dimension are a big challenge. Special purpose quantum simulators, such as cold atoms in optical lattices promise a way forward, but they are limited: calibration of the model parameters in these analog devices, limitations in the temperatures that can be accessed, and the limitation to models that can be naturally implemented in these analog quantum simulators. A small quantum computer, working as a quantum simulator following the ideas of Feynman, can thus be very valuable tool for solving the ground states, low lying excited states, and dynamics of such quantum models as long as the models contain few terms. For simulation of materials or molecules on the other hand, the N^4 two-body terms in the Coulomb interaction Hamiltonian require substantial algorithmic advances before they can be feasible even on the fastest imaginable quantum computer.

**Alan Aspuru-Guzik**

Professor, Department of Chemistry and Chemical Biology, Harvard University, http://aspuru.chem.harvard.edu

"Quantum chemistry: a promising application for early quantum computers"

About 30% of supercomputer time of the Department of Energy is used for the simulation of chemicals and materials. Access to exact, rather than approximate quantum solutions in this domain can lead to disruption in the landscape of materials science, pharma, and other related disciplines. The White House's Materials Genome Initiative recognizes materials design by screening as one of the areas where the US can gain substantial competitive advantage in the upcoming decades.

In 2005, we began work on how to simulate chemistry with a quantum computer. Back then, we showed the promise of quantum computers for this application. We used the gate model, Troterrization and phase estimation for the energy readout. Since then, we have made much more progress in characterizing the algorithms, error correction schemes and resources necessary for simulating chemical systems using that approach and in carrying out several demonstration experiments with collaborators around the world.

We have also have developed three new approaches, two of them are what I catalog as "Beyond Trotter" approaches: The variational quantum eigensolver (VQE) and the adiabatic quantum chemistry (AQChem) approaches can allow for simulation using much more modest resources. I will provide a bird's eye view of the progress to date, summarize the gate-model results and requirements and go deeper in describing the variational quantum eigensolver and the adiabatic quantum chemistry approaches. I will end by posing a challenge for IBM and other private companies building quantum computers: ``Give us a small quantum computer, and we will give you ready-to-run practical chemical applications''.

**Alexey Gorshkov**

NIST

Persistence of locality in systems with power-law interactions

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in lattice models with interactions featuring power-law decay with distance. The bound contains two terms: One accounts for the short-ranged part of the interactions and decays exponentially in space, reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at long distances. We demonstrate that these two contributions not only bound but qualitatively reproduce the short and long distance dynamical behavior following a local quench in an XY chain and a transverse field Ising chain. In addition to providing an accurate description of dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified with a variety of ultracold atomic and solid-state systems. In particular, we will show some very recent preliminary experimental data from an ion system in the group of Chris Monroe.

**Jens Eisert**

Frie Universitat Berlin

What can we do with a small quantum simulator?

This talk explores the no man's land between small quantum processors that can be easily simulated classically and large-scale machines that could easily implement Shor’s algorithm, the land in which `quantum supremacy' is expected to occur. Starting point are questions on what one can expect from quantum simulators available with close to present technology, in what way they may outperform classical computers, and how the problem of certification and validation emerges. Two examples will be in the center of the talk: On the one hand, we will have a look at experiments and theoretical descriptions of quantum simulators constituted of ultra-cold atoms in optical lattices, probing questions of non-equilibrium and the dynamics of quantum phase transitions. On the other, we will pose questions and provide some answers concerning the possibility of classically certifying the correctness of linear optical boson sampling.

[1] Braun, Friesdorf, Hodgman, Schreiber, Ronzheimer, Riera, Eisert, Bloch, Schneider, in preparation.[2] Kliesch, Kastoryano, Gogolin, Riera, Eisert, arXiv:1309:0816.

[3] Trotzky, Chen, Flesch, McCulloch, Schollwoeck, Eisert, Bloch, Nature Physics 8, 325 (2012).

[4] Gogolin, Kliesch, Aolita, Eisert, in preparation and arXiv:1306.3995.

[5] Aaronson, Arkhipov, arXiv:1309.7460.

**Andrew Childs**

Institute for Quantum Computing, University of Waterloo

Simulating Hamiltonian dynamics

The task of simulating quantum systems was the original motivation for quantum computers and remains one of their most promising potential applications. I will review the state of the art in algorithms for simulating Hamiltonian dynamics with an eye toward simulations that might be implemented on a small quantum computer. Specifically, I describe two recent approaches, one based on discrete-time quantum walk and another on fractional-query simulation, that outperform traditional methods based on product formulas.

This talk is based in part on joint work with Dominic Berry, Richard Cleve, Robin Kothari, and Rolando Somma.

**Robin Blume-Kohout**

Sandia National Labs

Implications of analog simulation for computation and complexity

Analog quantum simulation -- the kind of simulation you do in optical lattices, without error correction -- may or may not actually work. Oddly enough, everybody knows whether or not it will work... but half of us know that it will, and half know it won't! Both possible answers have interesting implications for computational complexity. In addition to discussing these implications, I'll use analog simulation as inspiration to try and answer the question "What kind of algorithms could run usefully on a small quantum computer?"

**David Ceperley**

University of Illinois Urbana-Champaign

The sign problem for many-electron systems

While thermodynamic properties of many bosonic systems are "solvable " using Monte Carlo methods on classical computers, except for a few counterexamples, fermion systems have the "sign problem" and "exact" computations are limited to relatively small systems. Generalization of the bosonic methods to fermion systems exist, but are approximate in general. We speculate on how quantum computers could be used to either do the computation or find the limits of computation on classical computers.

**Andrew Cross**

IBM T. J. Watson Research Center

Toward subthreshold fault-tolerant quantum error correction with superconducting qubits

Although quantum states are fragile, the theory of fault-tolerant quantum computing gives us considerable hope that small multi-qubit demonstrations are the first step of many toward realizing powerful large-scale quantum computers. If we had a small quantum computer, one with on the order of a one hundred noisy qubits, a compelling use for such a computer is first to demonstrate a subthreshold active quantum memory and ultimately to construct a logical qubit that lives practically forever. In this talk I will present two related results. First, I give estimated error rate requirements for a subthreshold memory using a "rotated" surface code. Second, I will describe a recent experimental demonstration at IBM of a quantum parity check using three coupled transmons. Together these results suggest that the goal of demonstrating a subthreshold quantum memory is within reach.

### Speakers

John Preskill, Caltech

Andrew Childs, Waterloo

Andrew Cross, IBM Yorktown

Robin Blume-Kohout, Sandia

Alan Aspuru-Guzik, Harvard

Matthias Troyer, ETH

Andrew Landahl, Sandia

Alexey Gorshkov, NIST

Jens Eisert, Berlin

Frank Verstraete, Vienna and Ghent

David Ceperley, UIUC

Glenn Martyna, IBM Yorktown

### Dates

Dec. 9-11th, 2013

### Location

IBM TJ Watson Research Center Yorktown Heights, NY

### Organizing Committee

Richard Cleve, IQC

Jay Gambetta, IBM

Daniel Gottesman, PI (chair)

Keith Lee, PI

Graeme Smith, IBM

John Smolin, IBM