## “*Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.*”

—Richard Feynman

Technological progress goes hand in hand with incessant advances in computing power. Modern personal electronic devices have the computational power of a supercomputer from just a decade ago. Computer-aided designs, logistics, data analysis and cognitive computing form an essential part of modern life. However, current progress in down-scaling transistors reaches physical limits when approaching atomic scales, and heat dissipation becomes a severe issue when increasing transistor densities.

Above all, certain complex physical problems such as computing energy spectra, correlations or time dynamics in molecular and condensed matter systems are beyond the reach of classical computers.

These computations require exponential resources. The reason for this is the exponential growth of Hilbert space with the number of particles, preventing the computation of systems with more than a modest number of 50 particles. With a few more particles, even future supercomputers are destined to fail.

“The goal is to build a quantum computing and simulation platform based on superconducting qubits to explore and potentially overcome the limits of classical computation.”—IBM scientist Stefan Filipp

In contrast, a quantum simulator has the potential to compute ground-state energies, energy spectra, time dynamics or correlations of such systems efficiently. Moreover, it is expected that certain types of optimization problems with application in logistics, time-scheduling and others can be solved more efficiently with the help of quantum effects.

In our laboratory, we explore quantum computing and simulation schemes based on analog and hybrid analog–digital schemes that will have practical implications before universal quantum computing platforms become reality.

## Experimental tools and methods

In experiments, we use superconducting qubits, which can be manipulated on short time scales with respect to their coherence times within a cryogenic environment.

Thanks to the relatively simple and reliable fabrication there exists a clear path towards a scalable architecture to realize the building blocks of a future universal quantum computer and for practical quantum simulation applications.

We are exploring qubit–qubit coupling schemes based on parametrically tuneable couplers and geometric phases.

In this way we achieve high-fidelity interactions between highly coherent superconducting qubits, which have the potential to simulate the dynamics of a large class of quantum systems.

The tuneable coupler has the potential to act as a quantum bus between multiple qubits in a qubit lattice.

To increase the coherence of the superconducting qubits we operate a UHV apparatus for specific treatments of surfaces and interfaces.

#### Mixing chamber plate of the dilution refrigerator with mounted sample enclosure.

#### Superconducting qubit device with two transmon-type qubits.

#### In a curved Hilbert space, the path determines the final state of a quantum system.

#### Scheme of a superconducting qubit lattice (blue dots) coupled via 4-way coupling devices (pink rectangles).

#### UHV sealing and surface preparation.

#### Binding energy of a hydrogen molecule as a function of the distance between the H atoms.

## Our focus

We are currently focusing on the scalability of the quantum platform.

By developing 3D integrated chip devices and integrated control electronics, problem sizes exceeding 50 and more qubits will become accessible and efficient simulations of quantum magnetism and chemical reaction processes will come into reach.

This effort is in close collaboration with the IBM Thomas J. Watson Research Center in Yorktown Heights, USA, where our colleagues are working on digital quantum computing.

First applications are small fermion systems such as the hydrogen molecule in a reduced, quantum magnetism such as anti-ferromagnetic spin systems and quantum enhanced optimization schemes with adiabatic control.

## Theory of quantum simulations of chemical systems

Recent advances in the field of quantum computing have boosted the hope that one day we might be able to solve complex materials-science problems using quantum computers.

The direct mapping of the molecular wave function to the qubit state allows the implementation of all quantum operations into a number of gates that only scales polynomially with system size.

A quantum computer could then be used for the simulation of chemical systems and their properties, including correlation functions and reaction rates.

Beyond this, a small quantum computer with on the order of 100 qubits will be able to address challenging problems in quantum chemistry that are beyond the reach of classical algorithms.

Improving quantum algorithms, such as by reducing the number of trotter steps required, might further facilitate this task.

Alternatively, one can also directly map a molecular Hamiltonian onto a quantum circuit to calculate the molecular properties using an analog quantum computing approach. This implementation exhibits the challenge of evaluating *k*-local terms, where *k* > 2 (3-, 4-, …, *n*-body interaction terms).

These terms originate from the fermion-to-qubit map implicit in the Jordan–Wigner transformation.As the number of fully coupled qubits is still fewer than 20, methods for optimizing qubit resources are highly desirable.

In fact, we recently showed [1] that the number of required qubits can be reduced by exploiting the block diagonality of the fermionic Hamiltonian.

The scheme is conceived as a pre-computational step that is performed prior to the actual quantum simulation.Among other things, it allows the simulation of the two-site Fermi-Hubbard model and of the hydrogen molecule using a two-qubit quantum computer.

## Publications

[1] N. Moll, A. Fuhrer, P. Staar, and I. Tavernelli,

“Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer,”

*J. Phys. A: Math. Theor*. **49**, 295301 (2016).

[2] S. Sheldon, L.S. Bishop, E. Magesan, S. Filipp, J.M. Chow, and J.M. Gambetta,

“Characterizing errors on qubit operations via iterative randomized benchmarking,”

*Phys. Rev. A* **93**, 12301 (2016).

[3] S. Gasparinetti, S. Berger, A.A. Abdumalikov, M. Pechal, S. Filipp, and A.J. Wallraff,

“Measurement of a vacuum-induced geometric phase,”

*Science Advances* **2**, e1501732 (2016).

[4] O. Viyuela, A. Rivas, S. Gasparinetti, A. Wallraff, S. Filipp, M.A. Martin-Delgado,

“A measurement Protocol for the topological Uhlmann phase,”

arXiv:1607.08778 [quant-ph] (2016).

[5] D.C. McKay, S. Filipp, A. Mezzacapo, E. Magesan, J.M. Chow, J.M. Gambetta,

“A universal gate for fixed-frequency qubits via a tunable bus,”

arXiv:1604.03076 [quant-ph] (2016).

## Ask the experts

## Funding sources

**SNF.** Swiss National Science Foundation. Project 200021 “Exploring Geometric Effects and Geometric Gates with Superconducting Circuits.”

**IARPA.** Intelligence Advanced Research Projects Activity. Project SLEEQ (Superconducting Logically Encoded Extensible Qubit) within the LogiQ Program.

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