Session H52: Quantum Simulation: Topology & Chemistry

Topological states of light in coupled microwave cavities

We present a unique photonic platform to explore quantum many-body phenomena in coupled cavity arrays. We create tight binding lattices with arrays of evanescently coupled three-dimensional coaxial microwave cavities. Topologically non-trivial band structures are engineered by utilizing the chiral coupling of the cavity modes to ferrite spheres in a magnetic field. Using screws made of different dielectric material, we can control every lattice site frequency, loss, and coupling strength to its neighbors. We then can probe each lattice site and measure the band structure, the Chern number of the bands, and time-resolved dynamics of pulses we inject at a particular site. These lattices can be cooled to superconducting temperatures to realize low disorder, long-coherence, topological tight binding models that are compatible with effective onsite photon-photon interactions by coupling lattice sites to superconducting qubits. This will allow us to explore the interplay between topology and coherent interaction in these artificial strongly-correlated photonic quantum materials.   

Tomography of topological microwave resonator arrays for quantum simulation with light

We have created topologically non-trivial states of light by engineering arrays of microwave resonators. Characterization of our lattices is paramount to realizing idealized many-body Hamiltonians, and we make use of a spectroscopic technique to perform full tomography of the Hamiltonian as well as to extract information about topological invariants of the system. By taking one and two site measurements we can fully extract the onsite and tunneling matrix elements of the Hamiltonian. The transmission between neighboring sites also reveals the phase of the tunnel coupling, thereby allow direct measurement of the flux in lattices with time-reversal breaking synthetic gauge fields. This measurement of the flux allows us to measure the projector onto the different bands in our system, which in turn allows us to calculate the Chern number of the various bands. We will discuss extending this technique to lattices with non-trivial real space curvature.   

Realization of space-time inversion-invariant topological semimetal-bands in superconducting quantum circuits.

Topological band theory has attracted much attention since several types of topological metals and semimetals have been explored. These robustness of nodal band structures are symmetry-protected, whose topological features have deepened and widened the understandings of condensed matter physics. Meanwhile, as artificial quantum systems superconducting circuits possess high controllability, supplying a powerful approach to investigate topological properties of condensed matter systems. We realize a Hamiltonian with space-time (PT) symmetry by mapping momentum space of nodal band structure to parameter space in a superconducting quantum circuit. By measuring energy spectrum of the system, we observe the gapless band structure of topological semimetals, shown as Dirac points in momentum space. The phase transition from topological semimetal to topological insulator can be realized by continuously tuning the parameter in Hamiltonian. We add perturbation to broken time reversal symmetry. As long as the combined PT symmetry is preserved, the Dirac points of the topological semimetal are still observable, suggesting the robustness of the topological protection of the gapless energy band. Our work open a platform to simulate the relation between the symmetry and topological stability in condensed matter systems.   

Quantum Bath Engineering of Permanent Chiral Currents in Cavity-Qubit Systems

Motivated by recent remarkable experiments [P. Roushan et al, arXiv arXiv:1606.00077] on creating and measuring chiral currents using superconducting qubits, we study here the case when such systems are subject to inevitable environmental effects. The experiments demonstrate the existence of a chiral current. However, such currents are not persistant given typical decoherence and decay times. Using quantum bath engineering techniques, we develop a scalable protocol for generating persistant currents even in the presence of such imperfections. This is done by striking a delicate balance between drive and dissipation to activate, with high fidelity, specific entangled states which are capable of carrying current. This demonstrates the power of quantum bath engineering approaches to realize highly non-trivial non-equilibrium steady states in Open Quantum Systems.   

Preparing states for quantum chemistry and physics on quantum computers

Simulation of chemistry and physics problems has emerged as one of the earliest potential applications of quantum computers. The preparation of specific quantum states is often either the objective of algorithms designed to treat these problems or plays a crucial role within them. On pre-threshold quantum devices, this preparation procedure is plagued by the influence of external noise or errors, ultimately limiting the set of states one can reliably prepare. In this talk, we discuss new methods for the preparation of both ground and excited states of quantum systems with techniques to mitigate the influence of noise on pre-threshold devices in these preparations. Example applications in the electronic structure of molecules will be used to demonstrate the performance of the methods.   

Variational quantum algorithms with significantly fewer measurements

Variational quantum algorithms provide an approach for using near-term quantum hardware to model diverse physical systems. Systems of interacting fermions, e.g. most materials and chemical reactions, are natural targets due to classical intractability at small sizes and the scientific value of solutions. However, recent work has cast doubt on the viability of chemistry applications due to an extremely large number of measurements that may be required. We overcome this problem by developing strategies which reduce the required measurements by orders of magnitude. Our approach involves an adaptive Bayesian model, simultaneous operator measurement, careful selection of basis functions and insights from N-representability theory. Most improvements are obtained by upper-bounding the required resources and then transforming the problem representation in a fashion that minimizes those upper-bounds. Our results suggest that even for some classically intractable molecules, energies can be measured to chemical precision using existing technology.   

Implementing a Variational Quantum Eigensolver using Superconducting Qubits

The problem of eigenvalue determination lies at the heart of a number of applications and technologies ranging from structural analysis to quantum simulation, and in particular quantum chemistry. While quantum computers promise to provide exponential improvements over classical techniques in our ability to solve these problems, there are significant technological challenges that must first be overcome. The variational quantum eigensolver (VQE)\footnote{A. Peruzzo, J. McClean et al., \textbf{Nat. Comms.} 5, 4213 (2014)}, is a hybrid quantum-classical algorithm designed to utilize both quantum and classical resources to find variational solutions to eigenvalue and optimization problems not accessible to traditional classical computers. We present initial steps towards the practical implementation of the VQE using superconducting qubits with reference to the extraction of the hydrogen energy spectrum. We explore the algorithm's ability to go beyond ground state estimation to determine molecular excited electronic states and investigate its intrinsic robustness to non-systematic sources of decoherence.   

Elucidating Reaction Mechanisms on Quantum Computers

We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant.   

Simulating Molecular Spectroscopy with Circuit Quantum Electrodynamics

Quantum simulation represents a powerful and promising means to overcome the bottleneck for simulating physical and chemical systems with classical computers. One of the major applications for quantum simulation is to solve molecular problems. However, the molecular simulation experiments performed so far are all confined to the study of static properties of molecules. In this talk, we present a method for simulating the dynamics and the absorption spectrum of molecules, and report the experimental results of its implementation using a superconducting device with a 3D circuit quantum electrodynamics architecture. We simulate the spectra for a variety of scenarios, in particular, for molecules with different Huang-Rhys parameters, which depend on the electron-phonon coupling strength for real molecules. Our simulation results show that our method can be achieved experimentally with high fidelity.   

Quantum emulation of molecular force fields: A blueprint for a superconducting architecture

We propose a flexible architecture of microwave resonators with tuneable couplings to perform quantum simulations of molecular chemistry problems. The architecture builds on the experience of the D-Wave design, working with nearly harmonic circuits instead of with qubits. This architecture, or modifications of it, can be used to emulate molecular processes such as vibronic transitions. Furthermore, we discuss several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity and finally the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices.   

Parity-Heap Transformations for Simulation of Fermionic Wavefunctions

An important application of quantum computing is the solution of electronic structure problems from quantum chemistry. These algorithms require a mapping of Fermionic operators into Pauli operators such as the Jordan-Wigner and Bravyi-Kitaev transformations, which introduce different gate-count overheads and runtimes. We introduce a general class of parity-heap transformations of which the Bravyi-Kitaev transform is a member. Different choices of heap result in new transformations. In particular, we study a new transform and associated encoding scheme which achieves better performance in realistic systems by generating the heap from the graph of actual qubit connectivity supported by quantum computing hardware.   

Energy Transfer in a System of Coupled Superconducting Qubits

We investigate energy transfer in a system of three capacitively coupled transmon qubits. Qubits 1 and 2 interact with a coplanar-waveguide transmission line, through which the system is energized, and qubit 3 with a large decay rate resonator through which its Purcell-limited decay is measured. We study the power spectral density of microwave radiation emitted back into the transmission line and into the resonator in dependence on various system parameters and interpret the results.