Marc-Antoine Lemonde, Vittorio Peano, Peter Rabl, Dimitris G. Angelakis

We propose a novel hybrid platform where solid-state spin qubits are coupled to the acoustic modes of a two-dimensional array of optomechanical nano cavities. Previous studies of coupled optomechanical cavities have shown that in the presence of strong optical driving fields, the interplay between the photon-phonon interaction and their respective inter-cavity hopping allows the generation of topological phases of sound and light. In particular, the mechanical modes can enter a Chern insulator phase where the time-reversal symmetry is broken. In this context, we exploit the robust acoustic edge states as a chiral phononic waveguide and describe a state transfer protocol between spin qubits located in distant cavities. We analyze the performance of this protocol as a function of the relevant system parameters and show that a high-fidelity and purely unidirectional quantum state transfer can be implemented under experimentally realistic conditions. As a specific example, we discuss the implementation of such topological quantum networks in diamond based optomechanical crystals where point defects such as silicon-vacancy centers couple to the chiral acoustic channel via strain.

# Category: highlights

## June 2019: Quantum supremacy with analog quantum processors for material science and machine learning

Quantum supremacy with analog quantum processors for material science and machine learning

J. Tangpanitanon, S. Thanasilp, M. A. Lemonde, D. G. Angelakis

arxiv.org/1906.03860

Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT) distribution. In this regime, the system uniformly explores its entire Hilbert space, which makes simulating such quantum dynamics with classical computational resources impossible for large systems. However, the latter has no direct application so far in solving a specific problem. In this work, we show that the same sampling complexity can be achieved from driven analog quantum processors, with less stringent requirements for coherence and control. More importantly, we discuss how to apply this approach to solve problems in quantum simulations of phases of matter and machine learning. Specifically, we consider a simple quantum spin chain with nearest-neighbor interactions driven by a global magnetic field. We show how quantum supremacy is achieved as a consequence of the thermalization due to the interplay between the disorder and the driven many-body dynamics. We analyze how the achieved PT distribution can be used as an accessible reference distribution to probe the many-body localization (MBL) phase transition. In the second part of our work, we show how our setup can be used for generative modeling machine learning tasks. We propose a novel variational hybrid quantum-classical approach, exploiting the system’s inherent tunable MBL dynamics, to train the device to learn distributions of complex classical data. The performance of our training protocol depends solely on the phase that the quantum system is in, which makes fine-tuning of local parameters not necessary. The protocol is implementable in a range of driven quantum many-body systems, compatible with noisy intermediate-scale quantum devices.

## March 2019: Two new works out! One on detecting topological order in quantum many-body systems in Phys. Rev. B and one in probing many-body localization in open photonic systems published in Phys. Rev. A

**Strongly correlated photon transport in a nonlinear photonic lattice with the disorder: Probing signatures of the localization transition**

T. F. See, V. M. Bastidas, J. Tangpanitanon, D. G. Angelakis

Phys. Rev. A. 99, 033835 (2019) [PDF]

We study the transport of few-photon states in open disordered nonlinear photonic lattices. More specifically, we consider a waveguide quantum electrodynamics (QED) setup where photons are scattered from a chain of nonlinear resonators with on-site Bose-Hubbard interaction in the presence of an incommensurate potential. Applying our recently developed diagrammatic technique that evaluates the scattering matrix (S matrix) via absorption and emission diagrams, we compute the two-photon transmission probability and show that it carries signatures of the underlying localization transition of the system. We compare the calculated probability to the participation ratio of the eigenstates and find close agreement for a range of interaction strengths. The scaling of the two-photon transmission probability suggests that there might be two localization transitions in the high energy eigenstates corresponding to interaction and quasiperiodicity respectively. This observation is absent from the participation ratio. We analyze the robustness of the transmission signatures against local dissipation and briefly discuss possible implementation using current technology.

** Detection of topological phases by quasilocal operators**

W. C. Yu, P.D. Sacramento, Y. Chao, D. G. Angelakis, Hai-Qing Lin

Phys. Rev. B 99, 115113 (2019) [PDF]

It was proposed recently by some of the authors that the quantum phase transition of a topological insulator like the Su-Schrieffer-Heeger (SSH) model may be detected by the eigenvalues and eigenvectors of the reduced density matrix. Here we further extend the scheme of identifying the order parameters by considering the SSH model with the addition of triplet superconductivity. This model has a rich phase diagram due to the competition of the SSH “order” and the Kitaev “order,” which requires the introduction of four order parameters to describe the various topological phases. We show how these order parameters can be expressed simply as averages of projection operators on the ground state at certain points deep in each phase and how one can simply obtain the phase boundaries. A scaling analysis in the vicinity of the transition lines is consistent with the quantum Ising universality class.

## September 2018 “Discrete time crystal in globally driven interacting quantum systems without disorder” (March 2019, published!)

Fig.1 (a) Schematic diagram showing the dynamics of the individual spins in our model for a small perturbation in the spin flip. The presence of interaction helps to synchronize the spins.

Authors

W. C. Yu, J. Tangpanitanon, A. W. Glaetzle, D. Jaksch, D. G. Angelakis

**Abstract**

Time crystals in periodically driven systems have initially been studied assuming either the ability to quench the Hamiltonian between different many-body regimes, the presence of disorder or long-range interactions. Here we propose a scheme to observe discrete time crystal dynamics in a one-dimensional driven quantum system of the Ising type with short-range interactions and no disorder. The system is subject only to a periodic kick by a global magnetic field, and no extra Hamiltonian quenching is performed.

Phys. Rev. A. 99, 033618 (2019) [PDF]

Fig.1 (a) Schematic diagram showing the dynamics of the individual spins in our model for a small perturbation in the spin flip. The presence of interaction helps to synchronize the spins.

Fig. 2(a) Color map of the Fourier spectrum of the stroboscopic magnetization in x direction with perturbation \epsilon as the driving parameter.

## Dec 2017-publication in Science: Spectroscopic signatures of localization with interacting photons in superconducting qubits (collaboration with Google-Martinis group)

The international team used photons in Google’s quantum chip to simulate the surprising and beautiful pattern of the ‘Hofstadter butterfly’, a fractal structure characterizing the behaviour of electrons in strong magnetic fields. The results, published 1 December in

Science, show how quantum simulators are starting to live up to their promise as powerful tools,…

Read more from CQT highlight for non specialists ” CQT researchers collaborate in quantum simulations on Google’s superconducting chip” and from USBC highlight ” Simulating physics “

This work is highlighted in 12 science news including Strait Time, phys.org, eurekalert, sciencedaily, tech2.org, housseniawriting, tuc.gr , asian scientist, technology networks, nanowerk, alphagalileo, mgronline

Science **358**, 6367, pp. 1175-1179 (2017)

**Authors**

P. Roushan, C. Neill, J. Tangpanitanon, V.M. Bastidas, A. Megrant, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Fowler, B. Foxen, E. Je rey, J. Kelly, E. Lucero, J. Mutus, M. Neeley, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. White, H. Neven, D. G. Angelakis, and J. Martinis

**Abstracts**

Quantized eigenenergies and their associated wave functions provide extensive information for predicting the physics of quantum many-body systems. Using a chain of nine superconducting qubits, we implement a technique for resolving the energy levels of interacting photons. We benchmark this method by capturing the main features of the intricate energy spectrum predicted for two-dimensional electrons in a magnetic field—the Hofstadter butterfly. We introduce disorder to study the statistics of the energy levels of the system as it undergoes the transition from a thermalized to a localized phase. Our work introduces a many-body spectroscopy technique to study quantum phases of matter.

## November 2017: Realizing topological relativistic dynamics with slow light polaritons at room temperature

**Authors**

M. Namazi, B. Jordaan, C. Noh, D. G. Angelakis, E. Figueroa

**Abstract**

Here we use a slow light quantum light-matter interface at room temperature to implement an analog simulator of complex relativistic and topological physics. We have realized the famous Jackiw-Rebbi model (JR), the celebrated first example where relativity meets topology. Our system is based upon interacting dark state polaritons (DSP’s) created by storing light in a rubidium vapor using a dual-tripod atomic system. The DSP’s temporal evolution emulates the physics of Dirac spinors and is engineered to follow the JR regime by using a linear magnetic field gradient. We also probe the obtained topologically protected zero-energy mode by analyzing the time correlations between the spinor components. Our implementation paves the way towards quantum simulation of more complex phenomena involving many quantum relativistic particles.

## May 2017: Quantum Simulators with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics

Check our book on “Quantum Simulators with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics” by Springer!

This book reviews progress towards quantum simulators based on photonic and hybrid light-matter systems, covering theoretical proposals and recent experimental work. Quantum simulators are specially designed quantum computers. Their main aim is to simulate and understand complex and inaccessible quantum many-body phenomena found or predicted in condensed matter physics, materials science and exotic quantum

See CQT highlight for non specialists.

## May 2017: A diagrammatic Diagrammatic Approach to Multiphoton Scattering

**Authors**

T.F. See, C. Noh, D.G. Angelakis, “A diagrammatic Diagrammatic Approach to Multiphoton Scattering”, Phys. Rev. A 95, 053845 (2017)

**Abstract**

We present a method to systematically study multiphoton transmission in one-dimensional systems comprised of correlated quantum emitters coupled to input and output waveguides. Within the Green’s function approach of the scattering matrix (S matrix), we develop a diagrammatic technique to analytically obtain the system’s scattering amplitudes while at the same time visualize all the possible absorption and emission processes. Our method helps to reduce the significant effort in finding the general response of a many-body bosonic system, particularly the nonlinear response embedded in the Green’s functions. We demonstrate our proposal through physically relevant examples involving scattering of multiphoton states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators in the Bose-Hubbard model.

## November 2016: Topological pumping of photons in nonlinear resonator arrays

” The inspiration for a new scheme to transport interacting quantum particles has its roots in Ancience Greece. In Thouless pumping, transport happens because of the topology of fields acting on the quantum particles – similar to the way that an Archimedes’ screw pump can move water up a hill,.. ”

Read more from CQT highlight for non specialists ” Topological scheme for transporting quantum particles inspired by Nobel winner’s work “

This work is also highlighted in 7 science news including EurekaAlert!, Phys.org, Health Medicinet, Nanowerk, Nanotechnology Now, Sky Nightly, and Space Daily.

**Authors**

J. Tangpatinanon, V. M. Bastidas, P. Roushan, S. Assam, D. Jaksch, D. G. Angelakis, “Topological pumping with photons in nonlinear resonator arrays”, Physical Review Letters, 117, 213603 (2016)

**Abstract**

We show how to implement topological or Thouless pumping of interacting photons in one-dimensional nonlinear resonator arrays by simply modulating the frequency of the resonators periodically in space and time. The interplay between the interactions and the adiabatic modulations enables robust transport of Fock states with few photons per site. We analyze the transport mechanism via an effective analytic model and study its topological properties and its protection to noise. We conclude by a detailed study of an implementation with existing circuit-QED architectures.

## April 2016: Review on “Quantum Simulations and Many-Body Physics with Light”

Our comprehensive review on “Quantum Simulations and Many-Body Physics with Light” is out at** Reports in Progress in Physics 80, 016401 (2016).**

In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms.. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibers interfaced with cold atoms.