Session B27: Superconducting Circuits: Quantum Simulations and Many-Body Physics

Probing remote entanglement in a localized system with a superconducting qubit quantum simulator.

Predicting the dynamics of quantum systems is a primary example of an intensive computational task that could be efficiently solved with a near term quantum computer.
To pursue this goal, we have fabricated a 9-qubit linear chain device made of superconducting circuits with nearest neighbor couplings. Our device is unique because it features frequency tunable qubits and an adjustable inter-qubit coupling strength, making it well suited to the simulation of quantum systems. We use the device to generate high-fidelity, multi-qubit, analog dynamics evolving under a Bose-Hubbard Hamiltonian.
In this talk, we discuss the calibration of this device for quantum simulation. Once calibrated we use this device to probe the basic physics of thermalization. Specifically, we use transport measurements to distinguish localized and diffusive behavior. To complement this, we use echo techniques to characterize the propagation of entanglement in these regimes. This shows qualitative differences between how energy and entropy flow in the system.   

A dissipatively stabilized Mott-insulator of photons

The rich physics of strongly-correlated quantum materials can be explored in synthetic systems built with microwave photons in superconducting circuits in the circuit QED paradigm. However, the intrinsic loss in photonic platforms makes many-body quantum state preparation a challenge. We build a 1D Bose-Hubbard lattice for photons where capacitively coupled transmon qubits serve as lattice sites, and the transmon anharmonicity corresponds to strong photon-photon interaction. We employ an engineered reservoir to realize a dissipatively stabilized site and couple it to the lattice to stabilize a n=1 Mott insulator. Site-resolved microscopy allow detailed studies of the thermalization process through the dynamics of defect propagation and removal in the Mott phase. By probing two-site correlations, we could investigate the emergence of correlations and entanglement in these driven-dissipative systems.   

A transmon based five-qutrit processor for simulations in high energy physics

Encoding quantum information in the higher energy levels of the transmon circuit provides a hardware efficient way to harness a larger Hilbert space in existing quantum processors while also increasing their connectivity. Furthermore, a network of qutrits (three-level systems) is naturally suited to experimentally demonstrate recently identified connections between high energy physics and quantum information, such as holographic quantum error correction codes and the physics of scrambling. Here we report on the control of a five-qutrit processor and our progress toward characterizing the scrambling of quantum information. We implement a circuit to measure the decay of out-of-time ordered correlators, a hallmark of scrambling, in a method that distinguishes between decoherence and scrambling. The same circuit can be viewed as a teleportation protocol where quantum information is scrambled by a black hole and then decoded through measurement of emitted Hawking photons.
  

Band Engineering for Quantum Simulation in Circuit QED

The field of circuit QED has emerged as a rich platform for both quantum com- putation and quantum simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit. In combination with qubit-mediated photon-photon interactions, these systems can be used to study dynamical phase transitions and many-body phenomena in driven-dissipative systems. In this talk, we will show how graph-theory and graph-level operations can be used to tailor the single-particle band structures of such systems. In particular, we will show that the process of taking a line graph produces controllably gapped flat bands at −2 and that subdividing all graph edges produces Dirac cones from formerly quadratic band edges and chiral flat bands at zero energy.   

Tunable-profile qubit-photon bound state interactions with superconducting circuits

Strongly coupling qubits to the band edge of a photonic crystal results in the formation of qubit-photon dressed bound states. The photonic components of these bound states are exponentially localized around the qubit positions and represent the inter-bound state interaction profiles. Tunability of the exponential localization length of bound state interactions has been experimentally demonstrated in superconducting circuits of two transmons coupled to a microwave photonic crystal [1]. To expand the range of 1D quantum models that can be probed with qubits coupled to photonic crystals, proposals have been put forth to engineer non-exponential interaction profiles by further dressing the systems with external driving fields [2]. We present experimental progress towards characterizing the effective bound states of transmons coupled to photonic crystals driven by auxiliary microwave tones. By driving the photonic crystal with multiple tones we aim to engineer non-exponential effective interactions, with the goal of accessing a broader class of tunable spin models.

[1] Sundaresan et al. arXiv:1801.10167
[2] Douglas et al. Nat Pho 9, 326–331, 2015   

Emulating Majorana Fermions Using Transmon Qubits with Application to Topological Quantum Computing

Majorana Fermions are fermionic modes with non-abelian dynamics and are of significant interest to realize topologically protected quantum processors. There have been signifcant efforts by the community to realize the Majorana modes in solid-state devices. Despite significant progress, fabricating and operating a Majorana qubit has proven to be extremely challenging.

In this talk, we propose a different approach: instead of trying to realize Majorana modes in solid-state systems such as Superconducting/Semiconducting naowires, we propose to engineer an array of transmon qubits to realize a meta material with Majorana modes. We will present an example design of such system, the chip layout, as well as discuss braiding, fusion, and readout schemes. We will also disucss intricaties and constraints associated with practical device fabrication procedures.   

High coherence quantum simulation of coherent backscattering in an effective two-level system composed of two superconducting qubits

In a recent experiment by Gustavsson et al. [1], a superconducting flux qubit was used to model scattering events using multiple Landau-Zener transitions by driving the qubit periodically back and forth through an avoided crossing. In highly coherent systems, time-reversal symmetry in the driving field should give rise to a dip in the average transition rate (averaged over many quantum trajectories), by analogy with weak localization in condensed matter systems. We experimentally emulate the scattering events with multiple Landau-Zener transitions in an effective two-level system, seeking to demonstrate the theoretically predicted weak localization phenomenon in this system, Ferrón et al. [2]. The effects of system-bath coupling are accurately simulated by a Floquet-Markov master equation.

[1] Phys. Rev. Lett. 110, 016603 (2013)
[2] Phys. Rev. B 95, 045412 (2017)   

Demonstration of a non-stoquastic Hamiltonian in coupled superconducting flux qubits

Currently available quantum annealers (QA) provide solutions to the transverse field Ising model with thousands of magnetically coupled qubits. To achieve a non-stoquastic Hamiltonian with QA, coupling via two canonically conjugate (orthogonal) degrees of freedom is necessary. Furthermore this orthogonal coupling can potentially enhance the performance of QA processors and enable an extended range of quantum simulations. Here we present one- and two-qubit microwave spectroscopy as well as time evolution measurements on two superconducting flux qubits coupled via two orthogonal degrees of freedom, charge and flux. We show that the electrostatic interaction, realized through a coupling capacitor, produces \sigma_y\sigma_y coupling in the computational basis and leads to broken gauge invariance. We also observe emergence of \sigma_x\sigma_x coupling through higher energy states of each rf-SQUID. Finally, we show that the reduced two qubit Hamiltonian is nonstoquastic across a wide range of parameters.   

Metamaterial Slow-Light Waveguide for Finite Range Interactions and Non-Markovian Dynamics with Superconducting Qubits

The ability to engineer the dispersion of light through subwavelength patterning of bulk materials has been a powerful tool for studying the influence of novel electromagnetic environments on light-matter interactions. Here, we present the experimental realization of an on-chip superconducting metamaterial waveguide composed of an array of coupled resonators of subwavelength size and negligible frequency disorder. By matching the array boundaries to 50Ω coplanar waveguides, our design achieves an 80MHz bandwidth photonic channel with nearly constant group index of ~650, as well as extinction of more than 70dB outside of the passband. Coupling transmon qubits to this metamaterial allows us to study non-Markovian dynamics of a single qubit’s interaction with the photonic bath, as well as collective non-Markovian dynamics of multiple qubits. Moreover, far from the passband, we can dynamically measure finite-range qubit-qubit interactions that extend beyond nearest neighbor and depend on detuning from the bandedge. We thus establish our metamaterial design as an attractive platform for studying photon-mediated non-Markovian dynamics and quantum many-body physics.   

Roadmap to a superconducting quantum many body simulator

A superconducting circuit constructed from a repeating pattern of identical unit cells comprising qubits or resonators can be used to simulate a quantum many body system of spins or bosons. While single or few qubit systems have been repeatedly demonstrated in the last few years, the majority of those require tuning each individual qubit frequency through individual control lines. Here, we propose how a larger two-dimensionsal system can be realized with far fewer control lines by focusing on qubit designs that can be uniformly fabricated, with deviation from the design frequency acting as disorder. We examine the operating regimes for such a system and the required fabrication accuracy, as well as readout and control schemes. We discuss how a such a superconducting system could be prepared in non-thermal states in different parts of the many-body spectrum, and consider what observables could be accessed and whether they could be used to test assumptions on entanglement entropy and eigenstate thermalization in 2D systems.   

Synthetic quantum materials in superconducting circuits

Superconducting circuits have emerged as a competitive platform for quantum computation, satisfying the challenges of controllability, long coherence and strong interactions. Here we apply this toolbox to the exploration of strongly correlated quantum matter, building a Bose-Hubbard lattice for photons in the strongly interacting regime. We develop a versatile recipe for the dissipative preparation of incompressible many-body phases through reservoir engineering and apply it in our system to realize the first Mott insulator of photons. Site- and time-resolved readout of the lattice allows microscopic observation of the lattice dynamics. The low entropy Mott state can serve as a starting point for studying other strongly correlated phases, e.g. a Tonks-Girardeau gas of interacting defects. The dissipative preparation demonstrated in this work also enable future exploration of elusive interacting topological phases.   

Time-Resolved Measurements of Energy Transport in a System of Coupled Superconducting Qubits Inspired by Simulations of Photosynthetic Processes

Engineered quantum systems have recently found application as a test-bed for answering open questions about energy transport in complex open quantum systems such as photosynthetic systems. Using a circuit incorporating three superconducting transmon qubits, we simulate energy transport with electron-phonon interactions, where we emulate longitudinal coupling to different types of phononic baths by applying engineered flux noise to the qubits. Previously, we considered the effects of noise on energy transport efficiency in steady-state measurements under continuous driving [1]. To study the transport of single photons, we now switch to pulsed excitations and time-resolved measurements. We verify the quantum nature of the excitations transported through the system in anti-bunching measurements, showing second-order correlation functions with g⁽²⁾(0) < 0.05, observe coherent oscillations of the emitted power indicative of static coherence, and study the efficiency of transport as a function of noise type.
[1] A. Potočnik et al., Nat. Comm. 9, 904 (2018)   

Quantum impurity in a 1D photonic crystal

Quantum impurity problems are described in terms of a single quantum-mechanical degree of freedom interacting with a dissipative reservoir. Superconducting circuits offer an ideal platform for studying the quantum dynamics of artificial atoms embedded in the electromagnetic continuum of a one-dimensional waveguide, reaching non-perturbative coupling regimes in the spin-boson model for an ohmic bath. Parallel experiments have explored transmon qubits strongly coupled to a photonic crystal, where the impurity hybridizes with the band structure resulting in a photonic bound state inside the gap. In this talk we present recent efforts in further pushing the coupling strength with the stepped impedance microwave crystal, using an artificial atom with a large magnetic moment, the fluxonium circuit. The goal of this experiment is to explore how photon scattering inside the waveguide is influenced by the significance of counter-rotating coupling terms and by the nonlinear photon dispersion in the crystal.   

Quantum impurity physics simulation with superconducting circuits I: perturbative regime

We report our progress in the field of quantum impurity simulations with superconducting circuits. Our simulator consists of a split Josephson junction terminating a high-impedance transmission line, which is made of a linear chain of up to 40,000 junctions [1,2]. In part I, we start with a relatively large area split-junction, such that its quartic anharmonicity can be treated as a perturbation. In this regime, the system is well-described by a Caldeira-Leggett model of a quantum degree of freedom interacting with an Ohmic bath. The interaction effects are revealed through the measurement of the frequency shifts of over 100 discrete modes of the bath. In part II, we explore small-area impurity junction where the non-linearity is non-perturbative. Now the system can be described by a boundary sine-Gordon quantum impurity model. It is expected that inelastic scattering of single photons becomes the dominant photon loss mechanism, with the loss frequency dependence containing information on the many-body correlation functions. We will present the measurements at various line impedances and impurity parameters.

[1] R. Kuzmin, R. Mencia, N. Grabon, N. Mehta, Y.-H. Lin, V. E. Manucharyan, arXiv 1805.07379
[2] R. Kuzmin, N. Mehta, N. Grabon, R. Mencia, V. E. Manucharyan, arXiv 1809.10739
  

Quantum impurity physics simulation with superconducting circuits II: many-body regime

We report our progress in the field of quantum impurity simulations with superconducting circuits. Our simulator consists of a split Josephson junction terminating a high-impedance transmission line, which is made of a linear chain of up to 40,000 junctions [1,2]. In part I, we start with a relatively large area split-junction, such that its quartic anharmonicity can be treated as a perturbation. In this regime, the system is well-described by a Caldeira-Leggett model of a quantum degree of freedom interacting with an Ohmic bath. The interaction effects are revealed through the measurement of the frequency shifts of over 100 discrete modes of the bath. In part II, we explore small-area impurity junction where the non-linearity is non-perturbative. Now the system can be described by a boundary sine-Gordon quantum impurity model. It is expected that inelastic scattering of single photons becomes the dominant photon loss mechanism, with the loss frequency dependence containing information on the many-body correlation functions. We will present the measurements at various line impedances and impurity parameters.
[1] R. Kuzmin, R. Mencia, N. Grabon, N. Mehta, Y.-H. Lin, V. E. Manucharyan, arXiv 1805.07379
[2] R. Kuzmin, N. Mehta, N. Grabon, R. Mencia, V. E. Manucharyan, arXiv 1809.10739