Cooling and Autonomous Feedback in a Bose-Hubbard Chain with Attractive Interactions

Quantum correlations and parameter estimation for two superconducting qubits interacting with a quantized field

In the present manuscript, we introduce a quantum system of two superconducting qubits (S-Qs) interacting with a quantized field under the influence of the Kerr nonlinear medium and Ising interaction. We formulate the Hamiltonian of the quantum model and determine the density operator of whole quantum system as well as quantum subsystems. We examine the dynamics of the quantumness measures for subsequent times including the S-Qs entanglement, S-Qs-field entanglement and quantum Fisher information in relation to the system parameters. Finally, we display the connection among the measures of quantumness during the time evolution.

Probing Site-Resolved Current in Strongly Interacting Superconducting Circuit Lattices

Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerful tools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of in situ particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore nonequilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.

Cavity-Based Reservoir Engineering for Floquet-Engineered Superconducting Circuits

Considering the example of superconducting circuits, we show how Floquet engineering can be combined with reservoir engineering for the controlled preparation of target states. Floquet engineering refers to the control of a quantum system by means of time-periodic forcing, typically in the high-frequency regime, so that the system is governed effectively by a time-independent Floquet Hamiltonian with novel interesting properties. Reservoir engineering, on the other hand, can be achieved in superconducting circuits by coupling a system of artificial atoms (or qubits) dispersively to pumped leaky cavities, so that the induced dissipation guides the system into a desired target state. It is not obvious that the two approaches can be combined, since reaching the dispersive regime, in which system and cavities exchange excitations only virtually, can be spoiled by driving-induced resonant transitions. However, working in the extended Floquet space and treating both system-cavity coupling as well as driving-induced excitation processes on the same footing perturbatively, we identify regimes, where reservoir engineering of targeted Floquet states is possible and accurately described by an effective time-independent master equation. We successfully benchmark our approach for the preparation of the ground state in a system of interacting bosons subjected to Floquet-engineered magnetic fields in different lattice geometries.

Photon Transport in a Bose-Hubbard Chain of Superconducting Artificial Atoms

We demonstrate nonequilibrium steady-state photon transport through a chain of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard model. Using transmission spectroscopy, we show that the system retains many-particle coherence despite being coupled strongly to two open spaces. We find that cross-Kerr interaction between system states allows high-contrast spectroscopic visualization of the emergent energy bands. For vanishing disorder, we observe the transition of the system from the linear to nonlinear regime of photon blockade in excellent agreement with the input-output theory. Finally, we show how controllable disorder introduced to the system suppresses nonlocal photon transmission. We argue that proposed architecture may be applied to analog simulation of many-body Floquet dynamics with even larger arrays of artificial atoms paving an alternative way towards quantum supremacy.

Dissipative Engineering of Gaussian Entangled States in Harmonic Lattices with a Single-Site Squeezed Reservoir

We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes nontrivial multipartite entangled states such as cluster states suitable for measurement-based quantum computation.

Supercorrelated Radiance in Nonlinear Photonic Waveguides

We study the collective decay of two-level emitters coupled to a nonlinear waveguide, for example, a nanophotonic lattice or a superconducting resonator array with strong photon-photon interactions. Under these conditions, a new decay channel into bound photon pairs emerges, through which spatial correlations between emitters are established by regular interference as well as interactions between the photons. We derive an effective Markovian theory to model the resulting decay dynamics of an arbitrary distribution of emitters and identify collective effects beyond the usual phenomena of super- and subradiance. Specifically, in the limit of many close-by emitters, we find that the system undergoes a supercorrelated decay process where all the emitters are either in the excited state or in the ground state but not in any of the intermediate states. The predicted effects can be probed in state-of-the-art waveguide QED experiments and provide a striking example of how the dynamics of open quantum systems can be modified by many-body effects in a nonharmonic environment.

Propagation and Localization of Collective Excitations on a 24-Qubit Superconducting Processor

Superconducting circuits have emerged as a powerful platform of quantum simulation, especially for emulating the dynamics of quantum many-body systems, because of their tunable interaction, long coherence time, and high-precision control. Here in experiments, we construct a Bose-Hubbard ladder with a ladder array of 20 qubits on a 24-qubit superconducting processor. We investigate theoretically and demonstrate experimentally the dynamics of single- and double-excitation states with distinct behaviors, indicating the uniqueness of the Bose-Hubbard ladder. We observe the linear propagation of photons in the single-excitation case, satisfying the Lieb-Robinson bounds. The double-excitation state, initially placed at the edge, localizes; while placed in the bulk, it splits into two single-excitation modes spreading linearly toward two boundaries, respectively. Remarkably, these phenomena, studied both theoretically and numerically as unique properties of the Bose-Hubbard ladder, are represented coherently by pairs of controllable qubits in experiments. Our results show that collective excitations, as a single mode, are not free. This work paves the way to simulation of exotic logic particles by subtly encoding physical qubits and exploration of rich physics by superconducting circuits.

Dynamical Phase Transitions in Sampling Complexity

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (ACM Press, New York, New York, USA, 2011), p. 333]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular, and optical systems.

Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as "fermionization" and "superbunching", can equivalently occur with attractive or repulsive interactions.

Universal Stabilization of a Parametrically Coupled Qubit

We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20  μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.

Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

Local probe of single phonon dynamics in warm ion crystals

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding non-equilibrium many-body physics. Here, we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.

An exhausting characterization of the coherence properties of quantum system becomes challenging with increasing system size. Here the authors demonstrate that phonon autocorrelation functions and quantum discord can be measured with local control, and validate it in a string of 42 trapped ions.

Many-Particle Dephasing after a Quench

After a quench in a quantum many-body system, expectation values tend to relax towards long-time averages. However, temporal fluctuations remain in the long-time limit, and it is crucial to study the suppression of these fluctuations with increasing system size. The particularly important case of nonintegrable models has been addressed so far only by numerics and conjectures based on analytical bounds. In this work, we are able to derive analytical predictions for the temporal fluctuations in a nonintegrable model (the transverse Ising chain with extra terms). Our results are based on identifying a dynamical regime of "many-particle dephasing," where quasiparticles do not yet relax but fluctuations are nonetheless suppressed exponentially by weak integrability breaking.

Stabilizing Entanglement via Symmetry-Selective Bath Engineering in Superconducting Qubits

Bath engineering, which utilizes coupling to lossy modes in a quantum system to generate nontrivial steady states, is a tantalizing alternative to gate- and measurement-based quantum science. Here, we demonstrate dissipative stabilization of entanglement between two superconducting transmon qubits in a symmetry-selective manner. We utilize the engineered symmetries of the dissipative environment to stabilize a target Bell state; we further demonstrate suppression of the Bell state of opposite symmetry due to parity selection rules. This implementation is resource efficient, achieves a steady-state fidelity F=0.70, and is scalable to multiple qubits.

Hardware-Efficient and Fully Autonomous Quantum Error Correction in Superconducting Circuits

Superconducting qubits are among the most promising platforms for building a quantum computer. However, individual qubit coherence times are not far past the scalability threshold for quantum error correction, meaning that millions of physical devices would be required to construct a useful quantum computer. Consequently, further increases in coherence time are very desirable. In this Letter, we blueprint a simple circuit consisting of two transmon qubits and two additional lossy qubits or resonators, which is passively protected against all single-qubit quantum error channels through a combination of continuous driving and engineered dissipation. Photon losses are rapidly corrected through two-photon drive fields implemented with driven superconducting quantum interference device couplings, and dephasing from random potential fluctuations is heavily suppressed by the drive fields used to implement the multiqubit Hamiltonian. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of 40 or more compared to the individual qubit T_{1} and T_{2} using this technique. We thus demonstrate that there is substantial headroom for improving the coherence of modern superconducting qubits with a fairly modest increase in device complexity.