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Register a new userQuantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
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We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincar{e} disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.
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Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincar{e} disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.
Superconducting circuits have become a leading quantum technology for testing fundamentals of quantum mechanics and for the implementation of advanced quantum information protocols. In this chapter, we revise the basic concepts of circuit network theory and circuit quantum electrodynamics for the sake of digital and analog quantum simulations of quantum field theories, relativistic quantum mechanics, and many-body physics, involving fermions and bosons. Based on recent improvements in scalability, controllability, and measurement, superconducting circuits can be considered as a promising quantum platform for building scalable digital and analog quantum simulators, enjoying unique and distinctive properties when compared to other advanced platforms as trapped ions, quantum photonics and optical lattices.
Conversion of vacuum fluctuations into real particles was first predicted by L. Parker considering an expanding universe, followed in S. Hawkings work on black hole radiation. Since their experimental observation is challenging, analogue systems have gained attention in the verification of this concept. Here we propose an experimental set-up consisting of two adjacent piezoelectric semiconducting layers, one of them carrying dynamic quantum dots (DQDs), and the other being p-doped with an attached gate on top, which introduces a space-dependent layer conductivity. The propagation of surface acoustic waves (SAWs) on the latter layer is governed by a wave equation with an effective metric. In the frame of the DQDs, this space- and time-dependent metric possesses a sonic horizon for SAWs and resembles that of a two dimensional non-rotating and uncharged black hole to some extent. The non-thermal steady state of the DQD spin indicates particle creation in form of piezophonons.
Quantum mechanical effects at the macroscopic level were first explored in Josephson junction-based superconducting circuits in the 1980s. In the last twenty years, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to quantum information processing with superconducting circuits. In addition, circuit QED enables the study of hybrid quantum systems interacting with microwave photons. Here, we review the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focussing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system. We discuss coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, we discuss important use cases of these ideas in quantum information processing and in quantum optics.
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting due to their particle statistics, and Feynman left as an open question whether it could be done, because of the need for non-local control. Here, we implement fermionic interactions with digital techniques in a superconducting circuit. Focusing on the Hubbard model, we perform time evolution with constant interactions as well as a dynamic phase transition with up to four fermionic modes encoded in four qubits. The implemented digital approach is universal and allows for the efficient simulation of fermions in arbitrary spatial dimensions. We use in excess of 300 single-qubit and two-qubit gates, and reach global fidelities which are limited by gate errors. This demonstration highlights the feasibility of the digital approach and opens a viable route towards analog-digital quantum simulation of interacting fermions and bosons in large-scale solid state systems.
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