Hyperbolic circuits
Theoretical studies and experiments in the last six years have revealed the potential for novel
behaviours and functionalities in device physics through the synthetic engineering of negatively-
curved spaces. For instance, recent developments in hyperbolic band theory have unveiled the emer-
gence of higher-dimensional eigenstates—features fundamentally absent in conventional Euclidean
systems [1–3]. At the same time, superconducting quantum circuits have emerged as a leading plat-
form for quantum analogue emulations and digital simulations in scalable architectures [4–6]. Here,
we introduce a scalable superconducting circuit framework for the analogue quantum emulation of
tight-binding models on hyperbolic and kagome-like lattices. Using this approach, we experimen-
tally realize three distinct lattices, including—for the first time to our knowledge—a hyperbolic
lattice whose unit cell resides on a genus-3 Riemann surface. Our method encodes the hyperbolic
metric directly into capacitive couplings between high-quality superconducting resonators, enabling
tenable reproduction of spectral and localization properties while overcoming major scalability and
spectral resolution limitations of previous designs. These results set the stage for large-scale ex-
perimental studies of hyperbolic materials in condensed matter physics and lay the groundwork for
realizing hyperbolic quantum processors, with potential implications for both fundamental physics
and quantum computing.
Fast Bosonic Control
We present a protocol for preparing oscillator states with n-fold rotational symmetry, which
include many logical codewords for bosonic quantum error correction codes. The protocol relies on a
multiphoton interaction between the oscillator and an auxiliary qubit. Further, we achieve arbitrary
control over the oscillator’s Hilbert space by using a combination of different multiphoton interaction
orders. We also discuss the preparation of rotationally-symmetric multi-oscillator states using a
generalized variant of the protocol. We show that the use of multiphoton qubit-oscillator interactions
can substantially reduce the state preparation time, in comparison to the linear qubit-oscillator
interactions that are usually employed. Furthermore, we perform numerical simulations that take
into account qubit and oscillator relaxation and dephasing using realistic planar superconducting
circuit parameters that validate the robustness of our protocol. Our findings can significantly
improve the performance of bosonic codes on planar superconducting hardware, which are an almost
inevitable necessity for scalable bosonic fault-tolerant superconducting quantum computers.