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arXiv:2505.05559 · PRX Quantum

Circuit-QED Lattice System with Flexible Connectivity and Gapped Flat Bands for Photon-Mediated Spin Models

Kellen O'Brien, Maya Amouzegar, Won Chan Lee, Martin A. Ritter, Alicia J. Kollár

Published Dec 5, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum spin models are ubiquitous in solid-state physics, but classical simulation of them remains extremely challenging. Experimental testbed systems with a variety of spin-spin interactions and measurement channels are therefore needed. One promising potential route to such testbeds is provided by microwave-photon-mediated interactions between superconducting qubits, where native strong light-matter coupling enables significant interactions even for virtual-photon-mediated processes. In this approach, the spin-model connectivity is set by the photonic mode structure, rather than the spatial structure of the qubit. Lattices of coplanar-waveguide (CPW) resonators have been demonstrated to allow extremely flexible connectivities and can therefore host a huge variety of photon-mediated spin models. However, large-scale CPW lattices with nontrivial band structures have never before been successfully combined with superconducting qubits. Here we present the first such device featuring a quasi-1D CPW lattice with multiple transmon qubits. We demonstrate that superconducting-qubit readout and diagnostic techniques can be generalized to this highly multimode environment and observe the effective qubit-qubit interaction mediated by the bands of the resonator lattice. This device completes the toolkit needed to realize CPW lattices with qubits in one or two Euclidean dimensions, or negatively curved hyperbolic space, and paves the way to driven-dissipative spin models with a large variety of connectivities.

DOI
10.1103/z9n2-mmmf

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Quantum spin models are ubiquitous in solid-state physics, but classical simulation of them remains extremely challenging. Experimental testbed systems with a variety of spin-spin interactions and measurement channels are therefore needed. One promising potential route to such testbeds is provided by microwave-photon-mediated interactions between superconducting qubits, where native strong light-matter coupling enables significant interactions even for virtual-photon-mediated processes. In this approach, the spin-model connectivity is set by the photonic mode structure, rather than the spatial structure of the qubit. Lattices of coplanar-waveguide (CPW) resonators have been demonstrated to allow extremely flexible connectivities and can therefore host a huge variety of photon-mediated spin models. However, large-scale CPW lattices with nontrivial band structures have never before been successfully combined with superconducting qubits. Here we present the first such device featuring a quasi-1D CPW lattice with multiple transmon qubits. We demonstrate that superconducting-qubit readout and diagnostic techniques can be generalized to this highly multimode environment and observe the effective qubit-qubit interaction mediated by the bands of the resonator lattice. This device completes the toolkit needed to realize CPW lattices with qubits in one or two Euclidean dimensions, or negatively curved hyperbolic space, and paves the way to driven-dissipative spin models with a large variety of connectivities.
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 Poincaré 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.
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Circuit QED systems provide an ideal platform for exploring the strong-coupling regime of multimode cavity QED. Here we present two new phenomena from multimode strong coupling: a circuit Lagrangian analysis which captures beyond tight-binding effects of strong photon-photon coupling and experimental observation of strong wave-mixing resonances in the qubit response. Our circuit analysis reveals qualitatively new features such as emergent band gaps, lifted degeneracies, broadened flat bands, and frequency-dependent hopping. Within the multimode photon environment, strong qubit-photon coupling in turn gives rise to multiphoton processes involving multiple normal modes. We demonstrate a strong four-wave-mixing process involving excitation of a qubit and simultaneous frequency conversion between modes. Notably, this wave-mixing process is dominated by localized flat-band modes of the photonic lattice, which exhibit the strongest coupling to the transmon qubit.
Qubits strongly coupled to a photonic crystal give rise to qubit-photon dressed bound states.These bound states, comprising the qubits and spatially localized photonic modes induced around the qubits, are the basis for many exotic physical scenarios.The localization of these states changes with qubit detuning from the photonic crystal band edge, offering an avenue of in situ control of bound-state interaction.Here, we present experimental results from a device with two transmon qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and interbound state interactions.We observe a fourth-order two-photon virtual process between bound states indicating strong coupling between the photonic crystal and transmon qubits.Because of their localization-dependent interaction, these states offer the ability to realize one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits' spatial organization.The widely tunable, strong, and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems that use bound states to build and study quantum spin models.
Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). Typically, semiconductor qubit-qubit coupling is short range, effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle (a few hundred nanometers). This is a significant constraint towards scaling of QD-based architectures to realize dense 1D or 2D arrays of QDs. Inspired by techniques originally developed for circuit QED, we recently demonstrated the strong coupling of individual electrons confined in GaAs quantum dots to individual microwave photons, making use of the enhanced electric component of the vacuum fluctuations of a resonator with impedance beyond the typical 50 Ohm of standard coplanar waveguides. In this hybrid technology, we recently realized a proof of concept experiment, where the coupling between a transmon and a double QD (DQD) is mediated by virtual microwave photon excitations in a high impedance SQUID array resonator, which acts as a quantum bus enabling long-range coupling between dissimilar qubits. Similarly, we achieved coherent coupling between two DQD charge qubits separated by approximately 50 um. In the dispersive regime, we spectroscopically observed qubit-qubit coupling as an avoided-crossing in the energy spectrum of the DQD charge qubits. The methods and techniques developed in this work are transferable to QD devices based on other material systems and can be beneficial for spin based hybrid systems.
Coherent and strong coupling between photons and solid-state qubits, in the form of circuit quantum electrodynamics (QED), has been harnessed for two-qubit gates mediated by photons and high-fidelity quantum non-demolition readout, which are the building blocks of large-scale quantum computation. Recently, circuit QED has been extended to gate-defined semiconductor quantum dots. In this thesis, we develop a novel hybrid circuit QED architecture composed of a high-impedance superconducting microwave resonator and spins localized in silicon-MOS quantum dots. To control and measure the spin degrees of freedom, this hybrid system needs to operate at finite magnetic field. Consequently, we develop and characterize microwave resonators based on thin niobium nitride (NbN) films featuring a high kinetic inductance. We demonstrate high-impedance resonators with magnetic field resilience and low photon loss rates. We then co-integrate the NbN resonators on silicon spin qubit chips. With a hole confined in a double quantum dot (DQD), we report the first realization of a strong hole charge-photon interaction bordering the ultra-strong coupling regime. At finite magnetic field, putting the spin transition energy in resonance with the microwave cavity, we observe large vacuum Rabi mode splittings, signature of a strong spin-photon coupling. Our findings are well captured by the modelling of a hole DQD with different anisotropic Zeeman response in each dot and spin-orbit coupling dependent tunnel rates. We also find a sizeable spin-photon coupling when the hole is localized in the single quantum dot, in line with recent theoretical predictions. The different works presented in this manuscript pave the way for circuit QED with hole spins in gate-defined semiconductor quantum dots.