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Engineering direct nonlinear coupling between microwave photons

Yvonne Y. Gao, Adrian Copetudo, Amon M. Kasper, Tanjung Krisnanda, Grégoire Veyrac, Shushen Qin, Hui Khoon Ng

Published Jul 6, 2026• 0 citations
Publisher

Abstract

Abstract The rich dynamics and large Hilbert space of quantum harmonic oscillators make them natural candidates for hardware-efficient and error-correctable quantum information processing. However, implementing direct entangling operations between oscillators remains an outstanding challenge. Existing strategies typically rely on parametrically activating interactions that necessarily populate the excited states of a nonlinear coupler, introducing additional dissipation channels and potential leakage outside the encoded manifold. Here, we present a fundamentally different approach to generate nonlinear coupling between bosonic modes: a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities, which does not populate the mediating coupler. Crucially, this dynamics preserves the bosonic code space throughout, which is essential for fault-tolerant bosonic quantum computation. We demonstrate that the engineered cross-Kerr can be used to directly implement controlled-phase gates between two oscillators encoded in the single- and two-photon subspaces. Further, we apply the engineered dynamics to implement code-space-preserving parity checks using one of the oscillators as an ancillary mode, demonstrating an all-bosonic syndrome extraction that extends the effective lifetime of a storage oscillator. This work establishes a qualitatively different strategy for bosonic control, providing a pathway toward fault-tolerant quantum information processing with purely bosonic gates and syndrome measurements.

DOI
10.21203/rs.3.rs-9951461/v1

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•May 1, 2026•0 citations
Abstract The rich dynamics and large Hilbert space of quantum harmonic oscillators make them natural candidates for hardware-efficient and error-correctable quantum information processing. However, implementing direct entangling operations between oscillators remains an outstanding challenge. Existing strategies typically rely on parametrically activating interactions that necessarily populate the excited states of a nonlinear coupler, introducing additional dissipation channels and potential leakage outside the encoded manifold. Here, we present a fundamentally different approach to generate nonlinear coupling between bosonic modes: a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities, which does not populate the mediating coupler. Crucially, this dynamics preserves the bosonic code space throughout, which is essential for fault-tolerant bosonic quantum computation. We demonstrate that the engineered cross-Kerr can be used to directly implement controlled-phase gates between two oscillators encoded in the single- and two-photon subspaces. Further, we apply the engineered dynamics to implement code-space-preserving parity checks using one of the oscillators as an ancillary mode, demonstrating an all-bosonic syndrome extraction that extends the effective lifetime of a storage oscillator. This work establishes a qualitatively different strategy for bosonic control, providing a pathway toward fault-tolerant quantum information processing with purely bosonic gates and syndrome measurements.
The rich dynamics and large Hilbert space of quantum harmonic oscillators make them natural candidates for hardware-efficient and error-correctable quantum information processing. However, implementing direct entangling operations between oscillators remains an outstanding challenge. Existing strategies typically rely on parametrically activating interactions that populate the excited states of a nonlinear element, which introduces additional dissipation channels and potential leakage from the encoded manifold. Here, we engineer a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities. Crucially, this dynamics does not excite the mediating nonlinear coupler, thereby suppressing coupler induced decoherence and leakage out of the bosonic code space. We use this direct nonlinear coupling to implement a controlled-phase gate within the single- and two-photon subspaces of two oscillators, deterministically generating entanglement between them. Finally, we use these engineered dynamics to implement a photon-number parity check on a storage cavity via purely bosonic interactions with an ancillary cavity, demonstrating an enhancement in the storage lifetime. Our work provides a promising pathway toward engineering robust operations that act entirely within a protected bosonic code space and realizing fault-tolerant quantum information processing with bosonic elements.
Bosonic codes offer a hardware-efficient strategy for quantum error correction by redundantly encoding quantum information in the large Hilbert space of a harmonic oscillator. However, experimental realizations of these codes are often limited by ancilla errors propagating to the encoded logical qubit during syndrome measurements. The Kerr-cat qubit has been proposed as an ancilla for these codes due to its theoretically-exponential noise bias, which would enable fault-tolerant error syndrome measurements, but the coupling required to perform these syndrome measurements has not yet been demonstrated. In this work, we experimentally realize driven parametric coupling of a Kerr-cat qubit to a high-quality-factor microwave cavity and demonstrate a gate set that would enable universal quantum control of the cavity. We measure the decoherence of the cavity in the presence of the Kerr-cat and discover excess dephasing due to heating of the Kerr-cat to excited states. By engineering frequency-selective dissipation to counteract this heating, we are able to eliminate this dephasing, thereby demonstrating a high on-off ratio of control. Our results pave the way toward using the Kerr-cat to fault-tolerantly measure error syndromes of bosonic codes. Biased noise qubits, which can selectively suppress certain types of noise, are advantageous for quantum error correction of bosonic codes. Here the authors make an important step in this direction by demonstrating quantum control of a harmonic oscillator with a biased noise qubit.
The pair coherent state (PCS) is a theoretical extension of the Glauber coherent state to two harmonic oscillators. It is an interesting class of non-Gaussian continuous-variable entangled state and is also at the heart of a promising quantum error correction code: the pair cat code. Here we report an experimental demonstration of the pair coherent state of microwave photons in two superconducting cavities. We implement a cross-cavity pair-photon driven dissipation process, which conserves the photon number difference between cavities and stabilizes the state to a specific complex amplitude. We further introduce a technique of quantum subspace tomography, which enables direct measurements of individual coherence elements of a high-dimensional quantum state without global tomographic reconstruction. We characterize our two-mode quantum state with up to 4 photons in each cavity using this subspace tomography together with direct measurements of the photon number difference and the joint Wigner function. We identify the spurious cross-Kerr interaction between the cavities and our dissipative reservoir mode as a prominent dephasing channel that limits the steady-state coherence in our current scheme. Our experiment provides a set of reservoir engineering and state characterization tools to study quantum optics and implement multi-mode bosonic codes in superconducting circuits.
Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approach for implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly-coherent beamsplitter and fast (~100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities' joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.
Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum operations, static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Here we study theoretical models of nonlinear oscillators describing superconducting quantum circuits with asymmetric Josephson-junction loops. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. We support our analytical results by numerical experiments and show that the effective Kerr-type couplings can be canceled by an interplay of higher-order nonlinearities. This can be better understood in a simplified model supporting only cubic and quartic nonlinearities. Our results show that a cubic interaction allows an increase in the effective rates of both linear and nonlinear operations without an increase in the undesired anharmonicity of an oscillator which is crucial for many bosonic encodings.
Quantum computing promises exponential advantages for simulating quantum systems and solving certain computational problems beyond the reach of classical computers, but the fragility of qubits and the resulting errors present a major challenge for scalable implementations. One promising approach is to engineer qubits whose physical noise processes are intrinsically biased, enabling more efficient quantum error correction. This dissertation investigates quantum computing with superconducting Kerr-cat qubits, a bosonic qubit architecture in which qubit states are encoded in coherent states of a nonlinear oscillator stabilized by a two-photon drive. This stabilization creates an effective double-well pseudo-potential that strongly suppresses bit-flip errors while enabling universal quantum control, leading to a noise-biased qubit. A superconducting device architecture based on SNAIL nonlinear oscillators is developed to realize Kerr-cat qubits with tunable parameters and high coherence, integrating readout resonators, dedicated filters, and microwave control lines for measurement and manipulation. Universal single-qubit gates are implemented using engineered single-photon and two-photon drives to deform the pseudo-potential, and a cat-quadrature readout method is employed to achieve high-fidelity quantum nondemolition measurement. The performance of the qubits is systematically characterized through lifetime measurements and benchmarking protocols, including quantum process tomography, gate set tomography, and dihedral randomized benchmarking, revealing a strongly biased noise structure with high performance. These results establish an experimental framework for the design, control, and characterization of Kerr-cat qubits and demonstrate their potential as hardware-efficient building blocks for scalable fault-tolerant quantum computing.