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arXiv:2510.27035 · Quantum

Fast Bosonic Control via Multiphoton Qubit-Oscillator Interactions

Noah Gorgichuk, Mohammad Ayyash, M. Mariantoni, Sahel Ashhab

Published Oct 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We study the problem of n -fold rotationally symmetric bosonic state preparation, which is of great importance to bosonic quantum error correction, using a multiphoton interaction between an oscillator and an auxiliary qubit. We present an n -photon Law-Eberly ( n LE) protocol that serves as an analytic baseline, alongside numerical optimal control calculations that further reduce state preparation time. We find that multiphoton control protocols substantially reduce preparation times for binomial, cat, and Gottesman-Kitaev-Preskill codewords compared to schemes relying on standard linear interactions. Further, we achieve arbitrary control over the oscillator's Hilbert space by combining different multiphoton interaction orders. We also extend these control improvements to the preparation of rotationally symmetric multi-oscillator states. Lastly, numerical simulations using realistic planar superconducting circuit parameters validate the robustness of our scheme against qubit and oscillator decoherence. Our findings can significantly enhance the performance of bosonic codes on planar superconducting hardware, an important ingredient for scalable fault-tolerant quantum computers.

DOI
10.22331/q-2026-10-01-2224

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We study the problem of n -fold rotationally symmetric bosonic state preparation, which is of great importance to bosonic quantum error correction, using a multiphoton interaction between an oscillator and an auxiliary qubit. We present an n -photon Law-Eberly ( n LE) protocol that serves as an analytic baseline, alongside numerical optimal control calculations that further reduce state preparation time. We find that multiphoton control protocols substantially reduce preparation times for binomial, cat, and Gottesman-Kitaev-Preskill codewords compared to schemes relying on standard linear interactions. Further, we achieve arbitrary control over the oscillator's Hilbert space by combining different multiphoton interaction orders. We also extend these control improvements to the preparation of rotationally symmetric multi-oscillator states. Lastly, numerical simulations using realistic planar superconducting circuit parameters validate the robustness of our scheme against qubit and oscillator decoherence. Our findings can significantly enhance the performance of bosonic codes on planar superconducting hardware, an important ingredient for scalable fault-tolerant quantum computers.
Encoding a qubit in the continuous degrees of freedom of a quantum system, such as bosonic modes, is a powerful alternative to modern quantum error correction (QEC). Among the most prominent bosonic QEC codes, binomial codes provide protection against loss and dephasing errors by encoding logical states in finite superpositions of Fock states with binomially weighted coefficients. While much attention has been given to their error-correcting capabilities and integration into fault-tolerant architectures, efficient methods for generating arbitrary binomial codewords remain scarce. In this work, we propose a scheme for generating these codewords by exploiting nonlinear multiphoton interactions between a continuous-variable bosonic mode (oscillator) and a two-level system (spin/qubit). Our proposed scheme assumes the ability to prepare the oscillator in an arbitrary Fock state and the qubit in an arbitrary superposition of its basis states and access to arbitrarily high multiphoton interactions. To enhance the experimental feasibility of our scheme, we further demonstrate how to reduce the required order parameter of multiphoton interactions by a factor of two for a special class of code states.
Bosonic quantum error correction codes encode logical qubits in the Hilbert space of one or multiple harmonic oscillators. A prominent class of bosonic codes is that of Gottesman-Kitaev-Preskill (GKP) codes of which implementations have been demonstrated with trapped ions and microwave cavities. In this paper, we investigate theoretically the preparation and error correction of a GKP qubit in a vibrational mode of a neutral atom stored in an optical dipole trap. This platform has recently shown remarkable progress in simultaneously controlling the motional and electronic degrees of freedom of trapped atoms. The protocols we develop make use of motional states and, additionally, internal electronic states of the trapped atom to serve as an ancilla qubit. We compare optical tweezer arrays and optical lattices and find that the latter provide more flexible control over the confinement in the out-of-plane direction, which can be utilized to optimize the conditions for the implementation of GKP codes. Concretely, the different frequency scales that the harmonic oscillators in the axial and radial lattice directions exhibit and a small oscillator anharmonicity prove to be beneficial for robust encodings of GKP states. Finally, we underpin the experimental feasibility of the proposed protocols by numerically simulating the preparation of GKP qubits in an optical lattice with realistic parameters.
Bosonic quantum error correction codes encode logical qubits in the Hilbert space of one or multiple harmonic oscillators. A prominent class of bosonic codes is that of Gottesman-Kitaev-Preskill (GKP) codes of which implementations have been demonstrated with trapped ions and microwave cavities. In this paper, we investigate theoretically the preparation and error correction of a GKP qubit in a vibrational mode of a neutral atom stored in an optical dipole trap. This platform has recently shown remarkable progress in simultaneously controlling the motional and electronic degrees of freedom of trapped atoms. The protocols we develop make use of motional states and, additionally, internal electronic states of the trapped atom to serve as an ancilla qubit. We compare optical tweezer arrays and optical lattices and find that the latter provide more flexible control over the confinement in the out-of-plane direction, which can be utilized to optimize the conditions for the implementation of GKP codes. Concretely, the different frequency scales that the harmonic oscillators in the axial and radial lattice directions exhibit and a small oscillator anharmonicity prove to be beneficial for robust encodings of GKP states. Finally, we underpin the experimental feasibility of the proposed protocols by numerically simulating the preparation of GKP qubits in an optical lattice with realistic parameters.
Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to be combined with higher level codes to achieve large-scale devices. We investigate concatenating these codes with the planar code in a measurement-based scheme for fault-tolerant quantum computation. We focus on binomial codes as the base level encoding, and estimate break-even points for such encodings under loss for various types of measurement protocol. These codes are more resistant to photon loss errors, but require both higher mean photon numbers and higher phase resolution for gate operations and measurements. We find that it is necessary to implement adaptive phase measurements, maximum likelihood quantum state inference, and weighted minimum weight decoding to obtain good performance for a planar code using binomial code qubits.
Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose 451±70 μs451 \pm 70~μ\mathrm{s}451±70 μs bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of 1.59±0.051.59 \pm 0.051.59±0.05. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes, particularly grid state encodings, offer a pathway to scalable fault-tolerant quantum computing in superconducting circuits. By leveraging the large Hilbert space of bosonic modes, quantum error correction can operate at the single physical unit level, therefore reducing drastically the hardware requirements to bring fault-tolerant quantum computing to scale. Going beyond the well-known Gottesman-Kitaev-Preskill (GKP) code, we discuss how using multiple bosonic modes to encode a single qubit offers increased protection against control errors and enhances its overall error-correcting capabilities. Given recent successful demonstrations of critical components of this architecture, we argue that it offers the shortest path to achieving fault tolerance in gate-based quantum computing processors with a MHz logical clock rate.