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arXiv:2604.07235

Analytical Fock-State Generation and SWAP using a Rabi-Driven Transmon

Natan Karaev, Eliya Blumenthal, Shay Hacohen-Gourgy

quant-phSubmitted Apr 8, 2026• Announced Apr 9, 2026• 0 citations• Revised Jun 17, 2026 (v2)
v1 · Apr 8, 2026v2 · Jun 17, 2026
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Abstract

Deterministic Fock-state generation and inter-mode SWAP are foundational primitives for bosonic quantum computing, yet most implementations rely on numerically optimized pulses, per-state calibration, strong dispersive coupling, or higher transmon levels, each adding control overhead that grows with system size. We present an analytical, calibration-light protocol operating entirely within the two-level g-e manifold of a weakly dispersively coupled transmon. A Rabi drive on the qubit, combined with a single sideband tone per mode, synthesizes an on-demand Jaynes-Cummings interaction whose entire family of pulse times follows the closed-form scaling $τ_n=τ_1/\sqrt{n}$. Once the single base time $τ_1$ is set, every higher-$n$ operation is fixed analytically, with no per-state retuning, shelving, or numerical optimization. On a superconducting flute cavity with two high-Q modes, we deterministically prepare Fock states through $|n{=}5\rangle$, realize an inter-mode SWAP characterized on vacuum, single-photon, and coherent-state inputs, and generate and coherently swap the dual-rail Bell state $(|1,0\rangle+|0,1\rangle)/\sqrt{2}$, confirming that the operation preserves inter-mode coherence. Because the pulses are constant-amplitude and free of per-state optimization, the achievable fidelity is set directly by ancilla coherence and drive-ramp duration; a master-equation analysis isolates these hardware factors and shows that the analytical scaling itself imposes no obstacle to high-fidelity operation at high $n$. Requiring only one sideband line per mode and a single Rabi drive, the protocol is well suited to weakly coupled, high-$Q$ 3D architectures where calibration economy and analytical pulse design are at a premium.

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Deterministic Fock-state generation and inter-mode SWAP are foundational primitives for bosonic quantum computing, yet most implementations rely on numerically optimized pulses, per-state calibration, strong dispersive coupling, or higher transmon levels, each adding control overhead that grows with system size. We present an analytical, calibration-light protocol operating entirely within the two-level g-e manifold of a weakly dispersively coupled transmon. A Rabi drive on the qubit, combined with a single sideband tone per mode, synthesizes an on-demand Jaynes-Cummings interaction whose entire family of pulse times follows the closed-form scaling τn=τ1/nτ_n=τ_1/\sqrt{n}τn​=τ1​/n​. Once the single base time τ1τ_1τ1​ is set, every higher-nnn operation is fixed analytically, with no per-state retuning, shelving, or numerical optimization. On a superconducting flute cavity with two high-Q modes, we deterministically prepare Fock states through ∣n=5⟩|n{=}5\rangle∣n=5⟩, realize an inter-mode SWAP characterized on vacuum, single-photon, and coherent-state inputs, and generate and coherently swap the dual-rail Bell state (∣1,0⟩+∣0,1⟩)/2(|1,0\rangle+|0,1\rangle)/\sqrt{2}(∣1,0⟩+∣0,1⟩)/2​, confirming that the operation preserves inter-mode coherence. Because the pulses are constant-amplitude and free of per-state optimization, the achievable fidelity is set directly by ancilla coherence and drive-ramp duration; a master-equation analysis isolates these hardware factors and shows that the analytical scaling itself imposes no obstacle to high-fidelity operation at high nnn. Requiring only one sideband line per mode and a single Rabi drive, the protocol is well suited to weakly coupled, high-QQQ 3D architectures where calibration economy and analytical pulse design are at a premium.
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High-coherence superconducting cavities offer a hardware-efficient platform for quantum information processing. To achieve universal operations of these bosonic modes, the requisite nonlinearity is realized by coupling them to a transmon ancilla. However, this configuration is susceptible to crosstalk errors in the dispersive regime, where the ancilla frequency is Stark shifted by the state of each coupled bosonic mode. This leads to a frequency mismatch of the ancilla drive, lowering the gate fidelities. To mitigate such coherent errors, we employ quantum optimal control to engineer ancilla pulses that are robust to the frequency shifts. These optimized pulses are subsequently integrated into a recently developed echoed conditional displacement protocol for executing single- and two-mode operations. Through numerical simulations, we examine two representative scenarios: the preparation of single-mode Fock states in the presence of spectator modes and the generation of two-mode entangled Bell-cat states. Our approach markedly suppresses crosstalk errors, outperforming conventional ancilla control methods by orders of magnitude. These results provide guidance for experimentally achieving high-fidelity multimode operations and pave the way for developing high-performance bosonic quantum information processors.
In this work, we develop a coherent control technique for cavity QED based on amplitude amplification. We consider two physical platforms. In the first setting, we study a three-level quantum emitter coupled to a single mode of an optical cavity and introduce a protocol for producing traveling single photons based on oblivious amplitude amplification. As the key ingredient of our protocol, we propose an extension of oblivious amplitude amplification which uses reflection unitaries solely on the signal qubit, along with UUU and U†U^\daggerU†, where the unitary UUU prepares the initial state. Our approach improves the scaling of the single-photon-generation protocol length from N∼1/pN\sim 1/pN∼1/p to N∼1/pN\sim 1/\sqrt{p}N∼1/p​, with ppp denoting the success probability of obtaining a short single photon from a single application of the weak control pulse. Furthermore, our protocol also reduces the error from intrinsic cavity loss compared to protocols using a single strong control pulse in various experimentally relevant regimes, suggesting the application of our methods for error reduction. In the second setting, we consider a superconducting qubit coupled to a single bosonic mode of a microwave cavity in a circuit QED architecture in the dispersive regime for preparing Fock states. Using fixed-point amplitude amplification, we obtain a protocol for preparing Fock states whose length scales as O(n1/4)O(n^{1/4})O(n1/4), where nnn is the number of photons. Additionally, as an application of our methods for state preparation, we describe a protocol for preparing NOON states.
Optimal creation of photon Fock states is of importance for quantum information processing and state engineering. Here an efficient strategy is presented for speeding up generation of photon Fock state in a superconducting circuit via counterdiabatic driving. A transmon qubit is dispersively coupled to a quantized electrical field. We address a Λ-configuration interaction between the composite system and classical drivings. Based on two Gaussian-shaped drivings, a single-photon Fock state can be generated adiabatically. Instead of adding an auxiliary counterdiabatic driving, our concern is to modify these two Rabi drivings in the framework of shortcut to adiabaticity. Thus an accelerated operation with high efficiency can be realized in a much shorter time. Compared with the adiabatic counterpart, the shortcut-based operation is significantly insusceptible to decoherence effects. The scheme could offer a promising way to deterministically prepare photon Fock states with superconducting quantum circuits.
Universal control of bosonic degrees of freedom provides a hardware-efficient route for quantum information processing with high-dimensional systems. Bosonic circuit quantum electrodynamics (cQED), which leverages auxillary transmons to coherently control long-lived superconducting cavities, is well suited to this goal. However, such systems are traditionally operated in the dispersive regime, where the nearly degenerate cavity transitions prohibit the direct addressability of individual excitation levels of the bosonic mode and increase gate complexity. Here, we achieve direct oscillator control by dynamically accessing the resonant Jaynes-Cummings (JC) interactions, implemented with a hardware that integrates on-chip broadband magnetic flux delivery with a bosonic memory housed in a 3D superconducting cavity with lifetime exceeding 0.5 ms. We demonstrate deterministic preparation of Fock states and their superpositions within 100s of nanoseconds by directly climbing the JC ladder, and realise efficient arbitrary rotations between any pair of Fock states. Our resonant control scheme provides an analytical method for manipulating the entire Hilbert space of the bosonic mode at rates fundamentally more favourable than traditional dispersive strategies. This on-demand access to JC interactions opens a promising path toward realising robust Fock-basis qudits and harnessing the rich dynamics of high-dimensional bosonic systems for quantum information processing.