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arXiv:2607.14239

Fock-state preparation based on amplitude amplification in cavity QED

Sharoon Austin, Zhi-Yuan Wei, Kartik Srinivasan, Alexey V. Gorshkov

quant-phSubmitted Jul 15, 2026• Announced Jul 17, 2026• 0 citations
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Abstract

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 $U$ and $U^\dagger$, where the unitary $U$ prepares the initial state. Our approach improves the scaling of the single-photon-generation protocol length from $N\sim 1/p$ to $N\sim 1/\sqrt{p}$, with $p$ 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 $O(n^{1/4})$, where $n$ is the number of photons. Additionally, as an application of our methods for state preparation, we describe a protocol for preparing NOON states.

Comments
14 pages, 9 figures

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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.
Large Fock states are important resources for bosonic quantum information and quantum-enhanced metrology, but preparing them with high probability at large excitation numbers remains challenging, as deterministic methods become increasingly control-intensive, while measurement-based approaches typically suffer from low heralding probabilities. Here we propose a protocol that combines quantum nondemolition photon-number encoding with quantum amplitude amplification to enable high-probability heralded generation of large Fock states. Starting from a cavity mode prepared in a coherent state, Quantum Phase Estimation encodes photon-number information into a multi-qubit register, while Quantum Amplitude Amplification boosts the probability of a desired target outcome before measurement. The scheme has an immediate implementation in dispersive circuit-QED, but can be analogously adapted to other bosonic platforms with QND photon-number readout, such as cavity-QED. With a register of up to eight qubits, near-deterministic preparation of Fock states with hundreds of excitations is possible. We also show that the protocol can serve as the first stage of an extension toward generating a two-mode NOON state via a conditional beam-splitter operation.
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Exact Fock-State Preparation with n1/4n^{1/4}n1/4 Circuit Depth
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This thesis addresses challenges in the experimental realisation of optical quantum computing with atom-cavity platforms and develops techniques for experimental quantum control that generalise across a range of quantum modalities. Within the framework of cavity quantum electrodynamics (cQED), methods are developed and numerically validated for fast and precise control of single atoms to generate photonic states of interest. In particular, we consider the generation of high-repetition-rate n-photon bursts and time-bin entangled states. These photonic resources are essential for applications such as boson sampling, multi-photon interference, optical quantum computing, and quantum-enhanced metrology. Experimental improvements in coherent population transfer are demonstrated using adaptive pulse shaping with acousto-optic modulators. Beyond photon generation, the thesis introduces general-purpose pulse-level techniques, including pulse distortion correction, memory-efficient pulse compression, and machine learning-based optimisation. These methods are shown to be transferable to other platforms, such as neutral atom arrays and superconducting qubits. A particular contribution is the implementation of scalable pulse generation using fixed-point compressed pulse representations on FPGA hardware, achieving substantial memory savings while maintaining high fidelity in simulations of quantum operations. Additionally, reinforcement learning is presented as a powerful tool for optimising complex quantum dynamics, with state-of-the-art results demonstrated across various simulated systems. Throughout the thesis, theoretical developments are supported by numerical simulations and partial experimental validation, providing important insights for the development of future quantum technologies.
The generation of high Fock states of light pulses and their superpositions with provable quantum non-Gaussian features is still very challenging, although the power of conditional methods to herald the approximate state from the available Gaussian states is growing. The atom-light interaction in the high- cavity has been considered a viable alternative to the heralded Fock states of the light pulses from nonlinear optics limited to three-photon Fock states for the last decade. Here, by optimizing the realistic protocol combining it with available optical delay elements, we conclusively predict filtering of Fock states up to ten photons with a high success rate of 20 % using a hierarchy of quantum non-Gaussian criteria. Moreover, the filtering protocol enables the preparation of superposition of Fock states, and we analyze this emerging case up to two photons with provable quantum non-Gaussian coherence and high success rate of 50 % . To demonstrate their quality for applications, we evaluate the robustness of such features, the bunching capability in a linear network, and the sensing capability to estimate the magnitude of unknown force, noise, and phase. These assessments outline the essential conditions and application criteria for realistic optical cavity QED interaction on light pulses to outperform photon detection methods.
We propose and experimentally demonstrate a new method to generate arbitrary Fock state superpositions in a superconducting quantum circuit, where a qubit is dispersively coupled to a microwave cavity mode. Here, the qubit is used to conditionally modulate the probability amplitudes of the Fock state components of a coherent state to those of the desired superposition state, instead of pumping photons one by one into the cavity as in previous schemes. Our method does not require the adjustment of the qubit frequency during the cavity state preparation and is more robust to noise and accumulation of experimental errors compared to previous ones. Using the method, we experimentally generate phase eigenstates under various Hilbert-space dimensions and squeezed states, which are useful for the quantum walk and high-precision measurement.