Generating Fock state exceeding 10000 excitations with near unit fidelity by adaptive generalized-parity measurement

Abstract

Fock states are fundamental quantum states with a precisely defined integer number of excitations, serving as the core basis for describing bosonic modes. Large Fock states provide irreplaceable non-classical resources for quantum information processing and quantum metrology. The deterministic generation of macroscopic photon-number Fock states has long been a difficult problem in the field of quantum optics. We propose an adaptive generalized parity measurement (GPM) protocol for generating Fock states with more than $10000$ excitations, avoiding low success probability subject to postselection and high cost under complex coherent controls. For general discrete-spectrum systems, e.g., a bosonic mode coupled to an ancillary qubit, we derive a construction rule in which the intervals between repeated measurements on qubit are updated adaptively based on the last outcome. It means that our protocol does not discard any measurement trajectory, dramatically different from the probabilistic protocols that retain only one prescribed trajectory of postselection. In the resonant Jaynes-Cummings model, a large coherent state can be almost deterministically transformed to a large Fock state of $n_t=\mathcal{O}(10^4)$ excitations by $10$ rounds of measurements, the average fidelity of which is about $87\%$. The success probability for obtaining $|20000-\sqrt{20000}\leq n_t\leq20000+\sqrt{20000}\rangle$ with a fidelity above $99\%$ is about $35\%$ with respect to the ensemble sampling. Our protocol is fault-tolerant in the presence of moderate measurement error and parametric imperfection. Also it remains effective when the system is prepared as displaced thermal states, showing reliable performance regardless of initial state.