In the study's model, the amplified protocol's single-run success probability for a 200-photon target was 0.997 (99.7%). The corresponding unamplified calculation gave 0.028 (2.8%) and called for about 105 repetitions to reach high-probability heralding. The amplified version used four Grover iterations.
A register marks the target
The proposal combines quantum-nondemolition (QND) photon-number encoding with quantum amplitude amplification (QAA). The QAA stage uses Grover iterations to mark and amplify the desired register outcome before one final measurement.
The modeled input is a coherent state in one resonator, with an M-qubit register prepared in its ground state. The target is a Fock state—a cavity state with a prescribed photon number—and the marked register outcome serves as the herald for that target.
The trade-off is depth for repetitions
Without QAA, the expected number of unamplified repetitions scales as O(1/a0), where a0 is the baseline target probability, and as the square root of the target photon number N for coherent inputs. The reported QAA overhead grows as the fourth root of N. In practical terms, the calculation trades more coherent depth in one run for fewer separate preparation attempts.
What the model found
The resource table evaluated targets of 3, 50, 100 and 200 photons with registers of 3, 6, 7 and 8 qubits, respectively. QAA single-run success probabilities were 0.992, 0.996, 0.973 and 0.997, compared with unamplified probabilities of 0.225, 0.054, 0.040 and 0.028.
With a fixed five-qubit register, amplified success remained close to unity across the accessible target range. For a ten-qubit register, the paper gives a 1,000-photon state as reachable with about six Grover iterations; it presents that figure as a scaling example, while the reported open-system simulations extend to N=200.
These figures are not accompanied by confidence intervals or statistical uncertainty estimates, and the number of stochastic trajectories is not reported.
Loss was included, but timings remain estimates
To include cavity photon loss, the authors used Monte Carlo quantum-jump trajectories for a Lindblad model during dispersive phase accumulation. The open-system simulations reported near-unit post-amplification success through N=200 with no more than four amplification iterations.
Under assumed gate durations and coherence parameters, the N=200 amplified run was estimated at 20–25 microseconds. The unamplified route needed about 105 repetitions and more than 150 microseconds cumulatively, excluding reset and readout delays. These are implementation-time estimates, not measured timings.
The gap to a device
The reported probabilities come from analytical calculations and numerical simulations in an arXiv version-1 preprint dated 20 August 2026; no laboratory preparation result is reported. The parallel implementation also requires dispersive shifts and inverse detunings spanning a broad binary-weight range, which the paper identifies as a hardware constraint.
A proposed route to two modes
The authors propose a further step toward a two-mode path-entangled state: prepare the Fock state in one resonator, add a vacuum second mode, apply an auxiliary-qubit-controlled beam-splitter exchange, and measure the qubit in a rotated basis. That extension is proposed rather than demonstrated, and the appendix characterizes direct two-mode coherent-state amplification as exponentially worse than single-mode Fock preparation, favoring a prepare-first, entangle-later sequence.
Paper data and sources
Original title: Preparation of Large Fock States in Resonators with High Probability
Authors: Lucas R. S. Santos, Ciro M. Diniz, Daniel Z. Rossatto, Celso J. Villas-Boas
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text