⚛️ nuclear theory

From twelve to three active qubits: Ancilla-recycled rodeo filtering for trapped neutron-proton scattering

This paper demonstrates that recycling a single ancilla qubit through mid-circuit measurement and reset reduces the active qubit requirement for rodeo filtering in trapped neutron-proton scattering simulations from 12 to 3, achieving a 75% hardware compression while maintaining accuracy comparable to static implementations.

Original authors: Myeong-Hwan Mun, Jubin Park, Myung-Ki Cheoun, Eunja Ha

Published 2026-08-28

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CC BY 4.0

Original authors: Myeong-Hwan Mun, Jubin Park, Myung-Ki Cheoun, Eunja Ha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the subatomic world, particles like neutrons and protons do not simply bounce off one another in empty space; they interact through a complex force that shapes the very nuclei of atoms. To understand this interaction, physicists often study how these particles scatter, or deflect, when they collide. However, simulating these collisions on a computer is notoriously difficult because the particles can exist in a vast, continuous range of energies. To make the problem manageable for today's quantum computers, researchers often trap the particles in a virtual box, forcing them into a discrete set of energy levels, much like a guitar string can only vibrate at specific notes. By measuring these trapped energy levels, scientists can work backward to understand how the particles would behave in the open, free space of the universe. The challenge lies in the hardware: current quantum processors are limited in the number of qubits, or quantum bits, they can use simultaneously. Many advanced algorithms require a large number of extra qubits to act as helpers, or "ancillas," to perform calculations, often consuming so much of the machine's capacity that there is little room left for the actual physics being studied.

A team of researchers has demonstrated a way to overcome this hardware bottleneck without losing accuracy. They focused on a specific method called rodeo filtering, a technique used to isolate a single energy level from a complex mix of possibilities. Traditionally, this method requires a separate helper qubit for every step of the calculation. If a process needs ten steps, it needs ten helper qubits running at the same time, which quickly exhausts the limited resources of current machines. The researchers asked a simple but profound question: could they reuse a single helper qubit, measuring it and resetting it after each step, rather than dedicating a new one for every step? This approach would trade the need for many simultaneous qubits for a sequence of operations that happen one after another, a classic trade-off between space and time.

To test this idea, the team modeled the scattering of a neutron and a proton, a fundamental interaction in nuclear physics. They set up two different experiments on two different quantum computers. The first experiment used a static approach on an IonQ device, where they dedicated twelve active qubits to the task: two for the neutron and proton system, and ten separate helper qubits for the ten steps of the calculation. This setup represents the traditional, resource-heavy way of doing things. The second experiment used a dynamic approach on an IBM device, where they used only three active qubits. In this version, a single helper qubit was measured, its result recorded, and then reset to its starting state to be used again for the next step. This allowed the same ten-step calculation to be performed with a fraction of the hardware.

The results showed that the dynamic, recycled approach worked just as well as the static one. Both methods successfully identified the same trapped energy level of the neutron-proton system. The researchers found that the energy value measured by the three-qubit machine was consistent with the value measured by the twelve-qubit machine and matched the known theoretical value with high precision. Specifically, the dynamic method reduced the number of simultaneously active qubits by 75 percent, shrinking the requirement from twelve down to three. This compression did not come at the cost of the quality of the data; the dynamic circuit retained the same ability to filter out the correct energy signal as the much larger static circuit.

However, the study also revealed important nuances about how these machines behave in the real world. While the three-qubit method saved space, it introduced new variables related to the timing and stability of the machine. When the researchers ran the dynamic experiment multiple times, they noticed that the exact center of the measured energy varied slightly from one run to another, even though the overall strength of the signal remained stable. This suggests that simply reusing a qubit is not a magic fix; it requires careful validation to ensure the machine is not introducing its own errors through the repeated measurement and reset process. The team found that by running the experiment in a specific, interleaved order—checking the center point at the beginning, middle, and end of the run—they could better control for these variations.

The significance of this work extends beyond just this single experiment. By proving that a helper qubit can be recycled, the researchers have shown that future quantum calculations can be scaled up to handle more complex nuclear systems without needing a proportional increase in hardware. Instead of being limited by the number of qubits available at one moment, scientists can now design algorithms that use the same qubits over and over again, freeing up the machine's capacity to focus on the physical system itself. This opens the door to more detailed studies of nuclear forces, potentially leading to a deeper understanding of how atomic nuclei are held together. The study confirms that while the hardware is still evolving, clever programming strategies can extract precise physical truths from today's imperfect machines, bridging the gap between theoretical models and the reality of quantum scattering.

Technical Summary: From Twelve to Three Active Qubits: Ancilla-Recycled Rodeo Filtering for Trapped Neutron–Proton Scattering

Problem Statement
Near-term quantum processors are constrained by the number of simultaneously usable qubits, a limitation that often forces auxiliary registers to consume a substantial fraction of available hardware before the physical system of interest can be enlarged. Spectral filtering algorithms, such as the rodeo algorithm, typically require a number of active qubits ( $W$ ) that scales linearly with the number of interrogation cycles ( $R$ ) plus the system size ( $n_s$ ), following $W = n_s + R$ . For a static implementation with $R=10$ cycles on a two-qubit system, this necessitates 12 active qubits. The challenge is to determine if the same nuclear spectral primitive can be compressed into a dynamic circuit without sacrificing the accuracy of the trapped-energy information required for scattering analysis.

Methodology
The authors implement an identical ideal $R=10$ rodeo filter in two distinct architecture-adapted forms to model neutron–proton ($np$) scattering in a weak harmonic trap:

Static Realization: A 12-qubit circuit executed on the IonQ Forte-1 device. This approach unrolls all 10 cycles onto 10 separate ancilla qubits, deferring all measurements until the end of the circuit.
Dynamic Realization: A 3-qubit circuit executed on the IBM Aachen device. This approach employs ancilla recycling, where a single ancilla qubit is measured and reset mid-circuit after each cycle. This allows the same ancilla to be reused for all 10 cycles, reducing the active width to $W = n_s + 1$ .

Both implementations target the $0^+$ square-well $np$ system at a trap frequency $\omega = 3.7$ MeV. The goal is to extract the trapped eigenenergy $E_2$ (reference value: 17.134039 MeV). The dynamic circuit utilizes ten mid-circuit measurements and nine resets, trading spatial resources for sequential control and increased latency. To assess precision and repeatability, the authors conducted three independent IBM batches using forward, reverse, and interleaved query protocols. The measured energy centers are mapped to the finite-confinement modified effective range expansion (MERE) quantity $K_{3.7} = p \cot \delta_{0,3.7}$ . Additionally, Sample-Based Quantum Diagonalization (SQD) is used to audit the postselected model-space support.

Key Contributions

Qubit Width Compression: The study demonstrates a 75% reduction in active qubit width (from 12 to 3) by replacing nine simultaneous ancillas with mid-circuit measurement and reset operations, while retaining the full $R=10$ filter selectivity.
Hardware Benchmarking: The paper provides a direct cross-platform comparison of a static IonQ implementation and a dynamic IBM implementation, isolating the effects of qubit-width compression and mid-circuit control on spectral accuracy.
Validation of Support Completeness: The authors verify that both implementations retain complete four-configuration support ( $S_{full} = \{00, 01, 10, 11\}$ ), ensuring that the exact effective-space level is recovered via SQD, rather than relying on generic error mitigation.
Scattering Input Mapping: The work successfully maps hardware-resolved energy uncertainties to the MERE input $K_{3.7}$ , demonstrating that the compressed dynamic circuit preserves the necessary precision for nuclear scattering inputs.

Results

Energy Precision: The static IonQ scan yielded a center displacement of $\Delta E_c = -0.568 \pm 0.694$ keV. The dynamic IBM interleaved scan yielded $\Delta E_c = -0.017 \pm 0.507$ keV. Both results are statistically consistent with the exact trapped level, showing that the 3-qubit dynamic circuit retains spectral precision comparable to the 12-qubit static result.
Repeatability and Variance: While the interleaved IBM protocol showed the strongest within-job control, the three independent IBM batches exhibited heterogeneous center shifts ( $\Delta E_c$ ranging from $+1.539$ to $-0.600$ keV) that exceeded finite-shot fluctuations. This indicates that stable postselection yield (amplitude retention) does not guarantee a stable spectral center.
MERE Output: The mapped values for $K_{3.7}$ were $0.13419 \pm 0.00020$ fm $^{-1}$ (IonQ) and $0.13435 \pm 0.00015$ fm $^{-1}$ (Interleaved IBM), both consistent with the exact value of $0.13436$ fm $^{-1}$ .
Simulation Limitations: Calibration-derived noisy simulations (Aer) failed to consistently predict the hardware repeatability, with simulated centers showing significant deviation from actual hardware batches.

Significance and Claims
The paper claims that ancilla recycling makes the rodeo filter width independent of the number of interrogation cycles ( $R$ ), thereby freeing qubits for the nuclear register while preserving finite-confinement scattering inputs. The authors emphasize that this is a space–time tradeoff, not a free reduction in cost, as it introduces mid-circuit latency and reset requirements.

Crucially, the authors state modestly that this work validates a single finite- $\omega$ scattering input rather than a complete determination of free-space phase shifts or scattering lengths. The primary significance lies in establishing that the number of rodeo cycles—and thus the ideal filter selectivity—can be increased without increasing the number of simultaneously active ancillas. This provides a practical path toward multi-level, multi-frequency trapped-spectrum calculations on near-term processors, provided that hardware-resolved energy uncertainties are properly propagated through the MERE and that run-dependent variations are accounted for through rigorous validation protocols (e.g., interleaved queries and independent batches).

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