⚛️ quantum physics

Data and code for collision-model Dicke-state preparation: depth-fidelity frontiers, circuit costs, and superconducting-processor measurements

This paper presents an open dataset and accompanying code detailing the preparation of Dicke states via a collision-based protocol, offering noiseless fidelity benchmarks across varying circuit depths and qubit counts, alongside resource estimates and experimental measurements on a 54-qubit superconducting processor to analyze the trade-offs between state-preparation fidelity, circuit cost, and hardware noise.

Original authors: Duc-Kha Vu, Minh Tam Nguyen, Şahin K. Özdemir, Özgür E. Müstecaplıoğlu, Fatih Ozaydin

Published 2026-09-01

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CC BY 4.0

Original authors: Duc-Kha Vu, Minh Tam Nguyen, Şahin K. Özdemir, Özgür E. Müstecaplıoğlu, Fatih Ozaydin

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 world of quantum computing, information is stored in tiny units called qubits. Unlike the bits in a standard computer that are either zero or one, qubits can exist in a delicate combination of both states at once. When many qubits are linked together, they can form a special kind of connection known as entanglement, where the state of one qubit instantly influences the others, no matter how far apart they are. Among the many ways to arrange these entangled groups, a specific family of states called Dicke states holds a unique place. Imagine a room full of people where a fixed number of them are holding a red ball, but no one knows exactly who is holding it; the red balls are shared equally among everyone in a way that is perfectly balanced. This is what a Dicke state looks like: a precise number of energy units, or excitations, are shared coherently across a group of qubits. These states are not just theoretical curiosities; they are powerful tools for sensing magnetic fields, building quantum networks, and detecting subtle changes in the environment that other states might miss. However, creating these states in a real machine is notoriously difficult. As the number of qubits grows, the task becomes harder, and the inevitable noise in the machine tends to destroy the delicate balance before the state is even finished.

A team of researchers has now released a comprehensive collection of data and computer code that maps out the path to creating these states more effectively. They focused on a method that treats the creation process like a series of brief, repeated meetings between the qubits and a helper particle. In this approach, a mobile helper qubit moves through the system, swapping bits of information with the main qubits in a controlled way. By adjusting how strong these interactions are and how many times they occur, the researchers found they could steer the system toward the desired Dicke state. The team did not just stop at a single successful attempt; they explored a vast landscape of possibilities. They simulated the process for systems ranging from five to fourteen qubits, testing hundreds of different depths, or lengths, of the interaction sequence. For every possible length of the process, they calculated the highest quality of the resulting state that could be achieved in a perfect, noise-free world. This created a detailed map, or frontier, showing exactly how the quality of the state improves as the process gets longer, and how much longer is needed to reach a specific level of perfection.

The researchers then took this theoretical map and tested it on a real quantum computer, a 54-qubit superconducting processor located in Finland. They selected a handful of specific states from their simulations and ran the corresponding circuits on the physical machine. The results were revealing. For the shortest, simplest versions of the process, the machine managed to retain about three-quarters of the ideal quality predicted by the simulations. This suggests that even with the noise and errors inherent in current hardware, these short circuits are robust enough to produce useful results. However, as the researchers pushed the process to be longer and more complex in an attempt to reach higher perfection, the results dropped sharply. The deepest, most complex circuits performed no better than a completely random, broken-down system. This stark contrast highlights a critical trade-off: while adding more steps can theoretically improve the state, the physical machine is not yet perfect enough to handle the extra time and complexity without losing the very coherence it is trying to build.

To help other scientists navigate this trade-off, the team provided a complete toolkit. They released the raw numbers from their simulations, the estimated cost of running these circuits in terms of the number of basic operations required, and the actual measurements from the real machine. This allows anyone to look up a specific goal, such as "I need a state with five qubits and two excitations," and see exactly how many steps are needed to get close to the best possible quality, and what the cost would be in terms of time and error. They also included the code to reproduce their work, ensuring that the path they found is open for others to verify and improve upon. The data shows that for many of the states they studied, a single round of interactions was often enough to reach the peak quality achievable within the limits of their search. In other cases, going deeper helped, but only up to a point where the noise of the machine began to overwhelm the benefits of the extra effort.

This work does not claim to have solved the problem of creating perfect quantum states on current hardware. Instead, it offers a clear, honest guide to the current limits. It shows that while we can prepare these complex states, the depth of the process is constrained by the quality of the machine itself. The researchers demonstrated that trying to force a deeper, more complex process often yields diminishing returns, as the machine's imperfections accumulate faster than the algorithm can correct them. By providing a full record of what works, what fails, and where the balance lies, this dataset serves as a benchmark for future improvements. It tells us that the path forward is not simply to build longer circuits, but to find the sweet spot where the circuit is long enough to be useful but short enough to survive the noise of the real world. The release of this data and code ensures that the community can build on these findings, testing new methods against a solid foundation of what has already been measured and understood.

Technical Summary: Data and Code for Collision-Model Dicke-State Preparation

Problem Statement
Dicke states, defined as multipartite entangled states with a fixed number of quantum excitations coherently shared among $N$ qubits, are critical resources for quantum sensing, networking, and collective phenomena. However, preparing these states with high fidelity remains a significant challenge, particularly as system size ( $N$ ) and excitation number ( $K$ ) increase. While previous theoretical proposals often treat gate count as the primary cost metric and noiseless fidelity as the figure of merit, they frequently fail to account for the trade-offs imposed by hardware constraints. On current superconducting processors, two-qubit error rates vary significantly across couplings, and finite coherence times constrain circuit duration. Consequently, optimizing solely for noiseless fidelity may select unnecessarily deep circuits that suffer from severe decoherence in practice. There is a lack of comprehensive datasets that simultaneously map the trade-off between preparation fidelity, circuit depth, and hardware-specific costs across a broad range of system sizes.

Methodology
This work presents an open dataset and accompanying code generated using a collision-based quantum protocol. In this model, a system is driven by a sequence of short unitary encounters (collisions) with ancillary units. Specifically, the protocol employs a mobile shuttle ancilla that mediates excitation-preserving partial-swap (pSWAP) collisions between otherwise uncoupled registers.

The methodology involves three distinct layers of data generation and validation:

Noiseless Frontier (L1): For 31 target Dicke states ( $D^K_N$ ) spanning $N=5$ to $14$ qubits and $K=2$ to $5$ excitations, the authors performed extensive numerical searches. For each state, they evaluated up to 256 collision-strength candidates over a depth range of $m=0$ to $200$ sub-rounds (where one full round equals $K$ sub-rounds). The search optimized collision strengths ( $\gamma_{in}, \gamma_{sh}$ ) and a subsequent single-qubit phase layer to maximize noiseless fidelity.
Circuit Cost (L2): The dataset assigns circuit costs to the operating points identified in L1. This includes exact counts of pSWAP interactions, derived all-to-all two-qubit gate counts (assuming a CNOT/CZ basis where a nontrivial pSWAP requires three entangling gates), and estimates for routing overheads on devices with restricted connectivity.
Hardware Measurements (L3): Selected circuit "arms" (specific parameter sets) were executed on the 54-qubit IQM Emerald superconducting processor. The experiment collected 88,656 shots across four target states and ten distinct circuit configurations. The study utilized a specific physical-qubit layout to minimize gate errors and included calibration snapshots to characterize device noise.

Key Contributions
The primary contribution of this work is the release of a comprehensive, multi-layered dataset and the associated codebase, organized into three linked layers:

L1 (Noiseless Frontier): A complete record of the best-found noiseless fidelities for 6,231 operating points (31 states $\times$ 201 depth budgets). Unlike companion works that report only converged points, this release provides the full depth axis and all 1.59 million candidate evaluations, allowing users to benchmark alternative optimization strategies.
L2 (Circuit Costs): A mapping of operating points to resource costs, including exact pSWAP counts and conservative upper bounds for all-to-all two-qubit gate counts. It explicitly identifies 544 cells where costs are upper bounds due to missing collision-strength data from a shallower search.
L3 (Hardware Record): Raw measurement counts, execution plans, calibration snapshots, and processed fidelities for 10 circuit arms. This includes a "depth series" measuring excitation-sector population ( $P_K$ ) at five depths to characterize decoherence, and a "layout experiment" to assess sensitivity to physical qubit assignment.

The accompanying code provides tools to reproduce the processed data, validate the collision-model invariants (specifically the pre-phase overlap invariance), and re-analyze the raw hardware data using different estimators.

Results

Fidelity-Depth Trade-off: The noiseless frontier reveals that for 14 of the 31 states, one full round ( $m=K$ ) is sufficient to achieve the highest fidelity within the explored range. For the remaining states, fidelity improves with depth, with the median depth required to reach 99% of the best-found fidelity being 14 sub-rounds.
Hardware Performance: On the IQM Emerald processor, the measured fidelity ( $F$ ) relative to the noiseless fidelity ( $F_{ideal}$ ) varies significantly with circuit depth. Shallow circuits (one full round) retained approximately 71–76% of their noiseless fidelity for $D^2_5$ and 20–51% for $D^3_8$ . In contrast, deeper reference circuits retained only 4–9% of their noiseless fidelity, approaching the performance of a fully decohered circuit.
Cost Analysis: The deep-search operating points achieved higher noiseless fidelities (median $F \approx 0.887$ ) but at a significantly higher gate cost (median 2,832 two-qubit gates) compared to one-round circuits (median 165 gates, $F \approx 0.850$ ).
Excitation Population: The measured population of the target excitation sector ( $P_K$ ) decreased with circuit depth, consistent with decoherence models. The data supports a fitted effective two-qubit gate duration of 100 ns.

Significance and Claims
The paper positions this release as a reusable benchmark for studying the trade-off between state-preparation fidelity, circuit cost, and hardware noise. The authors explicitly state that the dataset is not a prediction of hardware performance but a record of what is attainable under specific conditions.

Key claims regarding the utility of the release include:

Benchmarking: It allows for the comparison of alternative optimizers cell-by-cell across the entire depth axis, rather than at single converged points.
Resource-Constrained Optimization: Users can invert the fidelity-versus-cost curves to identify the deepest circuit fitting within a specific two-qubit gate budget.
Noise Model Validation: The depth series and layout experiment provide empirical data to score and refine noise models against measured depth dependence.
Reproducibility: The inclusion of raw counts, calibration snapshots, and verification scripts enables the reprocessing of data with different estimators (e.g., maximum-likelihood reconstruction) and serves as a unit test for independent implementations of the collision model.

The authors maintain a modest stance, noting that the reported fidelities are "best-found" values from specific searches rather than certified global optima, and that the hardware results characterize a specific session on a specific device rather than general protocol performance. The release is intended to facilitate the rigorous evaluation of the collision-model protocol's practical viability on near-term quantum hardware.

Technical Summary: Data and Code for Collision-Model Dicke-State Preparation

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