Programmable all-to-all entangling gates for cavity-coupled atoms

arXiv:2610.22220 · quant-ph · Submitted 2026-10-15 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Programmable all-to-all entangling gates for cavity-coupled atoms".

Mira: The gist: The authors design a high fidelity Mølmer Sørensen-like entangling gate between neutral atoms coupled to a photonic cavity, enabling programmable all-to-all connectivity through the shared cavity coupling.

Kai: First, who's behind it and why it matters.

Title and authors: Kai: The authors show how they can actively suppress the fidelity-lowering terms by optimizing the pump amplitude and tuning the ratio R12 = alpha minus one g0 over Omega <ref:FIGURE four <ref:2610.22220#pg3>.

Mira: So, by tuning R12 in that specific way, they’ve found a way to actively minimize those fidelity-lowering terms <FIGURE four <ref:2610.22220#pg3>.

Lev: That’s an active suppression strategy instead of just relying on passive hardware improvements for better components <FIGURE four <ref:2610.22220#pg3>.

Kai: They also show that increasing the atom-cavity coupling or pump amplitude can reduce interaction time and apply quantum optimal control techniques to fight cavity dissipation <SOURCES OF ERRORS>.

Mira: So, optimizing those parameters helps manage the limitations imposed by Q, which is omega c over two kappa <SOURCES OF ERRORS>.

Lev: That means we can push the limits of performance by using better control strategies instead of just waiting for better passive components <SOURCES OF ERRORS>.

Kai: They demonstrate that for Q equals ten seven and Q equals ten eight they get fidelities F equal to zero point nine eight six and F equals zero point nine nine two respectively <FIGURE five.

Mira: Those figures show that with better control over those parameters, we can get fidelities above zero point nine nine <FIGURE five.

Lev: That performance level is what we need for running real error correction codes on actual physical hardware <FIGURE five.

Kai: So the work shows that when you put in good control, you can get high fidelity even when the cavity coupling isn't perfect <ref:two thousand six hundred ten point two two two two zero#pg1.

Mira: It’s interesting how they found a way to handle the cavity dissipation which limits coherence <SOURCES OF ERRORS>.

Lev: That means we don't always have to just build bigger cavities; control strategies matter a lot in practice <SOURCES OF ERRORS>.

The paper's summary: Kai: Beyond just the fidelity numbers, they showed that the Mølmer Sørensen gate generates entangled states between any subset n of the total atoms N interacting with the cavity <FIGURE three <ref:2610.22220#pg3>.

Mira: This is a key feature because it means we can select exactly which qubits get entangled through local laser addressing <FIGURE three <ref:2610.22220#pg3>.

Lev: So, they’re not limited to just nearest neighbor interactions anymore; we can achieve arbitrary connectivity between any subset of atoms <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOMS>.

Kai: That’s the core promise: selective entanglement between any subset of separated atoms without needing physical transport <ref:two thousand six hundred ten point two two two two zero#pg5.

Mira: So this is a very powerful feature because it allows us to achieve arbitrary pair entanglement across the whole system <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOMS>.

Lev: If we can build systems with this kind of connectivity, it fundamentally changes the requirements for how we design our error correction codes <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOM.

Kai: So the system doesn't just offer a fixed connection anymore; it offers flexibility based on what you program into the laser fields <ref:two thousand six hundred ten point two two two two zero#pg5.

Mira: This means we can tailor the entanglement to exactly what our error correction code needs <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOMS>.

Lev: If this works, it means the architecture for large quantum processors shifts from fixed grids to something much more flexible <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOMS>.

The paper's improvements: Lev: So, to wrap up on this paper "Programmable all-to-all entangling gates for cavity-coupled atoms," the main thing is that they've moved the focus from fixed local connections to arbitrary connectivity through a shared photonic cavity <ref:2610.22220#pg1>.

Kai: They’ve shown that this allows for selective entanglement between any subset of separated atoms without needing physical transport or shuttling <ref:two thousand six hundred ten point two two two two zero#pg5.

Mira: This capability is really what lets us achieve arbitrary pair entanglement across the whole system <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOM>.

Lev: If we can scale this up, it changes how we think about integrating quantum processors into larger networks <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOM>.

Kai: This is a lot of potential for building more connected quantum processors with these new gates <ref:two thousand six hundred ten point two two two two zero#pg1.

Mira: It really lets us achieve arbitrary pair entanglement across the whole system <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOM>.

Lev: We need to keep pushing these control strategies to make this architecture viable for real quantum computing hardware <PROGRAMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOM>.

Conclusion: Kai: So, to wrap up on "Programmable all-to-all entangling gates for cavity-coupled atoms," we’ve seen how they use that shared photonic cavity mode to connect any subset of atoms through local laser addressing.

Mira: Right, and they make it really interesting because this setup eliminates the need for physical atom transport or shuttling entirely because the entanglement happens through that shared cavity coupling.

Lev: That bypasses motional errors and erasure errors by not physically moving anything at all, which is a huge win for scaling hardware.

Kai: The key result is they can select exactly which qubits get entangled through local laser addressing, meaning any subset of atoms can be entangled while the others just act as spectators.

Mira: This means this capability lets them achieve arbitrary pair entanglement across the whole system because they have control over which interactions happen.

Lev: If we can build systems with this kind of connectivity, it fundamentally changes the requirements for how we design our error correction codes.

Kai: So, this ability to select which atoms interact without moving them is the core promise of the work.

Mira: It’s not just about connecting neighbors; it’s about arbitrary pair entanglement across the entire set of N atoms.

Lev: That level of connectivity means we can design error correction codes that are much more efficient than those relying only on nearest neighbor gates.

Kai: They also showed that they can actively suppress the fidelity-lowering terms by optimizing the pump amplitude and tuning the ratio R12, which is alpha minus one times g0 over Omega.

Mira: So, by tuning R12 in that specific way, they’ve found a way to actively minimize those fidelity-lowering terms.

Lev: That’s an active suppression strategy instead of just relying on passive hardware improvements for better components.

Kai: They also showed that increasing the atom-cavity coupling or pump amplitude can reduce interaction time and apply quantum optimal control techniques to fight cavity dissipation.

Mira: So, optimizing those parameters helps manage the limitations imposed by Q, which is omega c over two kappa.

Lev: That means we can push the limits of performance by using better control strategies instead of just waiting for better passive components.

Kai: They demonstrated that for Q equals ten seven and Q equals ten eight they get fidelities F equal to zero point nine eight six and F equals zero point nine nine two respectively.

Mira: Those figures show that with better control over those parameters, we can get fidelities above zero point nine nine.

Lev: That performance level is what we need for running real error correction codes on actual physical hardware.

Kai: Overall, this paper "Programmable all-to-all entangling gates for cavity-coupled atoms" shows that exploiting a shared photonic cavity mode can mediate long range entangling operations without physical transport.

Mira: This capability is really what lets us achieve arbitrary pair entanglement across the whole system.

Lev: If we can scale this up, it changes how we think about integrating quantum processors into larger networks.

Angus Crookes, Ben Yuen, Angela Demetriadou

School of Physics and Astronomy, University of Birmingham

quant-ph

Submitted: 2026-10-15

Updated: 2026-10-15

Comments: 10 pages, 6 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 88/100

The gist: The gist: The authors design a high fidelity Mølmer Sørensen-like entangling gate between neutral atoms coupled to a photonic cavity, enabling programmable all-to-all connectivity through the

Key concepts

Mølmer-Sørensen (MS) Hamiltonian: This is a specific mathematical description of how the atoms interact with each other and with the cavity light. It uses three atomic energy levels ($ ext{|g angle}$, $ ext{|e angle}$, and $ ext{|r angle}$) to mediate coupling between them via cavity-assisted Raman transitions. This setup allows for controlled entanglement operations between different qubits.
Programmable All-to-All Connectivity: This capability means that any chosen subset of atoms can be entangled with each other, regardless of their initial spatial separation. This is achieved by using the shared photonic cavity as a medium to mediate interactions, eliminating the need for physically moving atoms between different interaction zones.
Cavity Dissipation (Q): This term quantifies how quickly energy leaks out of the photonic cavity, which limits how long entanglement can be maintained. The authors show that this limitation can be overcome by increasing the atom-cavity coupling or optimizing control parameters to maintain high gate fidelity.
Pump Amplitude Optimization: The fidelity of the gate is sensitive to experimental fluctuations. By tuning the ratio $R_{12} = |\alpha - 1|g_0/\Omega$, researchers can adjust the pump amplitude. This adjustment helps suppress errors caused by terms in the Hamiltonian, ensuring robust and high-fidelity entanglement even when parameters vary.

Summary

The gist: The authors design a high fidelity Mølmer Sørensen-like entangling gate between neutral atoms coupled to a photonic cavity, enabling programmable all-to-all connectivity through the shared cavity coupling.

Motivation and Problem Addressed

Fault tolerant quantum computers require entangling gates with low error rates and high fidelities [1–3]. Implementing arbitrary pair entanglement is necessary for quantum error correcting codes beyond nearest neighbour gates [4–8]. While ion traps offer high fidelity two qubit gates, implementing long range entanglement requires shuttling ions between interaction zones, which introduces motional errors and erasure errors [29–35]. This work overcomes these challenges by deriving a gate that enables entanglement between spatially separated qubits without physical transport or shuttling [2610.22220].

System Description and Hamiltonian

The system involves an ensemble of N atoms coupled to a photonic cavity, with a subset n of the atoms driven by two external laser fields [MØLMER SØRENSEN HAMILTONIAN]. The atoms have three levels in a Λ configuration, where the lower levels g⟩ and e⟩ form a qubit, and the upper level r⟩ mediates coupling between them via cavity assisted Raman transitions [MØLMER SØRENSEN HAMILTONIAN]. The full Hamiltonian describing this system is given by H = ωca†a + X N i=1 ωege⟩⟨e + ωrgr⟩⟨r + X N i=1 h g0r⟩⟨0a + g1r⟩⟨1a+h.c.i + X i∈n h omega˜(i) 0 r⟩⟨0+ omega˜(i) 1 r⟩⟨1 + h.c.i [MØLMER SØRENSEN HAMILTONIAN].

Gate Derivation and Operation

The derivation involves a series of unitary rotations, followed by adiabatically eliminating the upper level r⟩ to define an effective Hamiltonian (HMS) [APPENDIX A]. The resulting MS-like Hamiltonian is given by HMS = -1/∆ X N i=1 g21 - g20 2 a†aσ(i)z + g(x)eff a†e−iδ′t + aeiδ′t Sx + g(y)eff a†e−iδ′t − aeiδ′t Sy [MØLMER SØRENSEN HAMILTONIAN]. This Hamiltonian has the unitary evolution operator UMS = exp(-i((α(t)a†+α∗(t)a)Sx) e iβ(t)S2x [MØLMER SØRENSEN HAMILTONIAN]. The gate is robust to changes in the photon number state of the cavity because at time T = 2π/δ′ the parameter α(T) = α∗(T) = 0, making UMS(T) independent of a and a† [MØLMER SØRENSEN HAMILTONIAN].

Key Results and Performance

The gate fidelity is demonstrated to exceed F > 0.99 using experimentally realistic parameters, with higher fidelities achievable through optimal control of the pump amplitudes [Programmable all-to-all entangling gates for cavity-coupled atoms]. For two atoms (N = 2) both driven by the external laser, the UMS gate performs transformations equivalent to a controlled NOT gate up to a single qubit unitary rotation [FIG. 2]. The fidelity of the entangled state is robust to changes in the photon number state of the cavity, showing F = 0.993 for nc = 3 [FIG. 2]. Furthermore, the MS gate generates entangled states between any subset n of the total atoms N interacting with the cavity, and only those atoms for which pump amplitudes are non-zero become entangled [FIG. 3].

Error Sources and Mitigation

When g0 ≠ g1, the MS gate deviates from ideal operation due to two terms in the general Hamiltonian: an AC-Stark shift term (H(1)MS) and an orthogonal atom dependent force along the Sy axis (H(3)MS), both of which degrade fidelity [SOURCES OF ERRORS]. The fidelity can be controlled by optimizing the pump amplitude, as tuning the ratio R12 = α − 1g0/omega allows minimizing the contribution of the Stark shift term [FIGURE 4]. Additionally, cavity dissipation limits coherence, quantified by Q = ωc/2κ [SOURCES OF ERRORS]. However, this reduction can be mitigated by increasing atom-cavity coupling or pump amplitude to reduce interaction time and applying quantum optimal control techniques [SOURCES OF ERRORS]. The maximum fidelities achieved for Q = 107 and Q = 108 are F = 0.986 and F = 0.992 respectively [FIG. 5].

Conclusion

This scheme exploits a shared photonic cavity mode to mediate long range entangling operations, eliminating the need for physical transport or shuttling [Programmable all-to-all entangling gates for cavity-coupled atoms]. This capability provides a promising route towards scalable, highly connected quantum processors capable of efficiently implementing advanced quantum error correcting codes [PROGRAMMABLE ALL-TO-ALL ENTANGLING GATES FOR CAVITY-COUPLED ATOMS].

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Programmable all-to-all entangling gates for cavity-coupled atoms</ref:2610.22220]

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Implementing arbitrary pair entanglement is necessary for quantum error correcting codes beyond nearest neighbour gates [3].

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The ability to entangle arbitrary pairs of qubits also enables the implementation of quantum error correcting codes beyond those used in systems with only nearest neighbour entangling gates, such as the surface code [4–8].

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This work overcomes these challenges by deriving a gate that enables entanglement between spatially separated qubits without physical transport or shuttling.</ref:2610.22220]

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A Ransford, M. Allman, J. Arkinstall, J. Campora, S. F. Cooper, R. D. Delaney, J M Dreiling B Estey C Figgatt A Hall et al., Nature, 1 (2026).

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D Schoenberger J Hilder F Schmidt-Kaler and R Wille in 2025 IEEE International Conference on Quantum Software (QSW) (IEEE, 2025) pp. 123–129.

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J M Pino J M Dreiling C Figgatt J P Gaebler S A Moses M Allman C Baldwin M Foss-Feig D Hayes K Mayer et al., Nature 592, 209 (2021).

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P Jordan Zeitschrift f¨ur Physik 94, 531 (1935).

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Nature 614, 676 (2023).

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A Sørensen and K Mølmer Physical review letters 82, 1971 (1999).

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This work overcomes these challenges by deriving a gate that enables entanglement between spatially separated qubits without physical transport or shuttling.</ref:2610.22220]

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Implementing arbitrary pair entanglement is necessary for quantum error correcting codes beyond nearest neighbour gates [3].

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This work overcomes these challenges by deriving a gate that enables entanglement between spatially separated qubits without physical transport or shuttling.</ref:2610.22220]

Improvements for AI systems

Improved AI systems can implement non-local qubit connectivity through local laser addressing rather than requiring physical atom transport, which eliminates the need for physically move atoms to perform the gate.
The improved system can perform selective entanglement between any subset of separated atoms because the scheme allows any subset of atoms can be entangled through local laser addressing, with all other atoms acting as spectators to the gate.
These systems benefit from robustness against experimental fluctuations, as the Mølmer Sørensen-like gate is robust to changes in cavity photon number and demonstrates a "high fidelity exceeding F > 0.99".
The system can maintain high fidelity entanglement even with varying coupling strengths, as optimizing the pump amplitude can suppress errors by tuning the ratio R12, which is related to R12 = α − 1g0/omega.
The improved AI architecture can be designed for scalable, highly connected quantum processors by exploiting a shared photonic cavity mode to mediate long-range entangling operations.

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Key concepts

Summary

Improvements for AI systems

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