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Efficient preparation of entangled states in cavity QED with Grover's algorithm

T0 review · 2 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper shows that Grover's search algorithm, implemented by single-photon phase shifts in a cavity, can prepare collective Dicke, GHZ, and Schrödinger cat states of N atoms deterministically in O(N^{1/4}) scattering events, without…

desk verdict Dicke state preparation is genuinely new and sound, but the GHZ protocol fails in the ideal limit for N ≡ 2 mod 4. read the letter →

arxiv 2501.18881 v4 pith:T5STZLF2 submitted 2025-01-31 quant-ph physics.atom-ph

Omar Nagib , M. Saffman , K. M{o}lmer This is my paper · ORCID
classification quant-phphysics.atom-ph PACS 42.50.Pq03.67.Bg03.67.Lx
keywords Grover'salgorithmcavityQEDDickestatesGHZSchrödingercatentangledstatepreparationphotonscatteringphasegate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes using Grover's amplitude-amplification algorithm, implemented with single-photon scattering in cavity QED, to prepare entangled states of N atoms deterministically. The central claim is that collective Dicke states, GHZ states, and Schrödinger cat superpositions can be produced with only O($N^{{1/4}}$) photon scattering events, without individual addressing of the atoms. For up to 500 qubits, any Dicke state can be prepared perfectly in four or fewer Grover steps, i.e., eight or fewer scattered photons. This matters because current carving schemes succeed only probabilistically with a small overlap squared, while the Grover iteration amplifies the target amplitude deterministically in a few steps.

What carries the argument

The central object is the Grover iteration $G = \chi_i \chi_t$, where each $\chi$ is a conditional phase flip (oracle) that puts a minus sign on one state component and leaves the orthogonal component unchanged. In this protocol the oracles are implemented by the dispersive cavity QED Hamiltonian $H = \hbar\Omega \hat{m} \hat{n}_c$, where $\Omega = g^2/\Delta$ is the per-atom cavity frequency shift and $\hat{m}$ counts atoms in $|1\rangle$; a photon tuned to $\omega_m = \omega_0 + m\Omega$ acquires a $\pi$ phase upon reflection only when the ensemble occupies Dicke state $|m\rangle$. The initial-state oracle $\chi_i$ is enacted by global rotations $R^{\otimes N}(\phi)$ around the $y$-axis sandwiching a $\chi_0$ phase flip, so no single-qubit addressing is needed. The iteration acts as a rotation in the two-dimensional subspace spanned by $|\psi_i\rangle$ and $|\psi_t\rangle$, rotating by angle $\theta$ each step, which yields the target state exactly when $\sin[(2k+1)\theta/2] = 1$.

What would settle it

Reflect a sequence of single photons from a cavity containing $N$ atoms prepared in a Dicke state and tomographically reconstruct the final atomic state: if preparing $|m = N/2\rangle$ for $N = 100$ in the claimed at-most-four steps (eight photons) yields a fidelity below the predicted value (e.g., well below 99% at cooperativity $C = 10^4$), or if the required number of steps grows faster than $N^{1/4}$, the central claim is refuted. Equivalently, a direct measurement of the single-photon reflection phase for state $|m\rangle$ versus $|m\pm 1\rangle$ that shows a phase error of order $\kappa/\Omega$ or larger at the designed detunings would invalidate the oracle.

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Extended reading notes

Core claim

The paper establishes that Grover's search algorithm, normally used for unstructured database search, can be repurposed as a state-preparation engine for an atomic ensemble in a cavity. The key is that the two phase-inversion operations $\chi_i$ and $\chi_t$ of Grover's iteration can be realized by reflecting single photons off a cavity whose resonance frequency shifts by $m\Omega$ when $m$ atoms occupy the state $|1\rangle$; a photon resonant with the target Dicke state acquires a $\pi$ phase, while all other states see no phase change. Starting from a coherent spin state with a chosen rotation angle $\phi$, the Grover iteration $G = R^{\otimes N}(\phi)\chi_0 R^{\otimes N}(-\phi)\chi_m$ rotates the initial state into the target Dicke state $|m\rangle$ in $k$ steps, with $k \approx 0.88 N^{1/4} - 1/2$ for $m = N/2$ and $k \approx 1.24 m^{1/4} - 1/2$ for small $m$. The same mechanism prepares GHZ states by first preparing $|N/2\rangle$ and then rotating it into a superposition with large overlap with the extremal Dicke states $|0\rangle$ and $|N\rangle$, at comparable resource cost. The paper further analyzes errors from finite cavity resolution, spontaneous emission, and finite photon bandwidth, deriving infidelity scalings $1-F \sim C^{-1/2}$ (unheralded) and $C^{-2/3}$ (heralded), and reports numerical fidelities for $C=100$ cavities.

Load-bearing premise

The protocol assumes that a photon reflected from the cavity acquires exactly a $\pi$ phase shift when the atomic ensemble is in the target Dicke state and zero phase shift for every other Dicke state, requiring the dispersive limit $|\Delta| \gg g$ with $\Omega = g^2/\Delta$ much larger than the cavity linewidth $\kappa$ and negligible spontaneous emission.

Editorial extensions

If this is right

  • Any Dicke state $|m\rangle$ of $N \le 500$ qubits can be prepared deterministically with at most four Grover steps, i.e., eight scattered photons, using only global rotations and fixed-frequency photon pulses.
  • The protocol needs no individual addressing, no ancilla qubits, and no mid-circuit measurements, unlike circuit-based Dicke-state preparations with comparable $O(m^{1/4})$ depth.
  • GHZ states and Schrödinger cat superpositions of $N$ atoms can be prepared with $O(N^{1/4})$ photon scattering events, using the Dicke state $|N/2\rangle$ as a stepping stone.
  • For small $m$ (e.g., the W state $m=1$), preparation takes a single step independent of $N$, and the fidelity is nearly independent of qubit number.
  • With state-of-the-art high-cooperativity cavities ($C \approx 2\times 10^3$), heralded protocols reach 90–97% fidelity for Dicke states; reaching 99% requires $C > 10^4$ (heralded) or $C > 10^5$ (unheralded).

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • This suggests a general principle: any target state whose overlap with a preparable initial state scales as $N^{-\alpha}$ can be amplified in $O(N^\alpha)$ Grover steps; the Dicke and GHZ cases here correspond to $\alpha = 1/4$.
  • Because the oracle depth is constant (one photon reflection), the protocol is a physical realization of an $O(1)$-cost oracle, implying that other oracle-based quantum algorithms (e.g., amplitude estimation or fixed-point Grover search) could similarly be turned into state-preparation tools in cavity QED.
  • If the exact-$\pi$ phase condition is relaxed to a partial phase or to homodyne detection of the reflected photon, the scheme becomes a heralded near-deterministic preparation with a tradeoff between success probability and fidelity—a direction implicit in the paper's heralding discussion.
  • The same collective-coupling logic should transfer to other platforms where an ancilla (Rydberg atom or superconducting qubit) couples to the operator $\hat{m}$, so the protocol is not limited to optical cavities.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript proposes a cavity-QED implementation of Grover's amplitude amplification to prepare symmetric entangled states. For a target Dicke state |m>, a coherent spin state is amplified by alternating the oracle χ_m with a reflection about the initial state, each step being implemented by global pulses and two frequency-selected single-photon cavity reflections. The same construction is applied to GHZ states using the product oracle χ_0 χ_N and a rotated Dicke state as input, and to Schrödinger-cat states in a companion paper. The authors derive the required number of Grover steps from binomial overlaps, obtaining k ~ 0.88 N^{1/4} for m=N/2 and k ~ 1.24 m^{1/4} for fixed small m, and they give a simplified error analysis in terms of the cooperativity C, with numerical fidelities for realistic parameters.

Significance. If the ideal operations are exact, the protocol is conceptually attractive and the resource analysis is sound: the Grover rotation in the two-level subspace is exact, the step count follows from the independent geometric overlap of a coherent spin state with Dicke states, and the implementation uses only global rotations and frequency-selected photon reflections. The paper is transparent about finite-cooperativity errors and gives concrete numbers (e.g., C>10^4 for 99% fidelity). However, the GHZ protocol has a parity-dependent failure in the ideal limit that invalidates the GHZ claim for N ≡ 2 (mod 4), so the central claim is not yet fully supported.

major comments (2)
  1. [Preparation of a GHZ state, Eq. (7)] The oracle χ0χN marks the two-dimensional subspace spanned by |0...0> and |1...1>, not the GHZ state alone. For the initial state R(-ϕ)^⊗N|N/2> with the y-axis rotations used in Fig. 2 and ϕ=π/2 (the only angle that equalizes the two extremal amplitudes), the amplitudes on |0...0> and |1...1> are equal in magnitude but have relative sign (-1)^(N/2). For N ≡ 2 (mod 4), the marked component of the initial state is therefore (|0...0> - |1...1>)/√2, which is orthogonal to |GHZ>, and because χ0χN does not distinguish this state from |GHZ>, the Grover evolution takes place in a subspace orthogonal to |GHZ>; the fidelity to |GHZ> remains exactly zero. The authors need to specify a rotation axis or phase convention that yields equal and same-signed amplitudes (for example an x-axis rotation), and they must state the parity requirements on N, including the fact that odd N is not covered because |N/2> is not a Dicke state.
  2. [Error analysis, Eq. (8)] The minimization in the error analysis gives 1 - F ~ 2 sqrt(m/C), not 1/sqrt(C). The text states that d ~ (C/m)^(1/4) at the optimum, and substituting this value yields both error contributions scaling as sqrt(m/C); the √m factor is numerically significant for the larger m values shown in Fig. 4(a) and should be retained in the scaling law and in the discussion of the cooperativity required for a given target fidelity.
minor comments (4)
  1. [Table I] The infidelity column entries '0' for the ideal algorithms should be labeled as ideal-circuit infidelity; otherwise they can be read as contradicting the C-dependent infidelity entries in the physical-implementation rows.
  2. [Abstract and Outlook] The abstract claims deterministic preparation of Schrödinger-cat superpositions, but the protocol for cat states is only described in the companion paper [40]; the abstract should either cite that work or restrict the claim to the states treated in this Letter.
  3. [Fig. 4(c)] The caption of Fig. 4(c) does not state which Dicke state m is used in the infidelity-versus-C plot; because the scaling depends on m, this information is needed to interpret the quoted C thresholds.
  4. [Comparison with Ref. [41]] The statement that the present algorithm achieves a smaller actual number of steps than Ref. [41] is not quantified; a direct comparison table or explicit numbers should be provided.

Circularity Check

0 steps flagged · score 2.0 of 10

Not circular: Dicke and GHZ resource claims follow from the standard Grover rotation and an independent binomial-overlap calculation; the same-author companion citation [40] covers only supporting error-analysis and Cat-state extensions.

full rationale

The central derivation chain is self-contained. The protocol starts from the dispersive Hamiltonian H = ℏΩ m̂ n̂c and the ideal phase gate |m′⟩ → e^{iπδ_{m,m′}}|m′⟩, which are physical inputs, not outputs of the state-preparation claim. The overlap sin(θ/2) = sqrt(C(N,m)) cos^{N−m}(φ/2) sin^m(φ/2) is read directly from the binomial expansion of the coherent spin state in Eq. (4), and the asymptotic step count k ∼ 0.88 N^{1/4} − 1/2 follows from a Gaussian approximation to that binomial coefficient, an independent mathematical fact. The rotation angle φ is a control parameter chosen to satisfy the Grover resonance condition sin((2k+1)θ/2) = 1, so it is not a data-fitted constant disguised as a prediction. The GHZ protocol uses the same two-dimensional Grover rotation; its overlap estimate is geometric, and any failure for N ≡ 2 (mod 4) due to the anti-GHZ component is a correctness issue, not a circularity. The only same-author citation, Ref. [40], is used for the Cat-state extension and for detailed error scalings such as 1−F(χ0) ∼ 1/C and heralded C^{−2/3}, while the Letter itself presents numerical simulations in Fig. 4; thus the main Dicke and GHZ efficiency results do not reduce to that citation. No equation in the paper is equivalent by construction to its own input, so no circular step is exhibited.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim depends on the standard Grover rotation and the standard dispersive cavity QED phase gate. The rotation angle ϕ is a control parameter, not a fitted constant. No new physical entities are introduced. The principal domain assumption is the ideal deterministic phase gate, whose limitations are analyzed in the paper's error section.

free parameters (1)
  • Rotation angle ϕ (per step) = Chosen to satisfy sin[(2k+1)θ/2] = 1, e.g., θ = π/(2k+1)
    The initial coherent spin state is rotated by a global angle ϕ before and after the photon-scattering phase gate to implement the Grover diffusion. The angle is a control parameter tuned by the experimenter to make the final amplitude unity at an integer number of steps; it is not a data-fitted constant.
assumptions (5)
  • standard math Grover's algorithm rotates an arbitrary initial state to a target state in the two-dimensional subspace, Eq. (2).
    Invoked in 'Grover's algorithm' section; known quantum search result.
  • domain assumption Dispersive cavity QED Hamiltonian H = ℏΩ m̂ n̂c with Ω = g²/Δ in the limit |Δ| ≫ g.
    Assumed in 'State-dependent photon scattering'; standard for atomic ensembles in cavities.
  • domain assumption A single photon reflected from the cavity acquires exactly π phase shift for the resonant Dicke state and zero for all others, i.e., the phase gate is deterministic with no photon-atomic entanglement.
    Core physical premise; requires Ω ≫ κ and negligible spontaneous emission. The paper analyzes deviations in the error analysis section.
  • domain assumption The rotated Dicke state (CSS) overlaps the extremal Dicke states |0> and |N> with equal amplitudes, enabling GHZ amplification.
    Used in the GHZ preparation section; follows from symmetry of Dicke states but is stated without proof.
  • standard math Gaussian and Poissonian approximations to binomial coefficients for estimating k.
    Used to derive k ∼ 0.88 N^{1/4} and k ∼ 1.24 m^{1/4}; standard Stirling approximation.

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Cite this review

Pith. "Pith review of Efficient preparation of entangled states in cavity QED with Grover's algorithm." pith.science (2026). https://pith.science/paper/T5STZLF2

@misc{pith2026250118881,
  author       = {Pith},
  title        = {Pith review of: Efficient preparation of entangled states in cavity QED with Grover's algorithm},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T5STZLF2}},
  note         = {Machine review of arXiv:2501.18881}
}
abstract

We propose to employ the amplification mechanism of Grover's search algorithm to efficiently prepare entangled states of an ensemble of qubits. The conditional change of sign employed in the algorithm can be implemented by the phase shift of photons scattered on an optical cavity hosting an atomic ensemble. We show that collective Dicke states, GHZ states, and Schr\"odinger cat superpositions of $N$ atoms may be prepared deterministically by few ($\sim N^{1/4}$) photon scattering events without individual addressing of the atoms.

Figures

Figures reproduced from arXiv: 2501.18881 by the authors.

Figure 1
Figure 1. FIG. 1. (a) [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Physical implementation of the Grover iteration in [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Contour plot showing the number of steps [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (a) shows the results of numerical simulation of the fidelity in preparing various Dicke states for realistic parameters for current optical cavities with C = 102 [47]. The highest fidelity is limited to 70−80% for Dicke states with the smallest m (after which it decre…

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Forward citations

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Reference graph

Works this paper leans on

53 extracted references · 23 canonical work pages · cited by 1 Pith paper

  1. [1]

    Bärtschi and S

    A. Bärtschi and S. Eidenbenz, Deterministic preparation of Dicke states, in Lecture Notes in Computer Science (Springer International Publishing, 2019) p. 126–139

    work page 2019

  2. [2]

    Aktar, A

    S. Aktar, A. Bartschi, A.-H. A. Badawy, and S. Ei- denbenz, A divide-and-conquer approach to Dicke state preparation, IEEE Trans. Qu. Engineer.3, 1–16 (2022)

    2022

  3. [3]

    D. Cruz, R. Fournier, F. Gremion, A. Jeannerot, K. Komagata, T. Tosic, J. Thiesbrummel, C. L. Chan, N. Macris, M. Dupertuis, and C. Javerzac-Galy, Efficient quantum algorithms for GHZ and W states, and im- plementation on the IBM quantum computer, Adv. Qu. Technol. 2, 10.1002/qute.201900015 (2019)

    doi:10.1002/qute.201900015 2019

  4. [4]

    Kaye and M

    P. Kaye and M. Mosca, Quantum networks for gener- ating arbitrary quantum states, in Optical Fiber Com- munication Conference and International Conference on Quantum Information (Optica Publishing Group, 2001) p. PB28

    2001

  5. [5]

    Buhrman, M

    H. Buhrman, M. Folkertsma, B. Loff, and N. M. P. Neu- mann, State preparation by shallow circuits using feed forward, Quantum 8, 1552 (2024)

    2024

  6. [6]

    Piroli, G

    L. Piroli, G. Styliaris, and J. I. Cirac, Approximating Many-Body Quantum States with Quantum Circuits and Measurements, Phys. Rev. Lett.133, 230401 (2024)

    2024

  7. [7]

    S. C. Carrasco, M. H. Goerz, S. A. Malinovskaya, V. Vuletić, W. P. Schleich, and V. S. Malinovsky, Dicke State Generation and Extreme Spin Squeezing via Rapid Adiabatic Passage, Physical Review Letters132, 10.1103/physrevlett.132.153603 (2024)

    doi:10.1103/physrevlett.132.153603 2024

  8. [8]

    Sweke, I

    R. Sweke, I. Sinayskiy, and F. Petruccione, Dissipative preparation of large W states in optical cavities, Phys. 6 Rev. A 87, 042323 (2013)

    work page 2013

Show all 53 references
  1. [9]

    Wang and B

    Y. Wang and B. M. Terhal, Preparing Dicke states in a spin ensemble using phase estimation, Phys. Rev. A104, 032407 (2021)

    2021

  2. [10]

    C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, Experimental en- tanglement of four particles, Nature404, 256 (2000)

    2000

  3. [11]

    T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Realizationof thequantumtoffoli gate withtrappedions, Phys. Rev. Lett.102, 040501 (2009)

    2009

  4. [12]

    Sørensen and K

    A. Sørensen and K. Mølmer, Entanglement and quantum computation with ions in thermal motion, Phys. Rev. A 62, 022311 (2000)

    2000

  5. [13]

    Fedorov, L

    A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with super- conducting circuits, Nature481, 170–172 (2011)

    2011

  6. [14]

    M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frun- zio, S. M. Girvin, and R. J. Schoelkopf, Realization of three-qubit quantum error correction with superconduct- ing circuits, Nature482, 382–385 (2012)

    2012

  7. [16]

    Sørensen and K

    A. Sørensen and K. Mølmer, Spin-Spin Interaction and Spin Squeezing in an Optical Lattice, Phys. Rev. Lett. 83, 2274 (1999)

    1999

  8. [17]

    Bloch, J

    I. Bloch, J. Dalibard, and S. Nascimbène, Quantum sim- ulations with ultracold quantum gases, Nature Physics 8, 267 (2012)

    2012

  9. [18]

    Mølmer, L

    K. Mølmer, L. Isenhower, and M. Saffman, Efficient Grover search with Rydberg blockade, J. Phys. B: At. Mol. Opt. Phys.44, 184016 (2011)

    2011

  10. [19]

    Weimer, M

    H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, and H. P. Büchler, A Rydberg quantum simulator, Nature Physics 6, 382–388 (2010)

    2010

  11. [20]

    B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Ger- ritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, and C. F. Roos, Universal Digital Quan- tum Simulation with Trapped Ions, Science334, 57–61 (2011)

    2011

  12. [21]

    Bartschi and S

    A. Bartschi and S. Eidenbenz, Short-depth circuits for Dicke state preparation, in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, 2022) p. 87–96

    2022

  13. [22]

    A. S. Sørensen and K. Mølmer, Probabilistic Generation of Entanglement in Optical Cavities, Phys. Rev. Lett.90, 127903 (2003)

    2003

  14. [23]

    W. Chen, J. Hu, Y. Duan, B. Braverman, H. Zhang, and V. Vuletić, Carving Complex Many-Atom Entangled States by Single-Photon Detection, Phys. Rev. Lett.115, 250502 (2015)

    2015

  15. [24]

    A. S. Sørensen and K. Mølmer, Measurement Induced Entanglement and Quantum Computation with Atoms in Optical Cavities, Phys. Rev. Lett.91, 097905 (2003)

    2003

  16. [25]

    Ramette, J

    J. Ramette, J. Sinclair, Z. Li, and V. Vuletić, Carving en- tangled multiparticle states with exponentially improved fidelity, Phys. Rev. A111, 052426 (2025)

    2025

  17. [26]

    E. J. Davis, Z. Wang, A. H. Safavi-Naeini, and M. H. Schleier-Smith, Painting Nonclassical States of Spin or Motion with Shaped Single Photons, Phys. Rev. Lett. 121, 123602 (2018)

    2018

  18. [27]

    Welte, B

    S. Welte, B. Hacker, S. Daiss, S. Ritter, and G. Rempe, Cavity Carving of Atomic Bell States, Phys. Rev. Lett. 118, 210503 (2017)

    2017

  19. [28]

    McConnell, H

    R. McConnell, H. Zhang, J. Hu, S. Ćuk, and V. Vuletić, Entanglement with negative Wigner function of al- most 3,000 atoms heralded by one photon, Nature519, 439–442 (2015)

    2015

  20. [29]

    McConnell, H

    R. McConnell, H. Zhang, S. Ćuk, J. Hu, M. H. Schleier- Smith, and V. Vuletić, Generating entangled spin states for quantum metrology by single-photon detection, Phys. Rev. A 88, 063802 (2013)

    2013

  21. [30]

    S. L. Christensen, J.-B. Béguin, E. Bookjans, H. L. Sørensen, J. H. Müller, J. Appel, and E. S. Polzik, Quantum interference of a single spin excitation with a macroscopic atomic ensemble, Physical Review A89, 10.1103/physreva.89.033801 (2014)

    2014 doi

  22. [31]

    Ðorđević, P

    T. Ðorđević, P. Samutpraphoot, P. L. Ocola, H. Bernien, B. Grinkemeyer, I. Dimitrova, V. Vuletić, and M. D. Lukin, Entanglement transport and a nanophotonic in- terface for atoms in optical tweezers, Science 373, 1511–1514 (2021)

    2021

  23. [32]

    F. Haas, J. Volz, R. Gehr, J. Reichel, and J. Es- tève, Entangled States of More Than 40 Atoms in an Optical Fiber Cavity, Science 344, 180 (2014), https://www.science.org/doi/pdf/10.1126/science.1248905

    2014 doi

  24. [33]

    L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett.79, 325 (1997)

    1997

  25. [34]

    X. Wang, A. Sørensen, and K. Mølmer, Multibit gates for quantum computing, Phys. Rev. Lett.86, 3907 (2001)

    2001

  26. [35]

    Khazali and K

    M. Khazali and K. Mølmer, Fast multiqubit gates by adi- abatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits, Phys. Rev. X 10, 021054 (2020)

    2020

  27. [36]

    Keating, C

    T. Keating, C. H. Baldwin, Y.-Y. Jau, J. Lee, G. W. Bie- dermann, and I. H. Deutsch, Arbitrary Dicke-state con- trol of symmetric Rydberg ensembles, Phys. Rev. Lett. 117, 213601 (2016)

    2016

  28. [37]

    B.-B. Liu, Z. Shan, M.-R. Yun, D.-Y. Wang, B.-J. Liu, L.-L. Yan, M. Feng, and S.-L. Su, Robust three-qubit search algorithm in rydberg atoms via geometric control, Phys. Rev. A106, 052610 (2022)

    2022

  29. [38]

    Anikeeva, O

    G. Anikeeva, O. Marković, V. Borish, J. A. Hines, S. V. Rajagopal, E. S. Cooper, A. Periwal, A. Safavi-Naeini, E. J. Davis, and M. Schleier-Smith, Number partitioning with Grover’s algorithm in central spin systems, PRX Quantum 2, 020319 (2021)

    2021

  30. [39]

    S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, Single-step implemen- tation of high-fidelity n-bit Toffoli gates, Phys. Rev. A 101, 022308 (2020)

    2020

  31. [40]

    Nagib, M

    O. Nagib, M. Saffman, and K. Mølmer, Deterministic carving of quantum states with Grover’s algorithm, Phys. Rev. A 112, 012621 (2025)

    2025

  32. [41]

    J. Yu, S. R. Muleady, Y.-X. Wang, N. Schine, A. V. Gor- shkov, and A. M. Childs, Efficient preparation of Dicke states (2024), arXiv:2411.03428 [quant-ph]

    2024

  33. [42]

    Piroli, G

    L. Piroli, G. Styliaris, and J. I. Cirac, Quantum Circuits Assisted by Local Operations and Classical Communica- tion: Transformations and Phases of matter, Phys. Rev. Lett. 127, 220503 (2021)

    2021

  34. [43]

    M. T. Johnsson, N. R. Mukty, D. Burgarth, T. Volz, and G. K. Brennen, Geometric Pathway to Scalable Quantum Sensing, Phys. Rev. Lett.125, 190403 (2020). 7

    2020

  35. [44]

    L. J. Bond, M. J. Davis, J. Minář, R. Gerritsma, G. K. Brennen, and A. Safavi-Naini, Efficient State Prepara- tion for Metrology and Quantum Error Correction with Global Control (2023), arXiv:2312.05060 [quant-ph]

    2023 arXiv

  36. [45]

    S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity parallel entan- gling gates on a neutral-atom quantum computer, Nature 622, ...

    2023

  37. [46]

    J. A. Muniz, M. Stone, D. T. Stack, M. Jaffe, J. M. Kindem, L. Wadleigh, E. Zalys-Geller, X. Zhang, C.-A. Chen, M. A. Norcia, J. Epstein, E. Halperin, F. Hum- mel, T. Wilkason, M. Li, K. Barnes, P. Battaglino, T. C. Bohdanowicz, G. Booth, A. Brown, M. O. Brown, W. B. Cairncros...

    2025

  38. [47]

    R. M. Kroeze, B. P. Marsh, K.-Y. Lin, J. Keeling, and B. L. Lev, High Cooperativity Using a Confocal-Cavity– QED Microscope, PRX Quantum4, 020326 (2023)

    2023

  39. [48]

    S. K. Ruddell, K. E. Webb, M. Takahata, S. Kato, and T. Aoki, Ultra-low-loss nanofiber Fabry–Perot cavities optimized for cavity quantum electrodynamics, Optics Letters 45, 4875 (2020)

    2020

  40. [49]

    S. J. Garratt and S. Choi, Quantum Algorithm to Pre- pare Quasi-Stationary States (2024), arXiv:2407.07893 [quant-ph]

    2024 arXiv

  41. [50]

    Boissonneault, J

    M. Boissonneault, J. M. Gambetta, and A. Blais, Dis- persive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates, Physical Review A79, 10.1103/physreva.79.013819 (2009)

    2009 doi

  42. [51]

    Retzker, E

    A. Retzker, E. Solano, and B. Reznik, Tavis-Cummings model and collective multiqubit entanglement in trapped ions, Physical Review A75, 10.1103/physreva.75.022312 (2007)

    2007 doi

  43. [52]

    Niemczyk, From Strong to Ultrastrong Coupling in Circuit QED Architectures, Ph.D

    T. Niemczyk, From Strong to Ultrastrong Coupling in Circuit QED Architectures, Ph.D. thesis, Technische Uni- versität München, Garching, Germany (2011), PhD the- sis

    2011

  44. [53]

    Rollano, M

    V. Rollano, M. C. de Ory, C. D. Buch, M. Rubín-Osanz, D. Zueco, C. Sánchez-Azqueta, A. Chiesa, D. Granados, S. Carretta, A. Gomez, S. Piligkos, and F. Luis, High cooperativity coupling to nuclear spins on a circuit QED architecture, Commun. Phys.5, 246 (2022)

    2022

  45. [54]

    Chakram, A

    S. Chakram, A. E. Oriani, R. K. Naik, A. V. Dixit, K. He, A. Agrawal, H. Kwon, and D. I. Schuster, Seamless high- Q microwave cavities for multimode circuit QED, Physi- cal Review Letters127, 10.1103/physrevlett.127.107701 (2021)

    2021 doi

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